modeling long memory in stock market volatility inspired by the idea that regime switching may give rise to persistence that is observationally equivalent to a unit root we derive a regime switching process that exhibits long memory the feature of the process that generates long memory is a heavy tailed duration distribution using this process for volatility we obtain a regime switching stochastic volatility rssv model that we fit to daily s p returns from 1928 through 1995 by means of the efficient method of moments estimation emm method forecasts of rssv volatility given past returns can be generated by reprojection as we illustrate the rssv model is accepted according to the emm chi squared statistic using this statistic we also evaluate several other models that have been proposed in the literature and some modifications to them we find that models that exhibit long memory in volatility and heavy tails conditionally as does the rssv model fit the data whereas models without these characteristics do not we also find weak evidence that suggests the presence of an additional short memory component of volatility over and above the long memory component

wold decomposition prediction and parameterization of stationary processes with infinite variance a discrete time stochastic process t is said to be a p stationary process 1 p 2 if e left sum limits k 1 n b k x tk h right p e left sum limits k 1 n b k x tk right p for all integers n 1 t 1 t n h and scalars b 1 b n the class of p stationary processes includes the class of second order weakly stationary stochastic processes harmonizable stable processes of order 1 2 and p thorder strictly stationary processes for any nondeterministic process in this class a finite wold decomposition moving average representation and a finite predictive decomposition autoregressive representation are given without alluding to any notion of covariance or spectrum these decompositions produce two unique interrelated sequences of scalar which are used as parameters of the process t it is shown that the finite wold and predictive decomposition are all that one needs in developing a kolmogorov wiener type prediction theory for such processes

semi quantitative system identification abstract system identification takes a space of possible models and a stream of observational data of a physical system and attempts to identify the element of the model space that best describes the observed system in traditional approaches the model space is specified by a parameterized differential equation and identification selects numerical parameter values so that simulation of the model best matches the observations we present squid a method for system identification in which the space of potential models is defined by a semi quantitative differential equation sqde qualitative and monotonic function constraints as well as numerical intervals and functional envelopes bound the set of possible models the simulator sqsim predicts semi quantitative behavior descriptions from the sqde identification takes place by describing the observation stream in similar semi quantitative terms and intersecting the two descriptions to derive narrower bounds on the model space refinement is done by refuting impossible or implausible subsets of the model space squid therefore has strengths particularly robustness and expressive power for incomplete knowledge that complement the properties of traditional system identification methods we also present detailed examples evaluation and analysis of squid

some fundamental properties of local constraint propagation abstract in this paper we give results about termination of local constraint propagation algorithms under possibly infinite variable coverings the locally consistent arc consistent solution of a constraint problem if such a solution exists is shown to be unique and a sufficient condition on propagations is given to find that solution even in the presence of arbitrary infinite variable coverings

temporal constraint networks abstract this paper extends network based methods of constraint satisfaction to include continuous variables thus providing a framework for processing temporal constraints in this framework called temporal constraint satisfaction problem tcsp variables represent time points and temporal information is represented by a set of unary and binary constraints each specifying a set of permitted intervals the unique feature of this framework lies in permitting the processing of metric information namely assessments of time differences between events we present algorithms for performing the following reasoning tasks finding all feasible times that a given event can occur finding all possible relationships between two given events and generating one or more scenarios consistent with the information provided we distinguish between simple temporal problems stps and general temporal problems the former admitting at most one interval constraint on any pair of time points we show that the stp which subsumes the major part of vilain and kautz s point algebra can be solved in polynomial time for general tcsps we present a decomposition scheme that performs the three reasoning tasks considered and introduce a variety of techniques for improving its efficiency we also study the applicability of path consistency algorithms as preprocessing of temporal problems demonstrate their termination and bound their complexities

the complexity of some polynomial network consistency algorithms for constraint satisfaction problems abstract constraint satisfaction problems play a central role in artificial intelligence a class of network consistency algorithms for eliminating local inconsistencies in such problems has previously been described we analyze the time complexity of several node arc and path consistency algorithms and prove that arc consistency is achievable in time linear in the number of binary constraints the waltz filtering algorithm is a special case of the arc consistency algorithm in the edge labelling computational vision application the constraint graph is planar and so the time complexity is linear in the number of variables

constraint reasoning based on interval arithmetic the tolerance propagation approach abstract interval constraint satisfaction interval labeling systems have traditionally been based on local waltz filtering techniques that cannot in general determine global solutions in contrast this paper documents a related technique tolerance propagation tp that generalizes the idea of numerical exact value propagation into interval propagation in tp consistency techniques based on the topology of the constraint net can be combined with techniques of interval arithmetic in a new fruitful way in particular by tp it is possible to determine global solutions for interval constraint satisfaction problems with arbitrary accuracy and without losing all attractions of simple local computations

the essence of constraint propagation we show that several constraint propagation algorithms also called local consistency consistency enforcing waltz filtering or narrowing algorithms are instances of algorithms that deal with chaotic iteration to this end we propose a simple abstract framework that allows us to classify and compare these algorithms and to establish in a uniform way their basic properties

consistency and asymptotic normality of the quasi maximum likelihood estimator in igarch 1 1 and covariance stationary garch 1 1 models this paper provides a proof of the consistency and asymptotic normality of the quasi maximum likelihood estimator in garch 1 1 and igarch 1 1 models in contrast to the case of a unit root in the conditional mean the presence of a unit root in the conditional variance does not affect the limiting distribution of the estimators in both models estimators are normally distributed in addition a consistent estimator of the covariance matrix is available enabling the use of standard test statistics for inference

a theory of diagnosis from first principles suppose one is given a description of a system together with an observation of the system s behaviour which conflicts with the way the system is meant to behave the diagnostic problem is to determine those components of the system which when assumed to be functioning abnormally will explain the discrepancy between the observed and correct system behaviour we propose a general theory for this problem the theory requires only that the system be described in a suitable logic moreover there are many such suitable logics e g first order temporal dynamic etc as a result the theory accommodates diagnostic reasoning in a wide variety of practical settings including digital and analogue circuits medicine and database updates the theory leads to an algorithm for computing all diagnoses and to various results concerning principles of measurement for discriminating among competing diagnoses finally the theory reveals close connections between diagnostic reasoning and nonmonotonic reasoning

efficient protocols for generating bipartite classical distributions and quantum states we investigate the fundamental problem of generating bipartite classical distributions or quantum states by designing efficient communication protocols and proving their optimality we establish a number of intriguing connections to fundamental measures in optimization convex geometry and information theory 1 to generate a classical distribution p x y we tightly characterize the minimum amount of quantum communication needed by the psd rank of p as a matrix a measure recently proposed by fiorini et al proc 44th acm symp theory comput pp 95 106 2012 in studies of the minimum size of extended formulations of optimization problems such as tsp this echos the previous characterization for the optimal classical communication cost by the nonnegative rank of p the result is obtained via investigating the more general case of bipartite quantum state generation and designing an optimal protocol for it 2 when an approximation is allowed to generate a distribution x y p we present a classical protocol of the communication cost o c x y 1 where c x y is common information a well studied measure in information theory introduced by wyner ieee trans inf theory 21 2 163 179 1975 this also links nonnegative rank and common information two seemingly unrelated quantities in different fields 3 for approximately generating a quantum pure state we completely characterize the minimum cost by a corresponding approximate rank closing a possibly exponential gap left in ambainis etal siam j comput 32 6 1570 1585 2003

commonsense reasoning about causality deriving behavior from structure abstract this paper presents a qualitative reasoning method for predicting the behavior of mechanisms characterized by continuous time varying parameters the structure of a mechanism is described in terms of a set of parameters and the constraints that hold among them essentially a qualitative differential equation the qualitative behavior description consists of a discrete set of time points at which the values of the parameters are described in terms of ordinal relations and directions of change the behavioral description or envisionment is derived by two sets of rules propagation rules which elaborate the description of the current time point and prediction rules which determine what is known about the next qualitatively distinct state of the mechanism a detailed example shows how the envisionment method can detect a previously unsuspected landmark point at which the system is in stable equilibrium

sharp bounds for mutual covering a fundamental tool in network information theory is the covering lemma which lower bounds the probability that there exists a pair of random variables among a given number of independently generated candidates falling within a given set we use a weighted sum trick and talagrand s concentration inequality to prove new mutual covering bounds we identify two interesting applications 1 when the probability of the set under the given joint distribution is bounded away from 0 and 1 the covering probability converges to 1 doubly exponentially fast in the blocklength which implies that the covering lemma does not induce penalties on the error exponents in the applications to coding theorems and 2 using hall s marriage lemma we show that the maximum difference between the probability of the set under the joint distribution and the covering probability equals half the minimum total variation distance between the joint distribution and any distribution that can be simulated by selecting a pair from the candidates thus we use the mutual covering bound to derive the exact error exponent in the joint distribution simulation problem in both applications the determination of the exact exponential or double exponential behavior relies crucially on the sharp concentration inequality used in the proof of the mutual covering lemma

distributed channel synthesis two familiar notions of correlation are rediscovered as the extreme operating points for distributed synthesis of a discrete memoryless channel in which a stochastic channel output is generated based on a compressed description of the channel input wyner s common information is the minimum description rate needed however when common randomness independent of the input is available the necessary description rate reduces to shannon s mutual information this paper characterizes the optimal tradeoff between the amount of common randomness used and the required rate of description we also include a number of related derivations including the effect of limited local randomness rate requirements for secrecy applications to game theory and new insights into common information duality our proof makes use of a soft covering lemma known in the literature for its role in quantifying the resolvability of a channel the direct proof achievability constructs a feasible joint distribution over all parts of the system using a soft covering from which the behavior of the encoder and decoder is inferred with no explicit reference to joint typicality or binning of auxiliary interest this paper also generalizes and strengthens this soft covering tool

a critical examination of allen s theory of action and time abstract j f allen s theory of time and action is examined and found to be unsuitable for representing facts about continuous change a series of revisions to allen s theory is proposed in order to accommodate this possibility the principal revision is a diversification of the temporal ontology to include instants on the same footing as intervals a distinction is also made between two kinds of property called states of position and states of motion with respect to the logic of their temporal incidence as a consequence of these revisions it is also found necessary to diversify the range of predicates specifying temporal location finally it is argued that allen s category of processes is superfluous since it can be assimilated with the category of properties the implications of this assimilation for the representation of sentences containing verbs in the progressive aspect are discussed

quasi maximum likelihood estimation in conditionally heteroscedastic time series a stochastic recurrence equations approach this paper studies the quasi maximum likelihood estimator qmle in a general conditionally heteroscedastic time series model of multiplicative form xt t zt where the unobservable volatility t is a parametric function of xt 1 x t p t 1 t q for some p q 0 and zt is standardized i i d noise we assume that these models are solutions to stochastic recurrence equations which satisfy a contraction random lipschitz coefficient property these assumptions are satisfied for the popular garch asymmetric garch and exponential garch processes exploiting the contraction property we give conditions for the existence and uniqueness of a strictly stationary solution xt to the stochastic recurrence equation and establish consistency and asymptotic normality of the qmle we also discuss the problem of invertibility of such time series models 1 introduction gaussian quasi maximum likelihood estimation that is likelihood estimation under the hypothesis of gaussian innovations is a popular method which is widely used for inference in time series models however it is often a nontrivial task to establish the consistency and asymptotic normality of the quasi maximum likelihood estimator qmle applied to specific models and therefore an in depth analysis of the probabilistic structure generated by the model is called for a classical example of this kind is the seminal paper by hannan 18 on estimation in linear arma time series in this paper we study the qmle for a general class of conditionally heteroscedastic time series models which includes garch asymmetric garch and exponential garch recall that a garch p q generalized autoregressive conditionally heteroscedastic of order p q process 4 i s def ined by

the likelihood encoder for lossy compression a likelihood encoder is studied in the context of lossy source compression the analysis of the likelihood encoder is based on the soft covering lemma it is demonstrated that the use of a likelihood encoder together with the soft covering lemma yields simple achievability proofs for classical source coding problems the cases of the point to point rate distortion function the rate distortion function with side information at the decoder i e the wyner ziv problem and the multi terminal source coding inner bound i e the berger tung problem are examined in this paper furthermore a non asymptotic analysis is used for the point to point case to examine the upper bound on the excess distortion provided by this method the likelihood encoder is also related to a recent alternative technique using the properties of random binning

multiple description coding with many channels an achievable region for the l channel multiple description coding problem is presented this region generalizes two channel results of el gamal and cover 1982 and of zhang and berger 1987 it further generalizes three channel results of gray and wyner 1974 and of zhang and berger a source that is successively refinable on chains is shown to be successively refinable on trees a new outer bound on the rate distortion rd region for memoryless gaussian sources with mean squared error distortion is also derived the achievable region meets this outer bound for certain symmetric cases

extended gray wyner system with complementary causal side information we establish the rate region of an extended gray wyner system egw for 2 dms x y with two additional decoders having complementary causal side information we show that the 5 d rate region of the egw system is equivalent to the 3 d mutual information region consisting of the set of all triples of the form i x u i y u i x y u for some p u x y this correspondence greatly simplifies the exploration of the the extreme points of the rate region in addition to the operationally significant extreme points of the original gray wyner rate region which include wyner s common information gacs korner common information and the information bottleneck the extreme points of the rate region for the egw system also include the korner graph entropy the privacy funnel and excess functional information as well as three new quantities of potential interest we further show that projections of the mutual information region yield the rate regions for many settings involving a two discrete memoryless source 2 dms including lossless source coding with causal side information distributed channel synthesis and lossless source coding with a helper to further motivate the mutual information region itself we draw analogies between set operations and its extreme points this allows us to find random variables that can be considered as intersection difference and symmetric difference of two random variables finally we establish the rate regions for two related setups to the egw system namely the noncausal egw system and the lossy egw system

local search with constraint propagation and conflict based heuristics search algorithms for solving csp constraint satisfaction problems usually fall into one of two main families local search algorithms and systematic algorithms both families have their advantages designing hybrid approaches seems promising since those advantages may be combined into a single approach in this paper we present a new hybrid technique it performs a local search over partial assignments instead of complete assignments and uses filtering techniques and conflict based techniques to efficiently guide the search this new technique benefits from both classical approaches a priori pruning of the search space from filtering based search and possible repair of early mistakes from local search we focus on a specific version of this technique tabu decision repair experiments done on open shop scheduling problems show that our approach competes well with the best highly specialized algorithms

the detection and estimation of long memory in stochastic volatility abstract we propose a new time series representation of persistence in conditional variance called a long memory stochastic volatility lmsv model the lmsv model is constructed by incorporating an arfima process in a standard stochastic volatility scheme strongly consistent estimators of the parameters of the model are obtained by maximizing the spectral approximation to the gaussian likelihood the finite sample properties of the spectral likelihood estimator are analyzed by means of a monte carlo study an empirical example with a long time series of stock prices demonstrates the superiority of the lmsv model over existing short memory volatility models

new results in binary multiple descriptions an encoder whose input is a binary equiprobable memoryless source produces one output of rate r 1 and another of rate r 2 let d 1 d 2 and d 0 respectively denote the average error frequencies with which the source data can be reproduced on the basis of the encoder output of rate r l only the encoder output of rate r 2 only and both encoder outputs the two descriptions problem is to determine the region r of all quintuples r 1 r 2 d 1 d 2 d 0 that are achievable in thc usual shannon sense let r d 1 d log 2 d 1 d log 2 1 d denote the error frequency rate distortion function of the source the no excess rate case prevails when r 1 r 2 r d 0 and the excess rate case when r 1 r 2 r d 0 denote the section of r at r 1 r 2 d 0 by d r 1 r 2 d 0 d 1 d 2 r 1 r 2 d 1 d 2 d 0 in r in the no excess rate case we show that a portion of the boundary of d r 1 r 2 d 0 coincides with the curve frac 1 2 d 1 2d 0 frac 1 2 d 2 2d 0 frac 1 2 1 2d 0 2 this curve is an extension of witsenhausen s hyperbola bound to the case d 0 0 it follows that the projection of r onto the d 1 d 2 plane at fixed d 0 consists of all d 1 geq d 0 and d 2 geq d 0 that lie on or above this hyperbola in the excess rate case we show by counterexample that the achievable region of el gamal and cover is not tight

variable and value ordering heuristics for the job shop scheduling constraint satisfaction problem abstract practical constraint satisfaction problems csps such as design of integrated circuits or scheduling generally entail large search spaces with hundreds or even thousands of variables each with hundreds or thousands of possible values often only a very tiny fraction of all these possible assignments participates in a satisfactory solution this article discusses techniques that aim at reducing the effective size of the search space to be explored in order to find a satisfactory solution by judiciously selecting the order in which variables are instantiated and the sequence in which possible values are tried for each variable in the csp literature these techniques are commonly referred to as variable and value ordering heuristics our investigation is conducted in the job shop scheduling domain we show that in contrast with problems studied earlier in the csp literature generic variable and value heuristics do not perform well in this domain this is attributed to the difficulty of these heuristics to properly account for the tightness of constraints and or the connectivity of the constraint graphs induced by job shop scheduling csps a new probabilistic framework is introduced that better captures these key aspects of the job shop scheduling search space empirical results show that variable and value ordering heuristics derived within this probabilistic framework often yield significant improvements in search efficiency and significant reductions in the search time required to obtain a satisfactory solution the research reported in this article was the first one along with the work of keng and yun 1989 to use the csp problem solving paradigm to solve job shop scheduling problems the suite of benchmark problems it introduced has been used since then by a number of other researchers to evaluate alternative techniques for the job shop scheduling csp the article briefly reviews some of these more recent efforts and shows that our variable and value ordering heuristics remain quite competitive

fractionally integrated generalized autoregressive conditional heteroskedasticity abstract the new class of fractionally integrated generalized autoregressive conditionally heteroskedastic figarch processes is introduced the conditional variance of the process implies a slow hyperbolic rate of decay for the influence of lagged squared innovations unlike i d processes for the mean maximum likelihood estimates mle of the figarch parameters are argued to be t 1 2 consistent the small sample behavior of an approximate mle procedure is assessed through a simulation study which also documents how the estimation of a standard garch model tends to produce integrated or igarch like estimates an empirical example with daily deutschmark u s dollar exchange rates illustrates the practical relevance of the new figarch specification

variable length compression allowing errors this paper studies the fundamental limits of the minimum average length of lossless and lossy variable length compression allowing a nonzero error probability epsilon for lossless compression we give nonasymptotic bounds on the minimum average length in terms of erokhin s rate distortion function and we use those bounds to obtain a gaussian approximation on the speed of approach to the limit which is quite accurate for all but small blocklengths 1 epsilon k h mathsf s k v mathsf s 2 pi 1 2 mathop rm exp q 1 left epsilon right 2 2 where q 1 left cdot right is the functional inverse of the standard gaussian complementary cumulative distribution function and v mathsf s is the source dispersion a nonzero error probability thus not only reduces the asymptotically achievable rate by a factor of 1 epsilon but this asymptotic limit is approached from below i e larger source dispersions and shorter blocklengths are beneficial variable length lossy compression under an excess distortion constraint is shown to exhibit similar properties

arc consistency for continuous variables reference lia article 1994 001doi 10 1016 0004 3702 94 90022 1view record in web of science record created on 2006 12 13 modified on 2017 05 12

on series representations for linear predictors the series expressions for the linear predictors of a stationary process have been known for a long time but necessary and sufficient conditions for the mean square convergence of these series are still not available it is shown that an equivalent problem is to find necessary and sufficient conditions for the invertibility of the infinite moving average representation of the process two known sufficient conditions are discussed and a more general condition that includes both as special cases is given the process that arises from fractional differencing of a random walk is discussed as an example

constraint propogation techniques for the disjunctive scheduling problem abstract constraint propagation is an elementary method for reducing the search space of combinatorial search and optimization problems which has become more and more important in the last decades the basic idea of constraint propagation is to detect and remove inconsistent variable assignments that cannot participate in any feasible solution through the repeated analysis and evaluation of the variables domains and constraints describing a specific problem instance the contribution of this paper is twofold the first contribution is a description of efficient constraint propagation methods also known as consistency tests for the disjunctive scheduling problem dsp which is a generalization of the classical job shop scheduling problem jsp applying an elementary constraint based approach involving a limited number of search variables we will derive consistency tests that ensure 3 b consistency we will further present and analyze both new and classical consistency tests which to some extent are generalizations of the aforementioned consistency tests involving a higher number of variables but still can be implemented efficiently with a polynomial time complexity further the concepts of energetic reasoning and shaving are analyzed and discussed the other contribution is a classification of the consistency tests derived according to the domain reduction achieved the particular strength of using consistency tests is based on their repeated application so that the knowledge derived is propagated i e reused for acquiring additional knowledge the deduction of this knowledge can be described as the computation of a fixed point since this fixed point depends upon the order of the application of the tests we first derive a necessary condition for its uniqueness we then develop a concept of dominance which enables the comparison of different consistency tests as well as a simple method for proving dominance an extensive comparison of all consistency tests is given quite surprisingly we will find out that some apparently stronger consistency tests are subsumed by apparently weaker ones at the same time an open question regarding the effectiveness of energetic reasoning is answered

cusp catastrophe model for sudden changes in a person s behavior standard research methods that employ questionnaires surveys and statistics do not provide the complete information necessary to fully account for the factors behind a sudden behavioral change such as that of an employee abruptly resigning from his job for this reason the catastrophe theory and qualitative simulation are used since the strict and rigorous mathematical catastrophe model cannot adapt to vague incomplete and time varying data a qualitative quantitative hybrid cusp model is proposed in this study it integrates qualitative simulation qsim with fuzzy set theory to facilitate the computing process a case study is used to explain and validate the proposed method results indicate that this proposed method can be used to model the person s sudden behavioral change and to explore the trajectory and mechanism of the change

distributed simulation of continuous random variables we establish the first known upper bound on the exact and wyner s common information of n continuous random variables in terms of the dual total correlation between them which is a generalization of mutual information in particular we show that when the pdf of the random variables is log concave there is a constant gap of n 2 log e 9n log n between this upper bound and the dual total correlation lower bound that does not depend on the distribution the upper bound is obtained using a computationally efficient dyadic decomposition scheme for constructing a discrete common randomness variable w from which the n random variables can be simulated in a distributed manner we then bound the entropy of w using a new measure which we refer to as the erosion entropy

one shot lossy quantum data compression we provide a framework for one shot quantum rate distortion coding in which the goal is to determine the minimum number of qubits required to compress quantum information as a function of the probability that the distortion incurred upon decompression exceeds some specified level we obtain a one shot characterization of the minimum qubit compression size for an entanglement assisted quantum rate distortion code in terms of the smooth max information a quantity previously employed in the one shot quantum reverse shannon theorem next we show how this characterization converges to the known expression for the entanglement assisted quantum rate distortion function for asymptotically many copies of a memoryless quantum information source finally we give a tight finite blocklength characterization for the entanglement assisted minimum qubit compression size of a memoryless isotropic qubit source subject to an average symbolwise distortion constraint

on the foundations of relaxation labeling processes a large class of problems can be formulated in terms of the assignment of labels to objects frequently processes are needed which reduce ambiguity and noise and select the best label among several possible choices relaxation labeling processes are just such a class of algorithms they are based on the parallel use of local constraints between labels this paper develops a theory to characterize the goal of relaxation labeling the theory is founded on a definition of con sistency in labelings extending the notion of constraint satisfaction in certain restricted circumstances an explicit functional exists that can be maximized to guide the search for consistent labelings this functional is used to derive a new relaxation labeling operator when the restrictions are not satisfied the theory relies on variational cal culus it is shown that the problem of finding consistent labelings is equivalent to solving a variational inequality a procedure nearly identical to the relaxation operator derived under restricted circum stances serves in the more general setting further a local convergence result is established for this operator the standard relaxation labeling formulas are shown to approximate our new operator which leads us to conjecture that successful applications of the standard methods are explainable by the theory developed here observations about con vergence and generalizations to higher order compatibility relations are described

deciding linear inequalities by computing loop residues v r pratt has shown that the real and integer feastbdlty of sets of linear mequallues of the form x y c can be decided quickly by examining the loops m certain graphs pratt s method is generahzed first to real feaslbdlty of mequahues m two variables and arbitrary coefficients and ultimately to real feaslbdlty of arbitrary sets of hnear mequahtles the method is well suited to apphcatlons m program verification

a consistent nonparametric test of ergodicity for time series with applications we propose a set of algorithms for testing the ergodicity of empirical time series without reliance on a specific parametric framework it is shown that the resulting test asymptotically obtains the correct size for stationary and nonstationary processes and maximal power against non ergodic but stationary alternatives the test will not reject in the presence of nonstationarity that does not lead to ergodic failure the method is used to investigate debates over stability of monetary aggregates relative to gdp and the mean reversion hypothesis with respect to high frequency data on exchange rates both the monte carlo and data analysis results suggest that the test has good size and power performance

technical communique interval constraint propagation with application to bounded error estimation for a large class of bounded error estimation problems the posterior feasible set s for the parameters can be defined by nonlinear inequalities the set inversion approach combines classical interval analysis with branch and bound algorithms to characterize s unfortunately as bisections have to be done in all directions of the parameter space this approach is limited to problems involving a small number of parameters techniques based on interval constraint propagation make it possible to drastically reduce the number of bisections in this paper these techniques are combined with set inversion to bracket s between inner and outer subpavings union of nonoverlapping boxes when only interested in the feasible intervals for the parameters the set inversion approach becomes inefficient and a new algorithm able to compute these intervals is given this algorithm uses a new interval based local research to compute the smallest box that contains s it is then compared with existing methods on an example taken from the literature

achievable rates for multiple descriptions consider a sequence of independent identically distributed i i d random variables x l x 2 cdots x n and a distortion measure d x i x i on the estimates x i of x i two descriptions i x in 1 2 cdots 2 nr 1 and j x in 1 2 cdots 2 nr 2 are given of the sequence x x 1 x 2 cdots x n from these two descriptions three estimates i x x2 j x and hat x o i x j x are formed with resulting expected distortions e frac 1 n sum n k 1 d x k hat x mk d m m 0 1 2 we find that the distortion constraints d 0 d 1 d 2 are achievable if there exists a probability mass distribution p x p hat x 1 hat x 2 hat x 0 x with ed x hat x m leq d m such that r 1 i x hat x 1 r 2 i x hat x 2 where i cdot denotes shannon mutual information these rates are shown to be optimal for deterministic distortion measures

the logic of constraint satisfaction the constraint satisfaction problem csp formalization has been a productive tool within artificial intelligence and related areas the finite csp fcsp framework is presented here as a restricted logical calculus within a space of logical representation and reasoning systems fcsp is formulated in a variety of logical settings theorem proving in first order predicate calculus propositional theorem proving and hence sat the prolog and datalog approaches constraint network algorithms a logical interpreter for networks of constraints the constraint logic programming clp paradigm and propositional model finding and hence sat again several standard and some not so standard logical methods can therefore be used to solve these problems by doing this we obtain a specification of the semantics of the common approaches this synthetic treatment also allows algorithms and results from these disparate areas to be imported and specialized to fcsp the special properties of fcsp are exploited to achieve for example completeness and to improve efficiency it also allows export to the related areas by casting csp both as a generalization of fcsp and as a specialization of clp it is observed that some but not all fcsp techniques lift to csp and perhaps thereby to clp various new connections are uncovered in particular between the proof finding approaches and the alternative model finding approaches that have arisen in depiction and diagnosis applications

new strong direct product results in communication complexity we show two new direct product results in two different models of communication complexity our first result is in the one way public coin model let f x y z be a relation and e 0 be a constant let r1 pube f represent the communication complexity of f with worst case error e in this model we show that if for computing fk k independent copies of f in this model o k r1 pub1 3 f communication is used then the success is exponentially small in k we show a new tight characterization of communication complexity in this model which strengthens the tight characterization shown in jain et al 2008 we use this new characterization to show our direct product result and this characterization may also be of independent interest our second direct product result is in the model of two way public coin communication complexity we show a direct product result for all relations in this model in terms of a new complexity measure that we define our new measure is a generalization to nonproduct distributions of the two way product subdistribution bound of jain et al 2008 our direct product result therefore generalizes to nonproduct distributions their direct product result in terms of the two way product subdistribution bound as an application of our new direct product result we reproduce via completely different arguments strong direct product result for the set disjointness problem which was previously shown by klauck 2010 we show this by proving that our new complexity measure gives a tight lower bound of n for the set disjointness problem on n bit inputs this strengthens the linear lower bound on the rectangle corruption bound for set disjointness shown by razborov 1992 in addition we show that many previously known direct product results in this model are uniformly implied and often strengthened by our result

inference in arch and garch models with heavy tailed errors arch and garch models directly address the dependency of conditional second moments and have proved particularly valuable in modelling processes where a relatively large degree of fluctuation is present these include financial time series which can be particularly heavy tailed however little is known about properties of arch or garch models in the heavy tailed setting and no methods are available for approximating the distributions of parameter estimators there in this paper we show that for heavy tailed errors the asymptotic distributions of quasi maximum likelihood parameter estimators in arch and garch models are nonnormal and are particularly difficult to estimate directly using standard parametric methods standard bootstrap methods also fail to produce consistent estimators to overcome these problems we develop percentile t subsample bootstrap approximations to estimator distributions studentizing is employed to approximate scale and the subsample bootstrap is used to estimate shape the good performance of this approach is demonstrated both theoretically and numerically

thick set inversion abstract this paper deals with the set inversion problem x f 1 y in the case where the function f r n r m and the set y are both uncertain the uncertainty is treated under the form of intervals more precisely for all x f x is inside the box f x and the uncertain set y is bracketed between an inner set y and an outer set y the introduction of new tools such as thick intervals and thick boxes will allow us to propose an efficient algorithm that handles the uncertainty of sets in an elegant and efficient manner some elementary test cases that cannot be handled easily and properly by existing methods show the efficiency of the approach

on exact and renyi common informations recently two extensions of wyner s common information exact and renyi common informations were introduced respectively by kumar li and el gamal kle and the present authors the class of common information problems involves determining the minimum rate of the common input to two independent processors needed to exactly or approximately generate a target joint distribution for the exact common information problem exact generation of the target distribution is required while for wyner s and alpha renyi common informations the relative entropy and renyi divergence with order alpha were respectively used to quantify the discrepancy between the synthesized and target distributions the exact common information is larger than or equal to wyner s common information however it was hitherto unknown whether the former is strictly larger than the latter for some joint distributions in this paper we first establish the equivalence between the exact and infty renyi common informations and then provide single letter upper and lower bounds for these two quantities for doubly symmetric binary sources we show that the upper and lower bounds coincide which implies that for such sources the exact and infty renyi common informations are completely characterized interestingly we observe that for such sources these two common informations are strictly larger than wyner s this answers an open problem posed by kle furthermore we extend wyner s infty renyi and exact common informations to sources with countably infinite or continuous alphabets including gaussian sources

the local structure of image discontinuities in one dimension the detailed structure of intensities in the local neighborhood of an edge can often indicate the nature of the physical event givinig rise to that edge we argue that the limit as we approach arbitrarily close to either side of an edge of such image parameters as type of texture texture gradient color appropriate directional derivatives of intensity etc is a key aspect of this structure however the general problem of capturing this local structure is surprisingly complex thus we restrict ourselves in this paper to a relatively simple domain one dimensional cuts through idealized images modeled by piecewise smooth c1 functions corrupted by gaussian noise within this domain we define local structure to be the limit of the uncorrupted intensity and of its derivatives as we approach arbitrarily close to either side of a discontinuity we develop a technique that captures this local structure while simultaneously locating the discontinuities and demonstrate that these tasks are in fact inseparable the technique is an extension using estimation theory of the classical definition of discontinuity it handles in a consistent fashion both jump discontinuities in the function and jump discontinuities in its first derivative so called step edges are a special case of the former and roof edges of the latter it also integrates again in a consistent fashion information derived from a number of different neighborhood sizes

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

on the analytic representation of the leximin ordering and its application to flexible constraint propagation we discuss the basic formulation of constraint propagation problems and extend it to the flexible constraint propagation environment where constraints are represented as fuzzy subsets some methods for ordering alternative solutions with respect to a collection of flexible constraints are discussed along with their drawbacks among the methods introduced is the leximin method where we note its lack of an analytic formulation with the aid of the ordered weighted averaging owa operator we suggest an analytic formulation for the leximin method some properties of this formulation are provided we then describe the application of this new formulation for the leximin method to situations in which the constraints are describable in a linear fashion we show how we can use mixed integer programming techniques to find an optimal solution

entanglement assisted capacity of a quantum channel and the reverse shannon theorem the entanglement assisted classical capacity of a noisy quantum channel c sub e is the amount of information per channel use that can be sent over the channel in the limit of many uses of the channel assuming that the sender and receiver have access to the resource of shared quantum entanglement which may be used up by the communication protocol we show that the capacity c sub e is given by an expression parallel to that for the capacity of a purely classical channel i e the maximum over channel inputs spl rho of the entropy of the channel input plus the entropy of the channel output minus their joint entropy the latter being defined as the entropy of an entangled purification of spl rho after half of it has passed through the channel we calculate entanglement assisted capacities for two interesting quantum channels the qubit amplitude damping channel and the bosonic channel with amplification attenuation and gaussian noise we discuss how many independent parameters are required to completely characterize the asymptotic behavior of a general quantum channel alone or in the presence of ancillary resources such as prior entanglement in the classical analog of entanglement assisted communication communication over a discrete memoryless channel dmc between parties who share prior random information we show that one parameter is sufficient i e that in the presence of prior shared random information all dmcs of equal capacity can simulate one another with unit asymptotic efficiency

a property of quantum relative entropy with an application to privacy in quantum communication we prove the following information theoretic property about quantum states substate theorem let and be quantum states in the same hilbert space with relative entropy s c tr log log c then for all 0 there is a state such that the trace distance tr tr 2 and 2o c 2 it states that if the relative entropy of and is small then there is a state close to i e with small trace distance tr that when scaled down by a factor 2o c sits inside or becomes a substate of this result has several applications in quantum communication complexity and cryptography using the substate theorem we derive a privacy trade off for the set membership problem in the two party quantum communication model here alice is given a subset a n bob an input i i n and they need to determine if i i a privacy trade off for set membership in any two party quantum communication protocol for the set membership problem if bob reveals only k bits of information about his input then alice must reveal at least n 2o k bits of information about her input we also discuss relationships between various information theoretic quantities that arise naturally in the context of the substate theorem

theoretical results on fractionally integrated exponential generalized autoregressive conditional heteroskedastic processes abstract here we present a theoretical study on the main properties of fractionally integrated exponential generalized autoregressive conditional heteroskedastic fiegarch processes we analyze the conditions for the existence the invertibility the stationarity and the ergodicity of these processes we prove that if x t t z is a fiegarch p d q process then under mild conditions ln x t 2 t z is an arfima q d 0 with correlated innovations that is an autoregressive fractionally integrated moving average process the convergence order for the polynomial coefficients that describes the volatility is presented and results related to the spectral representation and to the covariance structure of both processes ln x t 2 t z and ln t 2 t z are discussed expressions for the kurtosis and the asymmetry measures for any stationary fiegarch p d q process are also derived the h step ahead forecast for the processes x t t z ln t 2 t z and ln x t 2 t z are given with their respective mean square error of forecast the work also presents a monte carlo simulation study showing how to generate estimate and forecast based on six different fiegarch models the forecasting performance of six models belonging to the class of autoregressive conditional heteroskedastic models namely arch type models and radial basis models is compared through an empirical application to brazilian stock market exchange index

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

on the computational complexity of querying bounds on differences constraints abstract given a consistent knowledge base formed by a set of constraints efficient query answering e g checking whether a set of constraints is consistent with the knowledge base or necessarily true in it is practically very important in the paper we consider bounds on differences which are an important class of constraints based on linear inequalities and we analyze the computational complexity of query answering more specifically we consider various common types of queries and we prove that if the minimal network produced by constraint satisfaction algorithms and characterizing the solutions to a set of constraints is maintained then the complexity of answering a query depends only on the dimension of the query and not on the dimension of the knowledge base which is usually much larger than the query we also analyse how the approach can be used to deal efficiently with a class of updates to the knowledge base some applications of the results are sketched in the conclusion

exact channel synthesis we consider the exact channel synthesis problem this problem concerns the determination of the minimum amount of information required to create exact correlation remotely when there is a certain rate of randomness shared by two terminals this problem generalizes an existing approximate version in which the generated joint distribution is required to be close to a target distribution under the total variation tv distance measure instead being exactly equal to the target distribution we provide single letter inner and outer bounds on the admissible region of the shared randomness rate and the communication rate for the exact channel synthesis problem these two bounds coincide for doubly symmetric binary sources we observe that for such sources the admissible rate region for exact channel synthesis is strictly included in that for the tv approximate version we also extend the exact and tv approximate channel synthesis problems to sources with countably infinite alphabets and continuous sources the latter includes gaussian sources as by products lemmas concerning soft covering under renyi divergence measures are derived

the communication complexity of correlation let x and y be finite nonempty sets and x y a pair of random variables taking values in x y we consider communication protocols between two parties alice and bob for generating x and y alice is provided an x x generated according to the distribution of x and is required to send a message to bob in order to enable him to generate y y whose distribution is the same as that of y x x both parties have access to a shared random string generated in advance let t x y be the minimum over all protocols of the expected number of bits alice needs to transmit to achieve this we show that i x y t x y i x y 2 log2 i x y o 1 we also consider the worst case communication required for this problem where we seek to minimize the average number of bits alice must transmit for the worst case x x we show that the communication required in this case is related to the capacity c e of the channel e derived from x y that maps x x to the distribution of y x x we also show that the required communication t e satisfies c e t e c e 2 log2 c e 1 o 1 using the first result we derive a direct sum theorem in communication complexity that substantially improves the previous such result shown by jain radhakrishnan and sen in proc 30th international colloquium of automata languages and programming icalp ser lecture notes in computer science vol 2719 2003 pp 300 315 these results are obtained by employing a rejection sampling procedure that relates the relative entropy between two distributions to the communication complexity of generating one distribution from the other

strong functional representation lemma and applications to coding theorems this paper shows that for any random variables x and y it is possible to represent y as a function of x z such that z is independent of x and i x z y le log i x y 1 4 bits we use this strong functional representation lemma sfrl to establish a bound on the rate needed for one shot exact channel simulation for general discrete or continuous random variables strengthening the results by harsha et al and braverman and garg and to establish new and simple achievability results for one shot variable length lossy source coding multiple description coding and gray wyner system we also show that the sfrl can be used to reduce the channel with state noncausally known at the encoder to a point to point channel which provides a simple achievability proof of the gelfand pinsker theorem

some defects in finite difference edge finders this work illustrates and explains various artifacts in the output of five finite difference edge finders those of j f canny 1983 1986 r a boie et al 1986 and r a boie and i j cox 1987 and three variations on that of d marr and e c hildreth 1980 reimplemented with a common output format and method of noise suppression these artifacts include gaps in boundaries spurious boundaries and deformation of region shape

temporal constraint satisfaction on causal models abstract causal models play a fundamental role in many intelligent problem solving activities such as diagnosis or simulation although the notion of causation is strictly related to the notion of time temporal knowledge and temporal reasoning have been often disregarded in problem solvers operating on causal models in this page we propose an approach to temporal constraint satisfaction on causal models the approach departs significantly from traditional approaches to temporal constraint satisfaction in our approach in fact we use synchronization mechanisms for dealing with events caused by a conjunction of other events in the paper we analyze the computation complexity of temporal constraint satisfaction on causal models showing that such a form of reasoning is intrinsically intractable i e it is intractable even if one limits the attention to a simple form of causal model and of consistency constraints however we show that it is possible to define sufficient conditions for temporal consistency that can be checked in polynomial time interestingly such conditions allow us to relate our approach to traditional approaches to temporal constraint satisfaction

towards a general theory of action and time abstract a formalism for reasoning about actions is proposed that is based on a temporal logic it allows a much wider range of actions to be described than with previous approaches such as the situation calculus this formalism is then used to characterize the different types of events processes actions and properties that can be described in simple english sentences in addressing this problem we consider actions that involve non activity as well as actions that can only be defined in terms of the beliefs and intentions of the actors finally a framework for planning in a dynamic world with external events and multiple agents is suggested

autoregressive representations of multivariate stationary stochastic processes consider a q variate weakly stationary stochastic process xn with the spectral density w the problem of autoregressive representation of xn or equivalently the autoregressive representation of the linear least squares predictor of xn based on the infinite past is studied it is shown that for every w in a large class of densities the corresponding process has a mean convergent autoregressive representation this class includes as special subclasses the densities studied by masani 1960 and pourahmadi 1985 as a consequence it is shown that the condition w 1 lqxq1 or minimality of xn is dispensable for this problem when w is not in this class or when w has zeros of order 2 or more it is shown that xn has a mean abel summable or mean compounded cesaro summable autoregressive representation

exponential separation of information and communication for boolean functions we show an exponential gap between communication complexity and information complexity by giving an explicit example of a partial boolean function with information complexity o k and distributional communication complexity 2k this shows that a communication protocol cannot always be compressed to its internal information by a result of braverman 2015 our gap is the largest possible by a result of braverman and rao 2014 our example shows a gap between communication complexity and amortized communication complexity implying that a tight direct sum result for distributional communication complexity cannot hold answering a long standing open problem another conceptual contribution of our work is the relative discrepancy method a new rectangle based method for proving communication complexity lower bounds for boolean functions powerful enough to separate information complexity and communication complexity

the token reification approach to temporal reasoning abstract the approach to temporal reasoning which has proven most popular in ai is the reified approach in this approach one introduces names for events and states and uses special predicates to assert that an event or state occurs or holds at a particular time however recently the reified approach has come under attack both on technical and on ontological grounds thus it has been claimed that at least some reified temporal logics do not give one more expressive power than provided by alternative approaches moreover it has been argued that the reification of event and state types in reified temporal logics rather than event and state tokens makes the ontology more complicated than necessary in this paper we present a new reified temporal logic called trl which we believe avoids most of these objections it is based on the idea of reifying event tokens instead of event types however unlike other such attempts our logic contains meaningful names for event tokens thus allowing us to quantify over all event tokens that meet a certain criterion the resulting logic is more expressive than alternative approaches moreover it avoids the ontologically objectionable reification of event types while staying within classical first order predicate logic

constraint propagation with interval labels abstract constraint propagation is often used in ai systems to perform inference about quantities this paper studies one particular kind of constraint propagation where quantities are labelled with signs or with intervals and these labels are propagated through recorded constraints we review the uses of such inference schemes in ai systems of various kinds and evaluate their strengths and weaknesses in particular we determine the completeness and running time of constraint propagation for various kinds of labels and constraints

on the role of the refinement layer in multiple description coding and scalable coding we clarify the relationship among several existing achievable multiple description rate distortion regions by investigating the role of refinement layer in multiple description coding specifically we show that the refinement layer in the el gamal cover egc scheme and the venkataramani kramer goyal vkg scheme can be removed as a consequence the egc region is equivalent to the egc region an antecedent version of the egc region while the vkg region when specialized to the 2 description case is equivalent to the zhang berger zb region moreover we prove that for multiple description coding with individual and hierarchical distortion constraints the number of layers in the vkg scheme can be significantly reduced when only certain weighted sum rates are concerned the role of refinement layer in scalable coding a special case of multiple description coding is also studied

accelerating filtering techniques for numeric csps search algorithms for solving numeric csps constraint satisfaction problems make an extensive use of filtering techniques in this paper we show how those filtering techniques can be accelerated by discovering and exploiting some regularities during the filtering process two kinds of regularities are discussed cyclic phenomena in the propagation queue and numeric regularities of the domains of the variables we also present in this paper an attempt to unify numeric csps solving methods from two distinct communities that of csp in artificial intelligence and that of interval analysis

planning routes through uncertain territory abstract planning routes and executing them requires both topological and metric information a natural implementation of a cognitive map might therefore consist of an assertional data base for topological information and a fuzzy map for the metric information a fuzzy map captures facts about objects by recording their relative positions orientations and scales in convenient frames of reference it is fuzzy in the sense that coordinates are specified to lie in a range rather than having fixed values the fuzzy map allows easy retrieval of information the same information is also represented in a discrimination tree which allows an object to be retrieved given its location and other attributes the problem of constructing a fuzzy map is more difficult we present a partial solution an algorithm that assimilates a fact first by imposing constraints on the fuzzy coordinates of the objects involved then by rearranging or growing the tree of frames of reference route planning is modelled as a process of finding the overall direction and topology of the path then filling in the details by deciding how to go around barriers it uses the retrieval algorithms our program spam carries out all these processes

the topology of boundaries abstract high level representations used in reasoning distinguish a special set of boundary locations at which function values can change abruptly and across which adjacent regions may not be connected standard models of space and time based on segmenting r n do not allow these possibilities because they have the wrong topological structure at boundaries this mismatch has made it difficult to develop formal mathematical models for high level reasoning algorithms this paper shows how to modify an r n model so as to have an appropriate topological structure it then illustrates how the new models support standard reasoning algorithms provide simple models for previously difficult situations and suggest interesting new analyses based on change or non change in scene topology

guaranteed nonlinear estimation using constraint propagation on sets bounded error estimation is the estimation of the parameter or state vector of a model from experimental data under the assumption that some suitably de ned errors should belong to some prior feasible sets when the model outputs are linear in the vector to be estimated a number of methods are available to enclose all estimates that are consistent with the data into simple sets such as ellipsoids orthotopes or parallelotopes thereby providing guaranteed set estimates in the nonlinear case the situation is much less developed and there are very few methods that produce such guaranteed estimates in this paper the discrete time problem is cast into the more general framework of constraint satisfaction problems algorithms rather classical in the area of interval constraint propagation are extended by replacing intervals by more general subsets of real vector spaces this makes it possible to propose a new algorithm that contracts the feasible domains for each uncertain variable optimally i e no smaller domain could be obtained and e ciently the resulting methodology is illustrated on discrete time nonlinear state estimation the state at time k is estimated either from past measurement only or from all measurements assumed to be available from the start even in the causal case prior information on the future value of the state and output vectors due for instance to physical constraints is readily taken into account

rough intervals enhancing intervals for qualitative modeling of technical systems the success of model based industrial applications generally depends on how exactly models reproduce the behavior of the real system that they represent however the complexity of industrial systems makes the construction of accurate models difficult an alternative is the qualitative description of process states for example by means of the discretization of continuous variable spaces in intervals in order to reach the required precision in the modeling of complex dynamic systems interval based representations usually produce qualitative models which are sometimes too large for practical use the approach introduced in this paper incorporates vague and uncertain information based on principles of the rough set theory as a way of enhancing the information contents in interval based qualitative models the resulting models are more compact and precise than ordinary qualitative models

technical communique nonlinear bounded error state estimation of continuous time systems this paper presents a first study on the application of interval analysis and consistency techniques to state estimation of continuous time systems described by nonlinear ordinary differential equations the approach is presented in a bounded error context and the resulting methodology is illustrated by an example

guaranteed robust nonlinear minimax estimation minimax parameter estimation aims at characterizing the set of all values of the parameter vector that minimize the largest absolute deviation between the experimental data and the corresponding model outputs it is well known however to be extremely sensitive to outliers in the data resulting e g of sensor failures in this paper a new method is proposed to robustify minimax estimation by allowing a prespecified number of absolute deviations to become arbitrarily large without modifying the estimates by combining tools of interval analysis and constraint propagation it becomes possible to compute the corresponding minimax estimates in an approximate but guaranteed way even when the model output is nonlinear in its parameters the method is illustrated on a problem where the parameters are not globally identifiable which demonstrates its ability to deal with the case where the minimax solution is not unique

the redundancy of source coding with a fidelity criterion 1 known statistics the problem of redundancy of source coding with respect to a fidelity criterion is considered for any fixed rate r 0 and any memoryless source with finite source and reproduction alphabets and a common distribution p the nth order distortion redundancy d sub n r of fixed rate coding is defined as the minimum of the difference between the expected distortion per symbol of any block code with length n and rate r and the distortion rate function d p r of the source p it is demonstrated that for sufficiently large n d sub n r is equal to spl part spl part r d p r ln n 2n o ln n n where spl part spl part r d p r is the partial derivative of d p r evaluated at r and assumed to exist for any fixed distortion level d 0 and any memoryless source p the nth order rate redundancy r sub n d of coding at fixed distortion level d or by using d semifaithful codes is defined as the minimum of the difference between the expected rate per symbol of any d semifaithful code of length n and the rate distortion function r p d of p evaluated at d it is proved that for sufficiently large n r sub n d is upper bounded by ln n n o ln n n and lower bounded by in n 2n o in n n as a by product the lower bound of r sub n d derived in this paper gives a positive answer to a conjecture proposed by yu and speed 1993