local linear regression smoothers and their minimax efficiencies in this paper we introduce a smooth version of local linear regression estimators and address their advantages the mse and mise of the estimators are computed explicitly it turns out that the local linear regression smoothers have nice sampling properties and high minimax efficiency they are not only efficient in rates but also nearly efficient in constant factors in the nonparametric regression context the asymptotic minimax lower bound is developed via the heuristic of the hardest onedimensional subproblem of donoho and liu connections of the minimax risk with the modulus of continuity are made the lower bound is also applicable for estimating conditional mean regression and conditional quantiles for both fixed and random design regression problems

on the efficient use of the informational content of estimating equations implied probabilities and euclidean empirical likelihood abstract a number of information theoretic alternatives to gmm have recently been proposed in the literature for practical use and general interpretation the main drawback of these alternatives particularly in the case of conditional moment restrictions is that they give up the computational and interpretational simplicity of quadratic optimization the main contribution of this paper is to analyze the informational content of estimating equations within the unified framework of chi square distance improved inference by control variables closed form formulae for implied probabilities and information theoretic interpretations of continuously updated gmm are discussed in the two cases of unconditional and conditional moment restrictions

ℋ 2 filtering of discrete time markov jump linear systems through linear matrix inequalities this paper addresses the 2 filtering design problem of discrete time markov jump linear systems first under the assumption that the markov parameter is measured the main contribution is on the lmi characterisation of all filters such that the estimation error remains bounded by a given 2 norm level yielding the complete solution of the mode dependent filtering design problem based on this result a robust filter design to deal with convex bounded parameter uncertainty is considered second from the same lmi characterisation a design procedure for mode independent filtering design is proposed some examples are solved for illustration and comparison

higher order properties of gmm and generalized empirical likelihood estimators in an effort to improve the small sample properties of generalized method of moments gmm estimators a number of alternative estimators have been suggested these include empirical likelihood el continuous updating and exponential tilting estimators we show that these estimators share a common structure being members of a class of generalized empirical likelihood gel estimators we use this structure to compare their higher order asymptotic properties we find that gel has no asymptotic bias due to correlation of the moment functions with their jacobian eliminating an important source of bias for gmm in models with endogeneity we also find that el has no asymptotic bias from estimating the optimal weight matrix eliminating a further important source of bias for gmm in panel data models we give bias corrected gmm and gel estimators we also show that bias corrected el inherits the higher order property of maximum likelihood that it is higher order asymptotically efficient relative to the other bias corrected estimators

a convex programming approach to h2 control of discrete time markovian jump linear systems in this paper we consider the h control problem for the class of discrete time 2 linear systems with parameters subject to markovian jumps using a convex programming approach we generalize the definition of the h norm from the deter2 ministic case to the markovian jump case and set a link between this norm and the observability and controllability gramians conditions for existence and derivation of a mean square stabilizing controller for a markovian jump linear system using convex analysis are established the main contribution of the paper is to provide a convex programming formulation to the h control problem so that several 2 important cases to our knowledge not analysed in previous work can be addressed regarding the transition matrix p for the markov chain two ij situations are considered the case in which it is exactly known and the case in which it is not exactly known but belongs to an appropriated convex set regarding the state variable and the jump variable the cases in which t

goodness of fit tests based on rao s divergence under sparseness assumptions in many practical situations the classical fixed cells assumptions to test goodness of fit are inappropriate and we consider an alternative set of assumptions which we call sparseness assumptions it is proved that under general conditions the proposed family of statistics based on rao s divergence is asymptotically normal when the sample size n and the number of cells m n tend to infinity so that n m n n 0 this result is extended to contiguous alternatives and subsequently it is possible to find the asymptotically most efficient member of the family

empirical likelihood and general estimating equations for some time so called empirical likelihoods have been used heuristically for purposes of nonparametric estimation owen showed that empirical likelihood ratio statistics for various parameters theta f of an unknown distribution f have limiting chi square distributions and may be used to obtain tests or confidence intervals in a way that is completely analogous to that used with parametric likelihoods our objective in this paper is twofold first to link estimating functions or equations and empirical likelihood second to develop methods of combining information about parameters we do this by assuming that information about f and theta is available in the form of unbiased estimating functions empirical likelihoods for parameters are developed and shown to have properties similar to those for parametric likelihood efficiency results for estimates of both theta and f are obtained the methods are illustrated on several problems and areas for future investigation are noted

flasque sheaves on posets and cohen macaulay unions of regular varieties the goal of this paper is to find new examples of cohen macaulay and non cohen macaulay rings among the coordinate rings of the unions of regular varieties the cohen macaulayness as well as other properties seminormality buchsbaumness etc was studied extensively for twodimensional varieties z 5 111 however for larger dimensions not much was known besides the reisner theorem lo which gives an equivalent combinatorial condition for the coordinate ring of the unions of coordinate linear subspaces stanley reisner or face rings 123 to be cohen macaulay the method used in this paper is to represent a ring as the section ring of a sheaf on a poset and then to apply theorem 6 4 of 131 more precisely for a finite set q of alline regular varieties we consider the poset x a of all intersections of elements of 0 and the sheaf a on x o of the coordinate rings of these intersections the restriction of regular functions defines a monomorphism p from the coordinate ring r of u u to the section ring s of d c the above mentioned result form 13 can be applied to r only if the two following restrictive conditions hold

cohen macaulay seminormalizations of unions of linear subspaces this paper is concerned with the unions of subspaces of an afiine space regarded as affine varieties let r denote the co ordinate ring of such a union then according to a theorem of orecchia s s the seminormaliza tion s of r can be represented as the section ring or pull back of the sheaf d of the co ordinate rings on the intersection poset x of the subspaces in this paper we give a homological condition on x and d equivalent to s being cohen macaulay theorem 4 3 two particular cases of this result have been known before the reisner theorem 6 covered the case of co ordinate subspaces when r s is the face ring of a complex and geramita and weibel 2 soived the problem for planes the main idea of the proof is to construct a resolution c of s consisting of s modules of a known depth and then estimate the depth of s by the length of c this idea was applied in 7 to the section rings of flasque sheaves since in this paper the sheaves are not necessarily flasque the con struction of c is a bit more complicated and involves the local tech cohomology of x with coefficients in a drawback of the method is that it gives very little information about r itself when it is not seminormal this paper is organized as follows in section 1 the terminology and background of sheaves on posets is given in section 2 we study the tech cohomology of a covering of a poset with coefficients in a sheaf the next section is technical in it we compare the depth of the rings of sections on certain closed subsets with their depth as modules over the ring of global sections in section 4 we prove the main result of the paper finally section 5 contains examples and some unsolved problems

powerful goodness of fit tests based on the likelihood ratio summary a new approach of parameterization is proposed to construct a general goodnessof fit test it can not only generate traditional tests including the kolmogorov smirnov cramer von mises and anderson darling tests but also produce new types of omnibus tests which are generally much more powerful than the old ones

sheaf theoretic investigation of cip method abstract the cip method is a numerical computational method in the computational fluid dynamics discovered by takewaki nishiguchi and yabe h takewaki a nishiguchi t yabe the cubic interpolated pseudo particle cip method for solving hyperbolic type equations j comput phys 61 1985 261 268 which shows nice properties as a numerical computational method but it is known that its mathematical essentials have not been revealed well in this article we investigate the cip method from an algebraic viewpoint then it is shown that the cip method is described well in terms of the sheaf theory

asymptotic optimality of empirical likelihood for testing moment restrictions we show by example that empirical likelihood and other commonly used tests for moment restrictions are unable to control the exponential rate at which the probability of a type i error tends to zero unless the possible distributions for the observed data are restricted appropriately from this it follows that for the optimality claim for empirical likelihood in kitamura 2001 to hold additional assumptions and qualifications are required under stronger assumptions than those in kitamura 2001 we establish the following optimality result i empirical likelihood controls the rate at which the probability of a type i error tends to zero and ii among all procedures for which the probability of a type i error tends to zero at least as fast empirical likelihood maximizes the rate at which the probability of a type ii error tends to zero for most alternatives this result further implies that empirical likelihood maximizes the rate at which the probability of a type ii error tends to zero for all alternatives among a class of tests that satisfy a weaker criterion for their type i error probabilities

mode independent cal h _ infty filters for markovian jump linear systems this note addresses the problem of hinfin filtering for continuous time linear systems with markovian jumping parameters the main contribution of the note is to provide a method for designing an asymptotically stable linear time invariant hinfin filter for systems where the jumping parameter is not accessible the cases where the transition rate matrix of the markov process is either exactly known or unknown but belongs to a given polytope are treated the robust hinfin filtering problem for systems with polytopic uncertain matrices is also considered and a filter design method based on a lyapunov function that depends on the uncertain parameters is developed the proposed filter designs are given in terms of linear matrix inequalities

splines with boundary conditions this paper explores spaces of splines satisfying boundary conditions using the long exact sequence for relative homology we relate them to the boundary complex of d where d is a planar simplicial complex which triangulates a pseudomanifold in this case there is a natural relationship between the hilbert polynomials which measure the dimension of c k r d for k 0 of the spline modules

combining estimators to improve structural model estimation and inference under quadratic loss asymptotically semi parametric estimators of the parameters in linear structural models have the same sampling properties in finite samples the sampling properties of these estimators vary and large biases may result for sample sizes often found in practice with a goal of improving asymptotic risk performance and finite sample efficiency properties we investigate the idea of combining correlated structural equation estimators with different finite and asymptotic sampling characteristics based on a quadratic loss measure we present evidence that the finite sample performance of the resulting combination estimator can be notably superior to that of a leading traditional moment based estimator

tests of independence for bivariate data with random censoring a contingency table approach procedures are proposed for testing the hypothesis of independence between two discrete or discretized random variables one or both of which may be randomly censored the censoring mechanisms can be either independent bivariate censoring or identical univariate censoring the proposed tests reduce to goodness of fit tests for log linear models applied to either complete or incomplete contingency tables three examples are analyzed for illustrative purposes

empirical likelihood based inference in conditional moment restriction models this paper proposes an asymptotically efficient method for estimating models with conditional moment restrictions our estimator generalizes the maximum empirical likelihood estimator mele of qin and lawless 1994 using a kernel smoothing method we efficiently incorporate the information implied by the conditional moment restrictions into our empirical likelihood based procedure this yields a one step estimator which avoids estimating optimal instruments our likelihood ratio type statistic for parametric restrictions does not require the estimation of variance and achieves asymptotic pivotalness implicitly the estimation and testing procedures we propose are normalization invariant simulation results suggest that our new estimator works remarkably well in finite samples

robust stability and stabilization of uncertain discrete time markovian jump linear systems this note deals with robust stability and control of uncertain discrete time linear systems with markovian jumping parameters systems with polytopic type parameter uncertainty in either the state space model matrices or in the transition probability matrix of the markov process are considered this note develops methods of robust stability analysis and robust stabilization in the mean square sense which are dependent on the system uncertainty the design of both mode dependent and mode independent control laws is addressed the proposed methods are given in terms of linear matrix inequalities numerical examples are provided to demonstrate the effectiveness of the derived results

efficient derivative pricing by the extended method of moments in this paper we introduce the extended method of moments xmm estimator this estimator accommodates a more general set of moment restrictions than the standard generalized method of moments gmm estimator more specifically the xmm differs from the gmm in that it can handle not only uniform conditional moment restrictions i e valid for any value of the conditioning variable but also local conditional moment restrictions valid for a given fixed value of the conditioning variable the local conditional moment restrictions are of special relevance in derivative pricing to reconstruct the pricing operator on a given day by using the information in a few cross sections of observed traded derivative prices and a time series of underlying asset returns the estimated derivative prices are consistent for a large time series dimension but a fixed number of cross sectionally observed derivative prices the asymptotic properties of the xmm estimator are nonstandard since the combination of uniform and local conditional moment restrictions induces different rates of convergence parametric and nonparametric for the parameters

bootstrap confidence regions in multinomial sampling power divergences can be used to give a measure of distance between two probability vectors in multinomial sampling arguments can be substituted by empirical and theoretical proportions to obtain confidence regions of parameters in this paper the bootstrap versions of these confidence regions are constructed monte carlo simulation experiments are carried out to calculate average coverage probabilities and to compare the behavior of the introduced procedures

geometrizing rates of convergence ii consider estimating a functional t f of an unknown distribution f in mathbf f from data x 1 cdots x n i i d f let omega varepsilon denote the modulus of continuity of the functional t over mathbf f computed with respect to hellinger distance for well behaved loss functions l t we show that inf t n sup mathbf f e fl t n t f is equivalent to l omega n 1 2 to within constants whenever t is linear and mathbf f is convex the same conclusion holds in three nonlinear cases estimating the rate of decay of a density estimating the mode and robust nonparametric regression we study the difficulty of testing between the composite infinite dimensional hypotheses h 0 t f leq t and h 1 t f geq t delta our results hold in the cases studied because the difficulty of the full infinite dimensional composite testing problem is comparable to the difficulty of the hardest simple two point testing subproblem

approximating the moments and distribution of the likelihood ratio statistic for multinomial goodness of fit abstract approximations were derived for the mean and variance of g 2 the likelihood ratio statistic for testing goodness of fit in a k cell multinomial distribution these approximate moments accurate to o n 3 may be used in fitting the distribution of g 2 extensive numerical studies of the exact and approximate distributions were performed in the special case of equiprobability the asymptotic chi squared distribution was found to fit poorly for k 4 satisfactory results were obtained using a multiplicative correction to the chi squared fit more sophisticated procedures using the beta distribution produced increased accuracy but at the cost of excessive computational labor

information and entropy econometrics editor s view amos golan department of economics american university roper 200 4400 massachusetts ave nw washington dc 20016 usa

distributed estimation and detection for sensor networks using hidden markov random field models we develop a hidden markov random field hmrf framework for distributed signal processing in sensor network environments under this framework spatially distributed observations collected at the sensors form a noisy realization of an underlying random field that has a simple structure with markovian dependence we derive iterated conditional modes icm algorithms for distributed estimation of the hidden random field from the noisy measurements we consider both parametric and nonparametric measurement error models the proposed distributed estimators are computationally simple applicable to a wide range of sensing environments and localized implying that the nodes communicate only with their neighbors to obtain the desired results we also develop a calibration method for estimating markov random field model parameters from training data and discuss initialization of the icm algorithms the hmrf framework and icm algorithms are applied to event region detection numerical simulations demonstrate the performance of the proposed approach

using permutations to detect dependence between time series abstract in this paper we propose an independence test between two time series which is based on permutations the proposed test can be carried out by means of different common statistics such as pearson s chi square or the likelihood ratio we also point out why an exact test is necessary simulated and real data return exchange rates between several currencies reveal the capacity of this test to detect linear and nonlinear dependences

an algorithm for constructing a basis for c r spline modules over polynomial rings let be a polyhedral complex embedded in the euclidean space e d and s r r 0 denote the set of all c r splines on then s r is an r module where r e x 1 x d is the ring of polynomials in several variables in this paper we state and prove the existence of an algorithm to write down a free basis for the above r module in terms of obvious linear forms defining common faces of members of this is done for the case when consists of a finite number of parallelopipeds properly joined amongst themselves along the above linear forms

a new look at the robust control of discrete time markov jump linear systems abstractin this paper we make a foray in the role played by a set of four operators on the study of robust h2 and mixed h2 h control problems for discrete time markov jump linear systems these operators appear in the study of mean square stability for this class of systems by means of new linear matrix inequality lmi characterisations of controllers which include slack variables that to some extent separate the robustness and performance objectives we introduce four alternative approaches to the design of controllers which are robustly stabilising and at the same time provide a guaranteed level of h2 performance since each operator provides a different degree of conservatism the results are unified in the form of an iterative lmi technique for designing robust h2 controllers whose convergence is attained in a finite number of steps the method yields a new way of computing mixed h2 h controllers whose conservatism decreases with iteration two numerical examples illustrate the applicability

goodness of fit tests in models for life history data based on cumulative hazard rates to check the validity of an assumed parametric model for survival data one may compare t the nonparametric nelson aalen plot of the cumulative hazard rate with a t the estimated parametric cumulative hazard rate being for example the maximum likelihood estimator convergence in distribution of n t a t and more general processes is studied employing the general framework of counting processes which allows for quite general models for life history data and for quite general censoring schemes the results are applied to the construction of 2 type statistics for goodness of fit cramer von mises and kolmogorov smirnov type tests are presented in the case where the unknown parameter is one dimensional

a family of confidence intervals for the ratio of two binomial proportions the power divergence family of statistics introduced by cressie and read 1984 journal of the royal statistical society series b 46 440 464 is used to obtain approximate confidence intervals for the ratio of two proportions intervals based on inverting the pearson likelihood ratio and freeman tukey statistics are included in this family small sample comparisons of the intervals are presented

neglected heterogeneity in moment condition models abstract the central concern of this paper is parameter heterogeneity in models specified by a number of unconditional or conditional moment conditions and thereby the provision of a framework for the development of apposite optimal m tests against its potential presence we initially consider the unconditional moment restrictions framework optimal m tests against moment condition parameter heterogeneity are derived with the relevant jacobian matrix obtained in terms of the second order own derivatives of the moment indicator in a leading case gmm and gel tests of specification based on generalized information matrix equalities appropriate for moment based models are described and their relation to optimal m tests against moment condition parameter heterogeneity examined a fundamental and important difference is noted between gmm and gel constructions the paper is concluded by a generalization of these tests to the conditional moment context and the provision of a limited set of simulation experiments to illustrate the efficacy of the proposed tests

benford s law and the fsd distribution of economic behavioral micro data abstract in this paper we focus on the first significant digit fsd distribution of european micro income data and use information theoretic entropy based methods to investigate the degree to which benford s fsd law is consistent with the nature of these economic behavioral systems we demonstrate that benford s law is not an empirical phenomenon that occurs only in important distributions in physical statistics but that it also arises in self organizing dynamic economic behavioral systems the empirical likelihood member of the minimum divergence entropy family is used to recover country based income fsd probability density functions and to demonstrate the implications of using a benford prior reference distribution in economic behavioral system information recovery

nonparametric option pricing under shape restrictions frequently economic theory places shape restrictions on functional relationships between economic variables this paper develops a method to constrain the values of the first and second derivatives of nonparametric locally polynomial estimators we apply this technique to estimate the state price density spd or risk neutral density implicit in the market prices of options the option pricing function must be monotonic and convex simulations demonstrate that nonparametric estimates can be quite feasible in the small samples relevant for day to day option pricing once appropriate theory motivated shape restrictions are imposed using s p 500 option prices we show that unconstrained nonparametric estimators violate the constraints during more than half the trading days in 1999 unlike the constrained estimator we propose

asymptotic efficiency in estimation with conditional moment restrictions abstract in this paper bounds on asymptotic efficiency are derived for a class of non parametric models the data are independent and identically distributed according to some unknown distribution f there is a given function of the data and a parameter the restrictions are that a conditional expectation of this function is zero at some point in the parameter space this point is to be estimated if f is assumed to be a multinomial distribution with known finite support then the problem becomes parametric and the bound can be obtained from the information matrix this bound turns out to depend only upon certain conditional moments and not upon the support of the distribution since a general f can be approximated by a multinomial distribution the multinomial bound applies to the general case

empirical likelihood for linear models empirical likelihood is a nonparametric method of inference it has sampling properties similar to the bootstrap but where the bootstrap uses resampling it profiles a multinomial likelihood supported on the sample its properties in i i d settings have been investigated in works by owen by hall and by diciccio hall and romano this article extends the method to regression problems fixed and random regressors are considered as are robust and heteroscedastic regressions to make the extension three variations on the original idea are considered it is shown that when some functionals of the distribution of the data are known one can get sharper inferences on other functionals by imposing the known values as constraints on the optimization the result is first order equivalent to conditioning on a sample value of the known functional the use of a euclidean alternative to the likelihood function is investigated a triangular array version of the empirical likelihood theorem is given the one way anova and heteroscedastic regression models are considered in detail an example is given in which inferences are drawn on the parameters of both the regression function and the conditional variance model

an information theoretic alternative to generalized method of moments estimation while optimally weighted gmm estimation has desirable large sample properties its small sample performance is poor in some applications we propose a computationally simple alternative for weakly dependent data generating mechanisms based on minimization of the kullback leibler information criterion conditions are derived under which the large sample properties of this estimator are similar to gmm i e the estimator will be consistent and asymptotically normal with the same asymptotic covariance matrix as gmm in addition we propose overidentifying and parametric restrictions tests as alternatives to analogous gmm procedures

semi parametric estimation of american option prices abstract we introduce a novel semi parametric estimator of american option prices in discrete time the specification is based on a parameterized stochastic discount factor and is nonparametric w r t the historical dynamics of the markovian state variables the historical transition density estimator minimizes a distance built on the kullback leibler divergence from a kernel transition density subject to the no arbitrage restrictions for a non defaultable bond the underlying asset and some american option prices we use dynamic programming to make explicit the nonlinear restrictions on the euclidean and functional parameters coming from option data we study asymptotic and finite sample properties of the estimators

score tests in gmm why use implied probabilities while simple to implement and thus attractive in practice the gmm score test of newey and west 1987 often displays upward size distortion under common scenarios involving skewed moment vectors or models with weak identification inference based on the generalized empirical likelihood gel is seen as a general solution to this problem kleibergen 2005 and more generally guggenberger and smith 2005 devised an elegant theory for the gel score tests however strictly speaking the gel score tests do not nest the newey west score test our paper provides a unified framework for score tests in gmm that nests all of the above as special cases and helps us to understand the precise mechanism by which the standard first order asymptotic theory on size and power well approximates the finite sample behavior of some score tests namely a subset of the gel score tests but not others special attention is paid to models with weak identification we also argue that the apparent computational burden of gel can be overcome in practice by recognizing the fundamental common role played by the gel implied probabilities under all special cases of our framework in particular we show that all the gel implied probabilities are asymptotically equivalent at a higher order both under the null and under appropriate sequences of alternatives and thus are exchangeable across computationally burdensome e g empirical likelihood and easy e g euclidean empirical likelihood gel score tests without affecting the first order asymptotics extensive simulation evidence is provided to corroborate our theoretical results the simulation results also support a simple and yet important insight on the power of the tests the use of implied probabilities to efficiently estimate the components of the score statistic namely the jacobian and the asymptotic variance of the moment vector can significantly improve the power of the score test in finite samples

empirical likelihood as a goodness of fit measure summary the method of empirical likelihood can be viewed as one of allocating probabilities to an n cell contingency table so as to minimise a goodness of fit criterion it is shown that when the cressie read power divergence statistic is used as the criterion confidence regions enjoying the same convergence rates as those found for empirical likelihood can be obtained for the entire range of values of the cressie read parameter including 1 maximum entropy 0 empirical likelihood and 1 pearson s z2 it is noted that in the power divergence family empirical likelihood is the only member which is bartlettcorrectable however simulation results suggest that for the mean using a scaled f distribution yields more accurate coverage levels for moderate sample sizes

mixed h sub 2 h sub spl infin control of discrete time markovian jump linear systems in this paper we consider the mixed h sub 2 h sub spl infin control problem for the class of discrete time linear systems with parameters subject to markovian jump linear systems it is assumed that both the state variable and the jump variable are available to the controller the transition probability matrix may not be exactly known but belongs to an appropriate convex set for this controlled discrete time markovian jump linear system the problem of interest can be stated in the following way find a robust with respect to the uncertainty on the transition markov probability matrix mean square stabilizing state and jump feedback controller that minimizes an upper bound for the h sub spl infin norm under the restriction that the h sub spl infin norm is less than a prespecified value spl delta the problem of the determination of the smallest h sub spl infin norm is also addressed we present an approximate version of these problems via linear matrix inequality optimization

robust and efficient estimation by minimising a density power divergence a minimum divergence estimation method is developed for robust parameter estimation the proposed approach uses new density based divergences which unlike existing methods of this type such as minimum hellinger distance estimation avoid the use of nonparametric density estimation and associated complications such as bandwidth selection the proposed class of density power divergences is indexed by a single parameter which controls the trade off between robustness and efficiency the methodology affords a robust extension of maximum likelihood estimation for which 0 choices of near zero afford considerable robustness while retaining efficiency close to that of maximum likelihood

the algebra of continuous piecewise polynomials abstract for a triangulated d dimensional region r d we consider the algebra c 0 of all continuous piecewise polynomial functions on we find generators for c 0 as an r algebra and use these to give an isomorphism between c 0 and a quotient of the face ring a of we then study the structure of c 0 as a module over r r y 1 y d the polynomial ring in d indeterminates giving generators for c 0 as an r module these form a free basis when is a shellable complex in general we show that c 0 is a free r module whenever is a disk

the moment corrected phi divergence test statistics for symmetry in this paper we consider the family of f divergence test statistics t n f s for the problem of symmetry in ixi contingency tables whose asymptotic distribution is chi square with i i 1 2 degrees of freedom and we propose a moment corrected f divergence test statistic in order to improve the accuracy of the chi square approximation of the distribution of t n f s under the hypothesis of symmetry

data tilting for time series summary we develop a general methodology for tilting time series data attention is focused on a large class of regression problems where errors are expressed through autoregressive processes the class has a range of important applications and in the context of our work may be used to illustrate the application of tilting methods to interval estimation in regression robust statistical inference and estimation subject to constraints the method can be viewed as empirical likelihood with nuisance parameters

h_ infty fuzzy control of nonlinear systems under unreliable communication links this paper investigates the problem of h infin fuzzy control of nonlinear systems under unreliable communication links the nonlinear plant is represented by a takagi sugeno t s fuzzy model and the control strategy takes the form of parallel distributed compensation the communication links existing between the plant and controller are assumed to be imperfect that is data packet dropouts occur intermittently which appear typically in a network environment and stochastic variables satisfying the bernoulli random binary distribution are utilized to model the unreliable communication links attention is focused on the design of h infin controllers such that the closed loop system is stochastically stable and preserves a guaranteed h infin performance two approaches are developed to solve this problem based on the quadratic lyapunov function and the basis dependent lyapunov function respectively several examples are provided to illustrate the usefulness and applicability of the developed theoretical results

a bayesian approach to diagnosis of asset pricing models a large literature has arisen which exploits a particular portfolio on the mean variance frontier determining a minimum variance bound on the set of stochastic discount factors state price to probability ratios this paper proposes a new variational characterization of the closely related set of state price densities based on minimization of the kullback leibler information criterion in contrast to the variance bound the resulting information bound automatically satisfies an important positivity constraint furthermore the information bound is determined by a portfolio which maximizes expected cara utility several interpretations of the information bound are given and empirical uses of it are illustrated

new methods for mode independent robust control of markov jump linear systems abstract this paper treats the h 2 and h controls of linear systems with markov jump disturbances via new design methods based on linear matrix inequalities lmis the proposed techniques are especially tailored to the scenario where the jump process cannot be measured and apply to homogeneous markov chains of any structure in the scenario of polytopic uncertainty affecting the system matrices new uncertainty dependent methods are introduced for the design of robust controllers several numerical examples illustrate situations where the proposed techniques are less conservative than the ones found in the literature

stability results for discrete time linear systems with markovian jumping parameters stability results for discrete time linear systems subject to random jumps in the parameters are obtained first necessary and sufficient conditions for mean square stability mss including the case in which the system is driven by an independent wide sense stationary random sequence are derived it is shown that mss is equivalent to the spectral radius of an augmented matrix being less than one or to the existence of a solution of a certain lyapunov equation in addition it is shown that the lyapunov equation can be derived in four equivalent forms and as a by product each one gives risc to an easier to check sufficient condition these results give inter alia a unified and rather complete picture for mss of markovian jump linear systems next we derive sufficient conditions for almost sure stability of the noiseless ease finally we conclude by presenting an illustrative application to adaptive filtering where a mild condition for almost sure convergence is provided

information theoretic approaches to inference in moment condition models one step efficient gmm estimation has been developed in the recent papers of back and brown 1990 imbens 1993 and qin and lawless 1994 these papers emphasized methods that correspond to using owen s 1988 method of empirical likelihood to reweight the data so that the reweighted sample obeys all the moment restrictions at the parameter estimates in this paper we consider an alternative klic motivated weighting and show how it and similar discrete reweightings define a class of unconstrained optimization problems which includes gmm as a special case such klic motivated reweightings introduce m auxiliary tilting parameters where m is the number of moments parameter and overidentification hypotheses can be recast in terms of these tilting parameters such tests when appropriately conditioned on the estimates of the original parameters are often startlingly more effective than their conventional counterparts this is apparently due to the local ancillarity of the original parameters for the tilting parameters

a new discrete time robust stability condition a new robust stability condition for uncertain discrete time systems with convex polytopic uncertainty is given it enables to check stability using parameter dependent lyapunov functions which are derived from lmi conditions it is shown that this new condition provides better results than the classical quadratic stability besides the use of a parameter dependent lyapunov function this condition exhibits a kind of decoupling between the lyapunov and the system matrices which may be explored for control synthesis purposes a numerical example illustrates the results

efficient robust regression via two stage generalized empirical likelihood large and finite sample efficiency and resistance to outliers are the key goals of robust statistics although often not simultaneously attainable we develop and study a linear regression estimator that comes close efficiency is obtained from the estimator s close connection to generalized empirical likelihood and its favorable robustness properties are obtained by constraining the associated sum of weighted squared residuals we prove maximum attainable finite sample replacement breakdown point and full asymptotic efficiency for normal errors simulation evidence shows that compared to existing robust regression estimators the new estimator has relatively high efficiency for small sample sizes and comparable outlier resistance the estimator is further illustrated and compared to existing methods via application to a real dataset with purported outliers

a tilting approach to ranking influence summary we suggest a new approach which is applicable for general statistics computed from random samples of univariate or vector valued or functional data to assessing the influence that individual data have on the value of a statistic and to ranking the data in terms of that influence our method is based on first perturbing the value of the statistic by tilting or reweighting each data value where the total amount of tilt is constrained to be the least possible subject to achieving a given small perturbation of the statistic and then taking the ranking of the influence of data values to be that which corresponds to ranking the changes in data weights it is shown both theoretically and numerically that this ranking does not depend on the size of the perturbation provided that the perturbation is sufficiently small that simple result leads directly to an elegant geometric interpretation of the ranks they are the ranks of the lengths of projections of the weights onto a line determined by the first empirical principal component function in a generalized measure of covariance to illustrate the generality of the method we introduce and explore it in the case of functional data where for example it leads to generalized boxplots the method has the advantage of providing an interpretable ranking that depends on the statistic under consideration for example the ranking of data in terms of their influence on the value of a statistic is different for a measure of location and for a measure of scale this is as it should be a ranking of data in terms of their influence should depend on the manner in which the data are used additionally the ranking recognizes rather than ignores sign and in particular can identify left and right hand tails of the distribution of a random function or vector

robust stability ℋ2 analysis and stabilisation of discrete time markov jump linear systems with uncertain probability matrix the stability and the problem of 2 guaranteed cost computation for discrete time markov jump linear systems mjls are investigated assuming that the transition probability matrix is not precisely known it is generally difficult to estimate the exact transition matrix of the underlying markov chain and the setting has a special interest for applications of mjls the exact matrix is assumed to belong to a polytopic domain made up by known probability matrices and a sequence of linear matrix inequalities lmis is proposed to verify the stability and to solve the 2 guaranteed cost with increasing precision these lmi problems are connected to homogeneous polynomially parameter dependent lyapunov matrix of increasing degree g the mean square stability mss can be established by the method since the conditions that are sufficient eventually turns out to also be necessary provided that the degree g is large enough the 2 guaranteed cost under mss is also studied here and an extension to cope with th

a simplified approach to computing efficiency bounds in semiparametric models using some standard hilbert space theory a simplified approach to computing efficiency bounds in semiparametric models is presented we use some interesting examples to illustrate this approach and also obtain some results which seem to be new to the literature

estimating model discrepancy a quantity 2 is defined as the discrepancy between an actual and an assumed statistical model an estimator is developed for the case in which data are grouped the estimator is based on pearson

unified inference for nonlinear factor models from panels with fixed and large time span abstract we provide unifying inference theory for parametric nonlinear factor models based on a panel of noisy observations the panel has a large cross section and a time span that may be either small or large moreover we incorporate an additional source of information provided by noisy observations on some known functions of the factor realizations the estimation is carried out via penalized least squares i e by minimizing the l 2 distance between observations from the panel and their model implied counterparts augmented by a penalty for the deviation of the extracted factors from the noisy signals of them when the time dimension is fixed the limit distribution of the parameter vector is mixed gaussian with conditional variance depending on the path of the factor realizations on the other hand when the time span is large the convergence rate is faster and the limit distribution is gaussian with a constant variance in this case however we incur an incidental parameter problem since at each point in time we need to recover the concurrent factor realizations this leads to an asymptotic bias that is absent in the setting with a fixed time span in either scenario the limit distribution of the estimates for the factor realizations is mixed gaussian but is related to the limiting distribution of the parameter vector only in the scenario with a fixed time horizon although the limit behavior is very different for the small versus large time span we develop a feasible inference theory that applies without modification in either case hence the user need not take a stand on the relative size of the time dimension of the panel similarly we propose a time varying data driven weighting of the penalty in the objective function which enhances efficiency by adapting to the relative quality of the signal for the factor realizations