second order and moderate deviations asymptotics for successive refinement we derive the optimal second order coding region and moderate deviations constant for successive refinement source coding with a joint excess distortion probability constraint we consider two scenarios 1 a discrete memoryless source dms and arbitrary distortion measures at the decoders and 2 a gaussian memoryless source gms and quadratic distortion measures at the decoders for a dms with arbitrary distortion measures we prove an achievable second order coding region using type covering lemmas by kanlis and narayan and by no ingber and weissman we prove the converse using the perturbation approach by gu and effros when the dms is successively refinable the expressions for the second order coding region and the moderate deviations constant are simplified and easily computable for this case we also obtain new insights on the second order behavior compared with the scenario where separate excess distortion proabilities are considered for example we describe a dms for which the optimal second order region transitions from being characterizable by a bivariate gaussian to a univariate gaussian as the distortion levels are varied we then consider a gms with quadratic distortion measures to prove the direct part we make use of the sphere covering theorem by verger gaugry together with appropriately defined gaussian type classes to prove the converse we generalize kostina and verdu s one shot converse bound for point to point lossy source coding we remark that this proof is applicable to general successively refinable sources in the proofs of the moderate deviations results for both scenarios we follow a strategy similar to that for the second order asymptotics and use the moderate deviations principle

hypothesis testing with multiterminal data compression the multiterminal hypothesis testing h xy against h xy is considered where x n x n and y n y n are separately encoded at rates r 1 and r 2 respectively the problem is to determine the minimum beta n of the second kind of error probability under the condition that the first kind of error probability alpha n leq epsilon for a prescribed 0 a good lower bound theta l r 1 r 2 on the power exponent theta r 1 r 2 epsilon lim inf n rightarrow infty 1 n log beta n is given and several interesting properties are revealed the lower bound is tighter than that of ahlswede and csiszar furthermore in the special case of testing against independence this bound turns out to coincide with that given by them the main arguments are devoted to the special case with r 2 infty corresponding to full side information for y n y n in particular the compact solution is established to the complete data compression cases which are useful in statistics from the practical point of view

on a mixture autoregressive conditional heteroscedastic model we propose a mixture autoregressive conditional heteroscedastic mar arch model for modeling nonlinear time series the models consist of a mixture of k autoregressive components with autoregressive conditional heteroscedasticity that is the conditional mean of the process variable follows a mixture ar mar process whereas the conditional variance of the process variable follows a mixture arch process in addition to the advantage of better description of the conditional distributions from the mar model the mararch model allows a more flexible squared autocorrelation structure the stationarity conditions autocorrelation function and squared autocorrelation function are derived construction of multiple step predictive distributions is discussed the estimation can be easily done through a simple em algorithm and the model selection problem is addressed the shape changing feature of the conditional distributions makes these models capable of modeling time series with multimodal conditional distr

detection of intensity bursts using hawkes processes an application to high frequency financial data given a stationary point process an intensity burst is defined as a short time period during which the number of counts is larger than the typical count rate it might signal a local nonstationarity or the presence of an external perturbation to the system in this paper we propose a procedure for the detection of intensity bursts within the hawkes process framework by using a model selection scheme we show that our procedure can be used to detect intensity bursts when both their occurrence time and their total number is unknown moreover the initial time of the burst can be determined with a precision given by the typical interevent time we apply our methodology to the midprice change in foreign exchange fx markets showing that these bursts are frequent and that only a relatively small fraction is associated with news arrival we show lead lag relations in intensity burst occurrence across different fx rates and we discuss their relation with price jumps

second order asymptotics for the gaussian mac with degraded message sets this paper studies the second order asymptotics of the gaussian multiple access channel with degraded message sets for a fixed average error probability varepsilon in 0 1 and an arbitrary point on the boundary of the capacity region we characterize the speed of convergence of rate pairs that converge to that boundary point for codes that have asymptotic error probability no larger than varepsilon as a stepping stone to this local notion of the second order asymptotics we study a global notion and establish relationships between the two we provide a numerical example to illustrate how the angle of approach to a boundary point affects the second order coding rate this is the first conclusive characterization of the second order asymptotics of a network information theory problem in which the capacity region is not a polygon

exponential strong converse for content identification with lossy recovery we revisit the high dimensional content identification with lossy recovery problem tuncel and gunduz 2014 and establish an exponential strong converse theorem as a corollary of the exponential strong converse theorem we derive an upper bound on the joint identification error and excess distortion exponent for the problem our main results can be specialized to the biometrical identification problem willems 2003 and the content identification problem tuncel 2009 since these two problems are both special cases of the content identification with lossy recovery problem we leverage the information spectrum method introduced by oohama and adapt the strong converse techniques therein to be applicable to the problem at hand

bootstrap and permutation tests of independence for point processes motivated by a neuroscience question about synchrony detection in spike train analysis we deal with the independence testing problem for point processes we introduce non parametric test statistics which are rescaled general u statistics whose corresponding critical values are constructed from bootstrap and randomization permutation approaches making as few assumptions as possible on the underlying distribution of the point processes we derive general consistency results for the bootstrap and for the permutation w r t to wasserstein s metric which induce weak convergence as well as convergence of second order moments the obtained bootstrap or permutation independence tests are thus proved to be asymptotically of the prescribed size and to be consistent against any reasonable alternative a simulation study is performed to illustrate the derived theoretical results and to compare the performance of our new tests with existing ones in the neuroscientific literature

the jackknife and the bootstrap for general stationary observations we extend the jackknife and the bootstrap method of estimating standard errors to the case where the observations form a general stationary sequence we do not attempt a reduction to i i d values the jackknife calculates the sample variance of replicates of the statistic obtained by omitting each block of l consecutive data once in the case of the arithmetic mean this is shown to be equivalent to a weighted covariance estimate of the spectral density of the observations at zero under appropriate conditions consistency is obtained if l l n rightarrow infty and l n n rightarrow 0 general statistics are approximated by an arithmetic mean in regular cases this approximation determines the asymptotic behavior bootstrap replicates are constructed by selecting blocks of length l randomly with replacement among the blocks of observations the procedures are illustrated by using the sunspot numbers and some simulated data

density estimation in the l infty norm for dependent data with applications to the gibbs sampler this paper investigates the density estimation problem in the lx norm for dependent data it is shown that the iid optimal minimax rates are also optimal for smooth classes of stationary sequences satisfying certain 8 mixing or absolutely regular conditions moreover for given 3 mixing coefficients bounds on uniform convergence rates of kernel estimators are computed in terms of the mixing coefficients the rates and the bounds obtained are not only for estimating the density but also for its derivatives the results are then applied to give uniform convergence rates in problems associated with the gibbs sampler

regression type inference in nonparametric autoregression we derive a strong approximation of a local polynomial estimator lpe in nonparametric autoregression by an lpe in a corresponding nonparametric regression model this generally suggests the application of regression typical tools for statistical inference in nonparametric autoregressive models it provides an important simplification for the bootstrap method to be used it is enough to mimic the structure of a nonparametric regression model rather than to imitate the more complicated process structure in the autoregressive case as an example we consider a simple wild bootstrap which is used for the construction of simultaneous confidence bands and nonparametric supremum type tests

the formation of black holes in spherically symmetric gravitational collapse we consider the spherically symmetric asymptotically flat einstein vlasov system we find explicit conditions on the initial data with adm mass m such that the resulting spacetime has the following properties there is a family of radially outgoing null geodesics where the area radius r along each geodesic is bounded by 2m the timelike lines r c 0 2m are incomplete and for r 2m the metric converges asymptotically to the schwarzschild metric with mass m the initial data that we construct guarantee the formation of a black hole in the evolution we give examples of such initial data with the additional property that the solutions exist for all r 0 and all schwarzschild time i e we obtain global existence in schwarzschild coordinates in situations where the initial data are not small some of our results are also established for the einstein equations coupled to a general matter model characterized by conditions on the matter quantities

second order residual analysis of spatiotemporal point processes and applications in model evaluation summary the paper gives first order residual analysis for spatiotemporal point processes that is similar to the residual analysis that has been developed by baddeley and co workers for spatial point processes and also proposes principles for second order residual analysis based on the viewpoint of martingales examples are given for both first and second order residuals in particular residual analysis can be used as a powerful tool in model improvement taking a spatiotemporal epidemic type aftershock sequence model for earthquake occurrences as the base line model second order residual analysis can be useful for identifying many features of the data that are not implied in the base line model providing us with clues about how to formulate better models

on the dispersions of the gel fand pinsker channel and dirty paper coding this paper studies the second order coding rates for memoryless channels with a state sequence known non causally at the encoder in the case of finite alphabets an achievability result is obtained using constant composition random coding and by using a small fraction of the block to transmit the empirical distribution of the state sequence for error probabilities less than 0 5 it is shown that the second order rate improves on an existing one based on independent and identically distributed random coding in the gaussian case dirty paper coding with an almost sure power constraint an achievability result is obtained using random coding over the surface of a sphere and using a small fraction of the block to transmit a quantized description of the state power it is shown that the second order asymptotics are identical to the single user gaussian channel of the same input power without a state

nonasymptotic and second order achievability bounds for coding with side information we present a novel nonasymptotic or finite blocklength achievability bounds for three side information problems in network information theory these include 1 the wyner ahlswede korner wak problem of almost lossless source coding with rate limited side information 2 the wyner ziv wz problem of lossy source coding with side information at the decoder and 3 the gel fand pinsker gp problem of channel coding with noncausal state information available at the encoder the bounds are proved using ideas from channel simulation and channel resolvability our bounds for all three problems improve on all previous nonasymptotic bounds on the error probability of the wak wz and gp problems in particular those derived by verdu using our novel nonasymptotic bounds we recover the general formulas for the optimal rates of these side information problems finally we also present achievable second order coding rates by applying the multidimensional berry esseen theorem to our new nonasymptotic bounds numerical results show that the second order coding rates obtained using our nonasymptotic achievability bounds are superior to those obtained using existing finite blocklength bounds

on the conditional smooth renyi entropy and its applications in guessing and source coding a novel definition of the conditional smooth renyi entropy which is different from that of renner and wolf is introduced it is shown that our definition of the conditional smooth renyi entropy is appropriate for providing lower and upper bounds on the optimal guessing moment in a guessing problem where the guesser is allowed to stop guessing and declare an error further a general formula for the optimal guessing exponent is presented in particular a single letterized formula for a mixture of i i d sources is obtained it is also shown that our definition is appropriate to characterize the optimal exponential moment of the codeword length in the problem of source coding with common side information available at the encoder and decoder under a constraint on the probability of a decoding error

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

the instability of naked singularities in the gravitational collapse of a scalar field one of the fundamental unanswered questions in the general theory of relativity is whether naked singularities that is singular events which are visible from inflnity may form with positive probability in the process of gravitational collapse the conjecture that the answer to this question is in the negative has been called cosmic censorship the present paper which is a continuation of the work in 1 2 3 and 4 addresses this question in the context of the spherical gravitational collapse of a scalar fleld the problem of a spherically symmetric self gravitating scalar fleld is formulated in terms of a 2 dimensional quotient space time manifold q with boundary see 1 the boundary ofq corresponds to the set of flxed points of the group action the center of symmetry which is a timelike geodesic i the manifoldq is endowed with a lorentzian metric gab an area radius function i i r

strong approximation of density estimators from weakly dependent observations by density estimators from independent observations we derive an approximation of a density estimator based on weakly dependent random vectors by a density estimator built from independent random vectors we construct on a sufficiently rich probability space such a pairing of the random variables of both experiments that the set of observations x 1 x n from the time series model is nearly the same as the set of observations y 1 y n from the i i d model with a high probability all sets of the form x 1 x n delta y 1 y n boolean and a 1 b 1 x x a d b d contain no more than o n 1 2 pi b i a i 1 log n elements respectively although this does not imply very much for parametric problems it has important implications in nonparametric statistics it yields a strong approximation of a kernel estimator of the stationary density by a kernel density estimator in the i i d model moreover it is shown that such a strong approximation is also valid for the standard bootstrap and the smoothed bootstrap using these results we derive simultaneous confidence bands as well as supremum type nonparametric tests based on reasoning for the i i d model

achievability proof via output statistics of random binning this paper introduces a new and ubiquitous framework for establishing achievability results in network information theory problems the framework uses random binning arguments and is based on a duality between channel and source coding problems furthermore the framework uses pmf approximation arguments instead of counting and typicality this allows for proving coordination and strong secrecy problems where certain statistical conditions on the distribution of random variables need to be satisfied these statistical conditions include independence between messages and eavesdropper s observations in secrecy problems and closeness to a certain distribution usually i i d distribution in coordination problems one important feature of the framework is to enable one to add an eavesdropper and obtain a result on the secrecy rates for free we make a case for generality of the framework by studying examples in a variety of settings including channel coding lossy source coding joint source channel coding coordination strong secrecy feedback and relaying in particular by investigating the framework for the lossy source coding problem over broadcast channel it is shown that the new framework provides a simple alternative scheme to the hybrid coding scheme in addition new results on secrecy rate region under strong secrecy criterion of wiretap broadcast channel and wiretap relay channel are derived in a set of accompanied papers we have shown the usefulness of the framework to establish achievability results for coordination problems including interactive channel simulation coordination via relay and channel simulation via another channel

uniformization and hybrid simulation analytic models of renewal processes in this paper we demonstrate the use of uniformization in the simulation of renewal processes using uniformization we represent the continuous random variable of interest as the first passage time of a continuous time stochastic process associated with a poisson process we then use this result to develop a hybrid simulation analytic method to model renewal processes the estimators obtained from the hybrid simulation analytic models have lower variance than the variance of the estimators of the traditional simulation models we also discuss the possible impact of this method on the future of simulation methodology

tests for parameter instability and structural change with unknown change point this paper considers tests for parameter instability and structural change with unknown change point the results apply to a wide class of parametric models that are suitable for estimation by generalized method of moments procedures the asymptotic distributions of the test statistics considered here are nonstandard because the change point parameter only appears under the alternative hypothesis and not under the null the tests considered here are shown to have nontrivial asymptotic local power against all alternatives for which the parameters are nonconstant the tests are found to perform quite well in a monte carlo experiment reported elsewhere copyright 1993 by the econometric society

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

inference when a nuisance parameter is not identified under the null hypothesis many econometric testing problems involve nuisance parameters which are not identified under the null hypotheses this paper studies the asymptotic distribution theory for such tests the asymptotic distributions of standard test statistics are described as functionals of chi square processes in general the distributions depend upon a large number of unknown parameters we show that a transformation based upon a conditional probability measure yields an asymptotic distribution free of nuisance parameters and we show that this transformation can be easily approximated via simulation the theory is applied to threshold models with special attention given to the so called self exciting threshold autoregressive model monte carlo methods are used to assess the finite sample distributions the tests are applied to u s gnp growth rates and we find that potter s 1995 threshold effect in this series can be possibly explained by sampling variation

testing separability in spatial temporal marked point processes nonparametric tests for investigating the separability of a spatial temporal marked point process are described and compared it is shown that a cramer von mises type test is very powerful at detecting gradual departures from separability and that a residual test based on randomly rescaling the process is powerful at detecting nonseparable clustering or inhibition of the marks an application to los angeles county wildfire data is given in which it is shown that the separability hypothesis is invalidated largely due to clustering of fires of similar sizes within periods of up to 3 9 years

information spectrum approach to second order coding rate in channel coding in this paper second order coding rate of channel coding is discussed for general sequence of channels the optimum second order transmission rate with a constant error constraint epsiv is obtained by using the information spectrum method we apply this result to the discrete memoryless case the discrete memoryless case with a cost constraint the additive markovian case and the gaussian channel case with an energy constraint we also clarify that the gallager bound does not give the optimum evaluation in the second order coding rate

infinite systems of interacting chains with memory of variable length a stochastic model for biological neural nets we consider a new class of non markovian processes with a countable number of interacting components at each time unit each component can take two values indicating if it has a spike or not at this precise moment the system evolves as follows for each component the probability of having a spike at the next time unit depends on the entire time evolution of the system after the last spike time of the component this class of systems extends in a non trivial way both the interacting particle systems which are markovian spitzer in adv math 5 246 290 1970 and the stochastic chains with memory of variable length which have finite state space rissanen in ieee trans inf theory 29 5 656 664 1983 these features make it suitable to describe the time evolution of biological neural systems we construct a stationary version of the process by using a probabilistic tool which is a kalikow type decomposition either in random environment or in space time this construction implies uniqueness of the stationary process finally we consider the case where the interactions between components are given by a critical directed erdos renyi type random graph with a large but finite number of components in this framework we obtain an explicit upper bound for the correlation between successive inter spike intervals which is compatible with previous empirical findings

channel coding rate in the finite blocklength regime this paper investigates the maximal channel coding rate achievable at a given blocklength and error probability for general classes of channels new achievability and converse bounds are given which are tighter than existing bounds for wide ranges of parameters of interest and lead to tight approximations of the maximal achievable rate for blocklengths n as short as 100 it is also shown analytically that the maximal rate achievable with error probability isclosely approximated by c v n q 1 where c is the capacity v is a characteristic of the channel referred to as channel dispersion and q is the complementary gaussian cumulative distribution function

discrete lossy gray wyner revisited second order asymptotics large and moderate deviations in this paper we revisit the discrete lossy gray wyner problem in particular we derive its optimal second order coding rate region its error exponent reliability function and its moderate deviations constant under mild conditions on the source to obtain the second order asymptotics we extend some ideas from watanabe s work in particular we leverage the properties of an appropriate generalization of the conditional distortion tilted information density which was first introduced by kostina and verdu the converse part uses a perturbation argument by gu and effros in their strong converse proof of the discrete gray wyner problem the achievability part uses two novel elements 1 a generalization of various type covering lemmas and 2 the uniform continuity of the conditional rate distortion function in both the source joint distribution and the distortion level to obtain the error exponent for the achievability part we use the same generalized type covering lemma and for the converse we use the strong converse together with a change of measure technique finally to obtain the moderate deviations constant we apply the moderate deviations theorem to probabilities defined in terms of information spectrum quantities

multiple tests based on a gaussian approximation of the unitary events method with delayed coincidence count the unitary events ue method is one of the most popular and efficient methods used over the past decade to detect patterns of coincident joint spike activity among simultaneously recorded neurons the detection of coincidences is usually based on binned coincidence count grun 1996 which is known to be subject to loss in synchrony detection grun diesmann grammont riehle aertsen 1999 this defect has been corrected by the multiple shift coincidence count grun et al 1999 the statistical properties of this count have not been further investigated until this work the formula being more difficult to deal with than the original binned count first we propose a new notion of coincidence count the delayed coincidence count which is equal to the multiple shift coincidence count when discretized point processes are involved as models for the spike trains moreover it generalizes this notion to nondiscretized point processes allowing us to propose a new gaussian approximation of the count since unknown parameters are involved in the approximation we perform a plug in step where unknown parameters are replaced by estimated ones leading to a modification of the approximating distribution finally the method takes the multiplicity of the tests into account via a benjamini and hochberg approach benjamini hochberg 1995 to guarantee a prescribed control of the false discovery rate we compare our new method mtgaue multiple tests based on a gaussian approximation of the unitary events and the ue method proposed in grun et al 1999 over various simulations showing that mtgaue extends the validity of the previous method in particular mtgaue is able to detect both profusion and lack of coincidences with respect to the independence case and is robust to changes in the underlying model furthermore mtgaue is applied on real data

exact simulation of point processes with stochastic intensities point processes with stochastic arrival intensities are ubiquitous in many areas including finance insurance reliability health care and queuing they can be simulated from a poisson process by time scaling with the cumulative intensity the paths of the cumulative intensity are often generated with a discretization method however discretization introduces bias into the simulation results the magnitude of the bias is difficult to quantify this paper develops a sampling method that eliminates the need to discretize the cumulative intensity the method is based on a projection argument and leads to unbiased simulation estimators it is exemplified for a point process whose intensity is a function of a jump diffusion process and the point process itself in this setting the method facilitates the exact sampling of both the point process and the driving jump diffusion process numerical experiments demonstrate the effectiveness of the method

an information spectrum approach to weak variable length source coding with side information this paper studies variable length vl source coding of general sources with side information novel one shot coding bounds for slepian wolf sw coding which give nonasymptotic tradeoff between the error probability and the codeword length of vl sw coding are established one shot results are applied to asymptotic analysis and a general formula for the optimal coding rate achievable by weakly lossless vl sw coding i e vl sw coding with vanishing error probability is derived our general formula reveals how the encoder side information and or vl coding improve the optimal coding rate in the general setting in addition it is shown that if the encoder side information is useless in weakly lossless vl coding then it is also useless even in the case where the error probability may be positive asymptotically

cumulants of hawkes point processes we derive explicit closed form expressions for the cumulant densities of a multivariate self exciting hawkes point process generalizing a result of hawkes in his earlier work on the covariance density and bartlett spectrum of such processes to do this we represent the hawkes process in terms of a poisson cluster process and show how the cumulant density formulas can be derived by enumerating all possible family trees representing complex interactions between point events we also consider the problem of computing the integrated cumulants characterizing the average measure of correlated activity between events of different types and derive the relevant equations

simulation of random processes and rate distortion theory we study the randomness necessary for the simulation of a random process with given distributions on terms of the finite precision resolvability of the process finite precision resolvability is defined as the minimal random bit rate required by the simulator as a function of the accuracy with which the distributions are replicated the accuracy is quantified by means of various measures variational distance divergence orstein 1973 prohorov 1956 and related measures of distance between the distributions of random process in the case of ornstein prohorov and other distances of the kantorovich vasershtein type we show that the finite precision resolvability is equal to the rate distortion function with a fidelity criterion derived from the accuracy measure this connection leads to new results on nonstationary rate distortion theory in the case of variational distance the resolvability of stationary ergodic processes is shown to equal entropy rate regardless of the allowed accuracy in the case of normalized divergence explicit expressions for finite precision resolvability are obtained in many cases of interest and connections with data compression with minimum probability of block error are shown

smoothing brascamp lieb inequalities and strong converses of coding theorems the brascamp lieb inequality in functional analysis can be viewed as a measure of the uncorrelatedness of a joint probability distribution we define the smooth brascamp lieb bl divergence as the infimum of the best constant in the brascamp lieb inequality under a perturbation of the joint probability distribution an information spectrum upper bound on the smooth bl divergence is proved using properties of the subgradient of a certain convex functional in particular in the i i d setting such an infimum converges to the best constant in a certain mutual information inequality we then derive new single shot converse bounds for the omniscient helper common randomness generation problem and the gray wyner source coding problem in terms of the smooth bl divergence where the proof relies on the functional formulation of the brascamp lieb inequality exact second order rates are thus obtained in the stationary memoryless and nonvanishing error setting these offer rare instances of strong converses second order converses for continuous sources when the rate region involves auxiliary random variables

on the dispersions of three network information theory problems we analyze the dispersions of distributed lossless source coding the slepian wolf problem the multiple access channel and the asymmetric broadcast channel for the two encoder slepian wolf problem we introduce a quantity known as the entropy dispersion matrix which is analogous to the scalar dispersions that have gained interest recently we prove a global dispersion result that can be expressed in terms of this entropy dispersion matrix and provides intuition on the approximate rate losses at a given blocklength and error probability to gain better intuition about the rate at which the nonasymptotic rate region converges to the slepian wolf boundary we define and characterize two operational dispersions 1 the local dispersion and 2 the weighted sum rate dispersion the former represents the rate of convergence to a point on the slepian wolf boundary whereas the latter represents the fastest rate for which a weighted sum of the two rates converges to its asymptotic fundamental limit interestingly when we approach either of the two corner points the local dispersion is characterized not by a univariate gaussian but a bivariate one as well as a subset of off diagonal elements of the aforementioned entropy dispersion matrix finally we demonstrate the versatility of our achievability proof technique by providing inner bounds for the multiple access channel and the asymmetric broadcast channel in terms of dispersion matrices all our proofs are unified by a so called vector rate redundancy theorem which is proved using the multidimensional berry esseen theorem

variate generation for accelerated life and proportional hazards models we use accelerated life and proportional hazards lifetime models to account for the effects of covariates on a random lifetime we find that variate generation algorithms for monte carlo simulation in both the renewal and nonhomogeneous poisson process cases are a simple extension of the inverse cumulative distribution function cdf technique

random number conversion and locc conversion via restricted storage we consider random number conversion rnc through random number storage with restricted size we clarify the relation between the performance of rnc and the size of storage in the framework of the first and second order asymptotics and derive their rate regions then we show that the results for rnc with restricted storage recover those for conventional rnc without storage in the limit of storage size to treat rnc via restricted storage we introduce a new kind of probability distributions named generalized rayleigh normal distributions using the generalized rayleigh normal distributions we can describe the second order asymptotic behavior of rnc via restricted storage in a unified manner as an application to quantum information theory we analyze locc conversion via entanglement storage with restricted size moreover we derive the optimal locc compression rate under a constraint of conversion accuracy

second order region for gray wyner network the coding problem over the gray wyner network is studied from the second order coding rates perspective a tilted information density for this network is introduced in the spirit of kostina verdu and under a certain regularity condition the second order region is characterized in terms of the variance of this tilted information density and the tangent vector of the first order region the second order region is proved by the type method the achievability part is proved by the type covering argument and the converse part is proved by a refinement of the perturbation approach that was used by gu effros to show the strong converse of the gray wyner network this is the first instance that the second order region is characterized for a multi terminal problem where the characterization of the first order region involves an auxiliary random variable

efficient simulation of clustering jumps with cir intensity we introduce a broad family of generalised self exciting point processes with cir type intensities and we develop associated algorithms for their exact simulation the underlying models are extensions of the classical hawkes process which already has numerous applications in modelling the arrival of events with clustering or contagion effect in finance economics and many other fields interestingly we find that the cir type intensity together with its point process can be sequentially decomposed into simple random variables which immediately leads to a very efficient simulation scheme our algorithms are also pretty accurate and flexible they can be easily extended to further incorporate externally excited jumps or to a multidimensional framework some typical numerical examples and comparisons with other well known schemes are reported in detail in addition a simple application for modelling a portfolio loss process is presented the online appendix is available at https doi org 10 1287 op

fixed length lossy compression in the finite blocklength regime this paper studies the minimum achievable source coding rate as a function of blocklength n and probability that the distortion exceeds a given level d tight general achievability and converse bounds are derived that hold at arbitrary fixed blocklength for stationary memoryless sources with separable distortion the minimum rate achievable is shown to be closely approximated by r d v d n q 1 where r d is the rate distortion function v d is the rate dispersion a characteristic of the source which measures its stochastic variability and q 1 is the inverse of the standard gaussian complementary cumulative distribution function

stability of nonlinear hawkes processes we address the problem of the convergence to equilibrium of a general class of point processes containing in particular the nonlinear mutually exciting point processes an extension of the linear hawkes processes and give general conditions guaranteeing the existence of a stationary version and the convergence to equilibrium of a nonstationary version both in distribution and in variation we also give a new proof of a result of kerstan concerning point processes with bounded intensity and general nonlinear dynamics satisfying a lipschitz condition

on the rate of convergence in the multivariate clt berry esseen theorems are proved in the multidimensional central limit theorem without using fourier methods an effective and simple estimate of the error in the clt for sums and convex sets using stein s method and induction is derived furthermore the error in the clt for multivariate functions of independent random elements is estimated extending results of van zwet and friedrich to the multivariate case

fractional hawkes processes abstract hawkes processes have a self excitation mechanism used for modeling the clustering of events observed in natural or social phenomena in the first part of this article we find the forward differential equations ruling the probability density function and the laplace s transform of the intensity of a hawkes process with an exponential decaying kernel in the second part we study the properties of the fractional version of this process the fractional hawkes process is obtained by subordinating the point process with the inverse of a stable levy process this process is not markov but the probability density function of its intensity is solution of a fractional fokker planck equation finally we find closed form expressions for moments and autocovariance of the fractional intensity

a tight upper bound for the third order asymptotics for most discrete memoryless channels this paper shows that the logarithm of the e error capacity average error probability for n uses of a discrete memoryless channel dmc is upper bounded by the normal approximation plus a third order term that does not exceed 1 2 logn o 1 if the e dispersion of the channel is positive this matches a lower bound by y polyanskiy 2010 for dmcs with positive reverse dispersion if the e dispersion vanishes the logarithm of the e error capacity is upper bounded by n times the capacity plus a constant term except for a small class of dmcs and e 1 2

second order noiseless source coding theorems shannon s celebrated source coding theorem can be viewed as a one sided law of large numbers we formulate second order noiseless source coding theorems for the deviation of the codeword lengths from the entropy for a class of sources that includes markov chains we prove a one sided central limit theorem and a law of the iterated logarithm

local propagation of impulsive gravitationalwaves in this paper we initiate the rigorous mathematical study of the problem of impulsive gravitational spacetime waves we construct such spacetimes as solutions to the characteristic initial value problem of the einstein vacuum equations with a data curvature delta singularity we show that in the resulting spacetime the delta singularity propagates along a characteristic hypersurface while away from that hypersurface the spacetime remains smooth unlike the known explicit examples of impulsive gravitational spacetimes this work in particular provides the first construction of an impulsive gravitational wave of compact extent and does not require any symmetry assumptions the arguments in the present paper also extend to the problem of existence and uniqueness of solutions to a larger class of nonregular characteristic data 2015 wiley periodicals inc

multidimensional residual analysis of point process models for earthquake occurrences residual analysis methods for examining the fit of multidimensional point process models are applied to point process models for the space time magnitude distribution of earthquake occurrences using in particular the multidimensional version of ogata s epidemic type aftershock sequence etas model and a 30 year catalog of 580 earthquakes occurring in bear valley california one method involves rescaled residuals obtained by transforming points along one coordinate to form a homogeneous poisson process inside a random irregular boundary another method involves thinning the point process according to the conditional intensity to form a homogeneous poisson process on the original untransformed space the thinned residuals suggest that the fit of the model may be significantly improved by using an anisotropic spatial distance function in the estimation of the spatially varying background rate using rescaled residuals it is shown that the temporal magnitude distribution of aftershock activity is not

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

writing on dirty paper corresp a channel with output y x s z is examined the state s sim n 0 qi and the noise z sim n 0 ni are multivariate gaussian random variables i is the identity matrix the input x in r n satisfies the power constraint l n sum i 1 n x i 2 leq p if s is unknown to both transmitter and receiver then the capacity is frac 1 2 ln 1 p n q nats per channel use however if the state s is known to the encoder the capacity is shown to be c ast frac 1 2 ln 1 p n independent of q this is also the capacity of a standard gaussian channel with signal to noise power ratio p n therefore the state s does not affect the capacity of the channel even though s is unknown to the receiver it is shown that the optimal transmitter adapts its signal to the state s rather than attempting to cancel it

reliability in source coding with side information we study error exponents for source coding with side information both achievable exponents and converse bounds are obtained for the following two cases lossless source coding with coded information and lossy source coding with full side information wyner ziv these results recover and extend several existing results on source coding error exponents and are tight in some circumstances our bounds have a natural interpretation as a two player game between nature and the code designer with nature seeking to minimize the exponent and the code designer seeking to maximize it in the wyner ziv problem our analysis exposes a tension in the choice of test channel with the optimal test channel balancing two competing error events the gaussian and binary erasure cases are examined in detail

non asymptotic converse bounds and refined asymptotics for two source coding problems in this paper we revisit two multi terminal lossy source coding problems the lossy source coding problem with side information available at the encoder and one of the two decoders which we term as the kaspi problem kaspi 1994 and the multiple description coding problem with one semi deterministic distortion measure which we refer to as the fu yeung problem fu and yeung 2002 for the kaspi problem we first present the properties of optimal test channels subsequently we generalize the notion of the distortion tilted information density for the lossy source coding problem to the kaspi problem and prove a non asymptotic converse bound using the properties of optimal test channels and the well defined distortion tilted information density finally for discrete memoryless sources we derive refined asymptotics which includes the second order large and moderate deviations asymptotics in the converse proof of second order asymptotics we apply the berry esseen theorem to the derived non asymptotic converse bound the achievability proof follows by first proving a type covering lemma tailored to the kaspi problem then properly taylor expanding the well defined distortion tilted information densities and finally applying the berry esseen theorem we then generalize the methods used in the kaspi problem to the fu yeung problem as a result we obtain the properties of optimal test channels for the minimum sum rate function a non asymptotic converse bound and refined asymptotics for discrete memoryless sources since the successive refinement problem is a special case of the fu yeung problem as a by product we obtain a non asymptotic converse bound for the successive refinement problem which is a strict generalization of the non asymptotic converse bound for successively refinable sources zhou tan and motani 2017

a general formula for channel capacity a formula for the capacity of arbitrary single user channels without feedback not necessarily information stable stationary etc is proved capacity is shown to equal the supremum over all input processes of the input output inf information rate defined as the liminf in probability of the normalized information density the key to this result is a new converse approach based on a simple new lower bound on the error probability of m ary hypothesis tests among equiprobable hypotheses a necessary and sufficient condition for the validity of the strong converse is given as well as general expressions for spl epsiv capacity

generation of synthetic spike trains with defined pairwise correlations recent technological advances as well as progress in theoretical understanding of neural systems have created a need for synthetic spike trains with controlled mean rate and pairwise cross correlation this report introduces and analyzes a novel algorithm for the generation of discretized spike trains with arbitrary mean rates and controlled cross correlation pairs of spike trains with any pairwise correlation can be generated and higher order correlations are compatible with common synaptic input relations between allowable mean rates and correlations within a population are discussed the algorithm is highly efficient its complexity increasing linearly with the number of spike trains generated and therefore inversely with the number of cross correlated pairs

maximum likelihood estimates of the fractal dimension for random spatial patterns summary two approximate maximum likelihood estimates of the fractal dimension are suggested for random point patterns and planar curves based on the distributions of the palm probability and the spectrum for estimation of the fractal dimension of self similar patterns in space we usually measure the slope of a linear log log relationship between pairs of points the box counting method plots the number of pixels which intersects the pattern under consider ation versus length of the pixel unit and the walking dividers method plots the total length of polygons which approximate the considered curves versus length of the polygon s side and so on see mandelbrot 1982 p 33 for example using these methods there has been a large number of papers reporting the dimensions of fractal sets especially since mandelbrot 1977 second order properties of a stochastic process such as the auto covariance and the spectrum are also available for examining self similarity and measuring its indices this is especially easy for stochastic processes on a real line for instance ogata 1988 and ogata abe 1991 applied one dimensional point processes to the occurrence times of major earthquakes in the world and japan for a time span of about one century investigating the self similarity by the auto covariance spectrum dispersion time curves and so called r s statistic in particular fractal dimension and the hurst number or the self similarity index are estimated objectively by maximizing a spectral log likelihood the maximum likelihood method is generally expected to provide an efficient estimate together with its standard error therefore in this paper we develop maximum likelihood methods for planar point and curve patterns two types of approximate likelihood functions are considered one is equivalent to an isotropic poisson likelihood by modelling an intensity function of points under the palm probability and the other is the so called spectral likelihood based on the distribution of the periodogram which is an estimate of the spectrum these two independent estimation methods are compared by using a certain artificially generated clustering point pattern then a map of epicentres of earthquakes and a topographic contour line are analyzed to compare the two methods

a rate of convergence result for a universal d semifaithful code the problem of optimal rate universal coding is considered in the context of rate distortion theory a d semifaithful universal coding scheme for discrete memoryless sources is given the main result is a refined covering lemma based on the random coding argument and the method of types the average codelength of the code is shown to approach its lower bound the rate distortion function at a rate o n sup 1 log n and this is conjectured to be optimal based on a result of a j pilc 1968 issues of constructiveness and universality are addressed

adaptive estimation for hawkes processes application to genome analysis the aim of this paper is to provide a new method for the detection of either favored or avoided distances between genomic events along dna sequences these events are modeled by a hawkes process the biological problem is actually complex enough to need a non asymptotic penalized model selection approach we provide a theoretical penalty that satisfies an oracle inequality even for quite complex families of models the consecutive theoretical estimator is

second order asymptotics in fixed length source coding and intrinsic randomness there is a difference between the optimal rates of fixed length source coding and intrinsic randomness when we care about the second order asymptotics we prove this difference for general information sources and then investigate independent and identically distributed i i d random variables and markovian variables as examples the difference is demonstrated through an investigation of the second order asymptotic behavior of the rates a universal fixed length source code attaining the second order optimal rate is also proposed the difference between the rates of fixed length source coding and intrinsic randomness proves that the outputs of fixed length source codes are not uniformly distributed

the time rescaling theorem and its application to neural spike train data analysis measuring agreement between a statistical model and a spike train data series that is evaluating goodness of fit is crucial for establishing the model s validity prior to using it to make inferences about a particular neural system assessing goodness of fit is a challenging problem for point process neural spike train models especially for histogram based models such as perstimulus time histograms psth and rate functions estimated by spike train smoothing the time rescaling theorem is a well known result in probability theory which states that any point process with an integrable conditional intensity function may be transformed into a poisson process with unit rate we describe how the theorem may be used to develop goodness of fit tests for both parametric and histogram based point process models of neural spike trains we apply these tests in two examples a comparison of psth inhomogeneous poisson and inhomogeneous markov interval models of neural spike trains from the supplementary eye field of a macque monkey and a comparison of temporal and spatial smoothers inhomogeneous poisson inhomogeneous gamma and inhomogeneous inverse gaussian models of rat hippocampal place cell spiking activity to help make the logic behind the time rescaling theorem more accessible to researchers in neuroscience we present a proof using only elementary probability theory arguments we also show how the theorem may be used to simulate a general point process model of a spike train our paradigm makes it possible to compare parametric and histogram based neural spike train models directly these results suggest that the time rescaling theorem can be a valuable tool for neural spike train data analysis

testing for jumps in a discretely observed process we propose a new test to determine whether jumps are present in asset returns or other discretely sampled processes as the sampling interval tends to 0 our test statistic converges to 1 if there are jumps and to another deterministic and known value such as 2 if there are no jumps the test is valid for all ito semimartingales depends neither on the law of the process nor on the coefficients of the equation which it solves does not require a preliminary estimation of these coefficients and when there are jumps the test is applicable whether jumps have finite or infinite activity and for an arbitrary blumenthal getoor index we finally implement the test on simulations and asset returns data

general nonasymptotic and asymptotic formulas in channel resolvability and identification capacity and their application to the wiretap channel several nonasymptotic formulas are established in channel resolvability and identification capacity and they are applied to the wiretap channel by using these formulas the epsi capacities of the above three problems are considered in the most general setting where no structural assumptions such as the stationary memoryless property are made on a channel as a result we solve an open problem proposed by han and verduacute moreover we obtain lower bounds of the exponents of error probability and the wiretapper s information in the wiretap channel

a discrete time model for daily s p500 returns and realized variations jumps and leverage effects abstract we develop an empirically highly accurate discrete time daily stochastic volatility model that explicitly distinguishes between the jump and continuous time components of price movements using nonparametric realized variation and bipower variation measures constructed from high frequency intraday data the model setup allows us to directly assess the structural inter dependencies among the shocks to returns and the two different volatility components the model estimates suggest that the leverage effect or asymmetry between returns and volatility works primarily through the continuous volatility component the excellent fit of the model makes it an ideal candidate for an easy to implement auxiliary model in the context of indirect estimation of empirically more realistic continuous time jump diffusion and levy driven stochastic volatility models effectively incorporating the interdaily dependencies inherent in the high frequency intraday data

capacity and random coding exponents for channel coding with side information capacity formulas and random coding exponents are derived for a generalized family of gel fand pinsker coding problems these exponents yield asymptotic upper bounds on the achievable log probability of error in our model information is to be reliably transmitted through a noisy channel with finite input and output alphabets and random state sequence and the channel is selected by a hypothetical adversary partial information about the state sequence is available to the encoder adversary and decoder the design of the transmitter is subject to a cost constraint two families of channels are considered 1 compound discrete memoryless channels cdmc and 2 channels with arbitrary memory subject to an additive cost constraint or more generally to a hard constraint on the conditional type of the channel output given the input both problems are closely connected the random coding exponent is achieved using a stacked binning scheme and a maximum penalized mutual information decoder which may be thought of as an empirical generalized maximum a posteriori decoder for channels with arbitrary memory the random coding exponents are larger than their cdmc counterparts applications of this study include watermarking data hiding communication in presence of partially known interferers and problems such as broadcast channels all of which involve the fundamental idea of binning

blockwise bootstrapped empirical process for stationary sequences we apply the bootstrap for general stationary observations proposed by kunsch to the empirical process for p dimensional random vectors it is known that the empirical process in the multivariate case converges weakly to a certain gaussian process we show that the bootstrapped empirical process converges weakly to the same gaussian process almost surely assuming that the block length l for constructing bootstrap replicates satisfies l n o n 1 2 varepsilon 0 varepsilon frac 1 2 and l n rightarrow infty an example where the multivariate setup arises are the robust gm estimates in an autoregressive model we prove the asymptotic validity of the bootstrap approximation by showing that the functional associated with the gm estimates is frechet differentiable

channel simulation with quantum side information we study and solve the problem of classical channel simulation with quantum side information at the receiver this is a generalization of both the classical reverse shannon theorem and the classical quantum slepian wolf problem the optimal noiseless communication rate is found to be reduced from the mutual information between the channel input and output by the holevo information between the channel output and the quantum side information our main theorem has two important corollaries the first is a quantum generalization of the wyner ziv problem rate distortion theory with quantum side information the second is an alternative proof of the tradeoff between classical communication and common randomness distilled from a quantum state the fully quantum generalization of the problem considered is quantum state redistribution here the sender and receiver share a mixed quantum state and the sender wants to transfer part of her state to the receiver using entanglement and quantum communication we present outer and inner bounds on the achievable rate pairs

on lewis simulation method for point processes a simple and efficient method of simulation is discussed for point processes that are specified by their conditional intensities the method is based on the thinning algorithm which was introduced recently by lewis and shedler for the simulation of nonhomogeneous poisson processes algorithms are given for past dependent point processes containing multivariate processes the simulations are performed for some parametric conditional intensity functions and the accuracy of the simulated data is demonstrated by the likelihood ratio test and the minimum akaike information criterion aic procedure

a case where interference does not affect the channel dispersion in 1975 carleial presented a special case of an interference channel called the very strong interference regime in which the interference does not reduce the capacity of the constituent point to point gaussian channels in this paper we show that in the strictly very strong interference regime the dispersions are similarly unaffected more precisely in this paper we characterize the second order coding rates of the gaussian interference channel in the strictly very strong interference regime in other words we characterize the speed of convergence of rates of optimal block codes toward a boundary point of the rectangular capacity region these second order coding rates are expressed in terms of the average probability of error and variances of appropriately defined information densities which coincide with the dispersion of the single user gaussian channel this allows us to conclude that the dispersions are unaffected by interference in this channel model

proof of the riemannian penrose inequality using the positive mass theorem we prove the riemannian penrose conjecture an important case of a con jecture 41 made by roger penrose in 1973 by defining a new flow of metrics this flow of metrics stays inside the class of asymptotically flat riemannian 3 manifolds with nonnegative scalar curvature which contain minimal spheres in particular if we consider a riemannian 3 manifold as a totally geodesic submanifold of a space time in the context of general relativity then outermost minimal spheres with total area a correspond to apparent horizons of black holes contributing a massa 16 scalar cur vature corresponds to local energy density at each point and the rate at which the metric becomes flat at infinity corresponds to total mass also called the adm mass the riemannian penrose conjecture then states that the total mass of an asymptotically flat 3 manifold with nonnegative scalar curvature is greater than or equal to the mass contributed by the black holes the flow of metrics we define continuously evolves the original 3 metric to a schwarzschild 3 metric which represents a spherically symmetric black hole in vacuum we define the flow such that the area of the minimal spheres which flow outward and hence the mass contributed by the black holes in each of the metrics in the flow is constant and then use the positive mass theorem to show that the total mass of the metrics is nonincreasing then since the total mass equals the mass of the black hole in a schwarzschild metric the riemannian penrose conjecture follows we also refer the reader to the beautiful work of huisken and ilmanen 30 who used inverse mean curvature flows of surfaces to prove that the total mass is at least the mass contributed by the largest black hole in sections 1 and 2 we motivate the problem discuss important quantities like total mass and horizons of black holes and state the positive mass theorem and the penrose conjecture for riemannian 3 manifolds in section 3 we give the proof of the riemannian penrose