robust methods for model order estimation model order estimation is a subject in time series analysis that deals with fitting a parametric model to a vector of observations this paper focuses on several model order estimators known in the literature and examines their performance under small deviations of the probability distribution of the noise with respect to a nominal distribution assumed in the model it is demonstrated that the standard estimators suffer from high sensitivity to deviations from the nominal distribution and a drastic performance degradation is experienced to overcome this problem robust estimators that are insensitive to small deviations from the nominal distribution are developed these estimators are based on a composition between model order estimation methods and robust statistical inference techniques known in the literature in addition a new estimator based on a locally best test for weak signals is presented both in nonrobust and robust versions the proposed robust model order estimators are developed on a heuristic basis and there is no claim of optimality but experimental results indicate that they provide significant improvement over the standard estimators

root n consistent semiparametric regression on considere une variable aleatoire x z dans 7b r p 7b r q on construit un estimateur generalisant l estimateur des moindres carres ordinaires en inserant des estimateurs non parametriques de la regression dans la projection orthogonale non lineaire sur z

the estimation of the model order in exponential families estimators are sought that achieve high exponential rate of decrease in the underestimation probability while keeping the overestimation probability exponent at a certain prescribed level it is assumed that a given integer is known to upper bound the true order some examples are given of possible applications of the proposed method in specific order estimation and hypothesis testing problems

modular forms on non linear double covers of algebraic groups we construct automorphic representations of non linear two fold covers of simply connected chevalley groups via residues of eisenstein series in the process we establish some basic results in representation theory of local groups

unitary shimura correspondences for split real groups we find a relationship between certain complementary series representations for nonlinear coverings of split simple groups and spherical complementary series for different linear groups the main technique is barbasch s method of calculating some intertwining operators purely in terms of the weyl group

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

learning high dimensional markov forest distributions analysis of error rates the problem of learning forest structured discrete graphical models from i i d samples is considered an algorithm based on pruning of the chow liu tree through adaptive thresholding is proposed it is shown that this algorithm is both structurally consistent and risk consistent and the error probability of structure learning decays faster than any polynomial in the number of samples under fixed model size for the high dimensional scenario where the size of the model d and the number of edges k scale with the number of samples n sufficient conditions on n d k are given for the algorithm to satisfy structural and risk consistencies in addition the extremal structures for learning are identified we prove that the independent resp tree model is the hardest resp easiest to learn using the proposed algorithm in terms of error rates for structure learning

empirical likelihood ratio confidence regions than are those based on student s t statistic an effective method is presented for computing empirical profile likelihoods for the mean of a vector random variable the method is a reduction by convex duality to an unconstrained minimization of a convex function on a low dimensional domain algorithms exist for finding the unique global minimum at a superlinear rate of convergence a byproduct is a noncombinatorial algorithm for determining whether a given point lies within the convex hull of a finite set of points the multivariate empirical likelihood regions are justified for functions of several means such as variances correlations and regression parameters and for statistics with linear estimating equations an algorithm is given for computing profile empirical likelihoods for these statistics

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

asymptotically optimal classification for multiple tests with empirically observed statistics the decision problem of testing m hypotheses when the source is kth order markov and there are m or fewer training sequences of length n and a single test sequence of length n is considered k m n n are all given it is shown what the requirements are on m n n to achieve vanishing exponential error probabilities and how to determine or bound the exponent a likelihood ratio test that is allowed to produce a no match decision is shown to provide asymptotically optimal error probabilities and minimum no match decisions as an important serial case the binary hypotheses problem without rejection is discussed it is shown that for this configuration only one training sequence is needed to achieve an asymptotically optimal test

a nonparametric test for serial independence of regression errors a test for serial independence of regression errors is proposed that is consistent in the direction of serial dependence alternatives of first order the test statistic is a function of a hoeffding blum kiefer rosenblatt type of empirical process based on residuals the resultant statistic converges surprisingly to the same limiting distribution as the corresponding statistic based on true errors

improved pivotal methods for constructing confidence regions with directional data abstract the importance of pivoting is well established in the context of nonparametric confidence regions it ensures enhanced coverage accuracy however pivoting for directional data cannot be achieved simply by rescaling a somewhat cumbersome pivotal method which involves passing first into a space of higher dimension has been developed by fisher and hall for samples of unit vectors although that method has some advantages over nonpivotal techniques it does suffer from certain drawbacks in particular the operation of passing to a higher dimension here we suggest alternative pivotal approaches the implementation of which does not require us to increase the intrinsic dimension of the data and which in practice seem to achieve greater coverage accuracy these methods are of two types new pivotal bootstrap techniques and techniques that exploit the implicit pivotalness of the empirical likelihood algorithm unlike the method proposed by fisher and hall these methods are also applicable to axia

bootstrap approximations in model checks for regression abstract let m m be a parametric model for an unknown regression function m for example m may consist of all polynomials or trigonometric polynomials with a given bound on the degree to check the full model m i e to test for h 0 m e m it is known that optimal tests should be based on the empirical process of the regressors marked by the residuals in this article we show that the distribution of this process may be approximated by the wild bootstrap the method is applied to simulated datasets as well as to real data

the mm me ml el ef and gmm approaches to estimation a synthesis abstract the 20th century began on an auspicious statistical note with the publication of karl pearson s philos mag ser 50 1900 157 goodness of fit test which is regarded as one of the most important scientific breakthroughs the basic motivation behind this test was to see whether an assumed probability model adequately described the data at hand pearson philos trans roy soc london ser a 185 1894 71 also introduced a formal approach to statistical estimation through his method of moments mm estimation ronald a fisher while he was a third year undergraduate at the gonville and caius college cambridge suggested the maximum likelihood estimation mle procedure as an alternative to pearson s mm approach in 1922 fisher published a monumental paper that introduced such basic concepts as consistency efficiency sufficiency and even the term parameter with its present meaning fisher philos trans roy soc london ser a 222 1922 309 provided the analytical foundation of mle and studied its efficiency relative to the mm estimator fisher j roy statist soc 87 1924a 442 established the asymptotic equivalence of minimum 2 and ml estimators and wrote in favor of using minimum 2 method rather than pearson s mm approach recently econometricians have found working under assumed likelihood functions restrictive and have suggested using a generalized version of pearson s mm approach commonly known as the gmm estimation procedure as advocated in hansen econometrica 50 1982 1029 earlier godambe ann math statist 31 1960 1208 and durbin j roy statist soc ser b 22 1960 139 developed the estimating function ef approach to estimation that has been proven very useful for many statistical models a fundamental result is that score is the optimum ef ferguson ann math statist 29 1958 1046 considered an approach very similar to gmm and showed that estimation based on the pearson 2 statistic is equivalent to efficient gmm golan et al maximum entropy econometrics robust estimation with limited data wiley new york 1996 developed entropy based formulation that allowed them to solve a wide range of estimation and inference problems in econometrics more recently imbens et al econometrica 66 1998 333 kitamura and stutzer econometrica 65 1997 861 and mittelhammer et al econometric foundations cambridge university press cambridge 2000 put gmm within the framework of empirical likelihood el and maximum entropy me estimation it can be shown that many of these estimation techniques can be obtained as special cases of minimizing cressie and read j roy statist soc ser b 46 1984 440 power divergence criterion that comes directly from the pearson 1900 2 statistic in this way we are able to assimilate a number of seemingly unrelated estimation techniques into a unified framework

testing for serial correlation against an arma 1 1 process abstract this article is concerned with tests for serial correlation in time series and in the errors of regression models in particular the nonstandard problem of testing for white noise against autoregressive moving average model arma 1 1 alternatives is considered the likelihood ratio lr sup lagrange multiplier lm and exponential average lm and lr tests are shown to be asymptotically admissible for arma 1 1 alternatives in addition they are shown to be consistent against all weakly stationary strong mixing non white noise alternatives simulation results compare the tests to several tests in the literature these results show that the lr and exp lr tests have very good all around power properties for nonseasonal alternatives

on the estimation of the order of a markov chain and universal data compression the authors estimate the order of a finite markov source based on empirically observed statistics the performance criterion adopted is to minimize the probability of underestimating the model order while keeping the overestimation probability exponent at a prescribed level a universal asymptotically optimal test in the sense just defined is proposed for the case where a given integer is known to be the upper bound of the true order for the case where such a bound is unavailable an alternative rule based on the lempel ziv data compression algorithm is shown to be asymptotically optimal also and computationally more efficient

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

the determination of optimum structures for the state space representation of multivariate stochastic processes when identifying a model for a multivariate stationary stochastic process an important problem is that of determining the structure of the state variable model several overlapping parameterizations can usually be fitted to a given process and the question arises as to which structure leads to the most accurate parameter estimates the accuracy of parameter estimates is often measured by the determinant of the fisher information matrix we show that all admissible structures will give asymptotically the same value to this criterion for finite data some structures may still be better than others and two heuristic structure estimation methods are analyzed some simulation results are also presented

generalized phase space projection for nonlinear noise reduction improved phase space projection methods adapted from related work in the linear signal processing field based on subspace decomposition are presented for application to the problem of additive noise reduction in the context of phase space analysis these methods improve upon existing methods such as broomhead king singular spectrum analysis projection by minimizing overall signal distortion subject to constraints on the residual error rather than using a direct least squares fit this results in a range of weighted projections which estimate and compensate for the portion of the principal component s singular values corresponding to noise rather than signal energy and which include least squares ls and least minimum mean square error lmmse as subcases the nature of phase space covariance the key element in construction of the projection matrix is examined across global phase spaces as well as within local neighborhood regions the resulting algorithm illustrated on a noisy henon map as well as on the task of speech enhancement is applicable to a wide variety of nonlinear noise reduction tasks

consistent bootstrap tests of parametric regression functions abstract this paper introduces specification tests of parametric mean regression models the null hypothesis of interest is that the parametric regression function is correctly specified the proposed tests are generalizations of the kolmogorov smirnov and cramer von mises tests to the regression framework they are consistent against all alternatives to the null hypothesis powerful against 1 n local alternatives not dependent on any smoothing parameters and simple to compute a wild bootstrap procedure is suggested to obtain critical values for the tests and is justified asymptotically a small scale monte carlo experiment shows that our tests especially cramer von mises test have outstanding small sample performance compared to some of the existing tests

a central limit theorem for generalized quadratic forms random variables of the form w n mathop sum limits 1 leqq i leqq n mathop sum limits text 1 leqq j leqq n w ijn x i x j are considered with x i independent not necessarily identically distributed and w ijn borel functions such that w ijn x i x j is square integrable and has vanishing conditional expectations e w ijn x i x j x i e w ijn x i x j x j 0 text a text s text a central limit theorem is proved under the condition that the normed fourth moment tends to 3 under some restrictions the condition is also necessary finally conditions on the individual tails of w ijn x i x j and an eigenvalue condition are given that ensure asymptotic normality of w n

model selection and the principle of minimum description length this article reviews the principle of minimum description length mdl for problems of model selection by viewing statistical modeling as a means of generating descriptions of observed data the mdl framework discriminates between competing models based on the complexity of each description this approach began with kolmogorov s theory of algorithmic complexity matured in the literature on information theory and has recently received renewed attention within the statistics community here we review both the practical and the theoretical aspects of mdl as a tool for model selection emphasizing the rich connections between information theory and statistics at the boundary between these two disciplines we find many interesting interpretations of popular frequentist and bayesian procedures as we show mdl provides an objective umbrella under which rather disparate approaches to statistical modeling can coexist and be compared we illustrate the mdl principle by considering problems in regression nonpar

diagnostic testing and evaluation of maximum likelihood models abstract the paper develops a unified theory of likelihood specification testing based on m estimators of auxiliary parameters the theory is sufficiently general to encompass a wide class of specification tests including moment based tests pearson type goodness of fit tests the information matrix test and the cox test the paper also presents a framework based on frechet differentiation for determining the effects of misspecification on the almost sure limits of parameter estimates and specification test statistics

universal classification for hidden markov models binary hypotheses testing using empirically observed statistics is studied in the neyman pearson formulation for the hidden markov model hmm an asymptotically optimal decision rule is proposed and compared to the generalized likelihood ratio test glrt which has been shown in earlier studies to be asymptotically optimal for simpler parametric families the proof of the main theorem is provided the result can be applied to several types of hmms commonly used in speech recognition and communication applications several applications are demonstrated

distribution free specification tests of conditional models this article proposes a class of asymptotically distribution free specification tests for parametric conditional distributions these tests are based on a martingale transform of a proper sequential empirical process of conditionally transformed data standard continuous functionals of this martingale provide omnibus tests while linear combinations of the orthogonal components in its spectral representation form a basis for directional tests finally neyman type smooth tests a compromise between directional and omnibus tests are discussed as a special example we study in detail the construction of directional tests for the null hypothesis of conditional normality versus heteroskedastic contiguous alternatives a small monte carlo study shows that our tests attain the nominal level already for small sample sizes

censored regression quantiles abstract the object of this paper is to demonstrate how the lad estimation method for the censored regression model can be extended to more general quantiles in this paper the form of the conditional quantiles for the censored regression models is heuristically derived and discussed the resulting estimators of the regression coefficients which include the censored lad estimator as a special case are shown to be consistent and asymptotically normally distributed under appropriately translated versions of the corresponding assumptions for the former approach consistent estimation of the asymptotic covariance matrix when the error terms are i i d is also treated the paper discussed how several quantile estimators might be combined to improve efficiency when the error terms are identically distributed and how tests of homoskedasticity and symmetry of the error distribution can be constructed using particular differences of the estimated coefficients

testing for differences between conditional means in a time series context in this article we study tests for equality of two regression curves when the inputs are driven by a time series the basic process underlying the test statistics is the empirical process of the time series marked by the difference in the pertaining dependent variables the main results hold under strict stationarity of the input variables but no mixing condition or special modeling of the time series will be necessary a simulation study is reported on which illustrates the quality of the distributional approximation and the power of the tests for small to moderate sample sizes an application to a real dataset is also included

stochastic complexity and modeling on demontre un theoreme fondamental qui donne une borne inferieure pour la longueur de code et donc pour les erreurs de prediction on definit les notions d information a priori et d information utile dans les donnees

universal coding information prediction and estimation a connection between universal codes and the problems of prediction and statistical estimation is established a known lower bound for the mean length of universal codes is sharpened and generalized and optimum universal codes constructed the bound is defined to give the information in strings relative to the considered class of processes the earlier derived minimum description length criterion for estimation of parameters including their number is given a fundamental information theoretic justification by showing that its estimators achieve the information in the strings it is also shown that one cannot do prediction in gaussian autoregressive moving average arma processes below a bound which is determined by the information in the data

consistent model specification tests for time series econometric models in this paper we consider general hypothesis testing problems for nonparametric and semiparametric time series econometric models we apply the general methodology to construct a consistent test for omitted variables and a consistent test for a partially linear model the proposed tests are shown to have asymptotic normal distributions under their respective null hypotheses we also discuss the problems of testing portfolio conditional mean variance efficiency and testing a semiparametric single index model monte carlo simulations are conducted to examine the finite sample performances of the nonparametric omitted variable test and the test for a partially linear specification

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

diagnostics for assessing regression models abstract we concern ourselves with diagnostics for checking the overall and local goodness of fit of a model s x used in the regression of y on x u 0 1 d the model for s x is a functional form that depends on a finite number of unknown parameters two statistics and w are proposed that measure the level of agreement between the model fit to the data and the nonparametric kernel estimator on m preselected points in u conditions are given under which and w are asymptotically equivalent both of these statistics measure overall lack of fit and are related to the deviance their asymptotic distribution under the null model and under local alternatives is derived this work is motivated by the local mean deviance plot of landwehr pregibon and shoemaker for assessing overall lack of fit in logistic regression their plot is summarized by our test statistics and is extended to other likelihood based regressions of y on x

on strong consistency of model selection in classification this paper considers model selection in classification in many applications such as pattern recognition probabilistic inference using a bayesian network prediction of the next in a sequence based on a markov chain the conditional probability p y y x x of class yisiny given attribute value xisinx is utilized by model we mean the equivalence relation in x for x x isinxx x harrp y y x x p y y x x forall yisiny by classification we mean the number of such equivalence classes is finite we estimate the model from n samples zn xi yi i 1 n isin xtimesy n using information criteria in the form empirical entropy h plus penalty term k 2 dn the model such that h k 2 dn is minimized is the estimated model where k is the number of independent parameters in the model and dn n 1 infin is a real nonnegative sequence such that lim supndn n 0 for autoregressive processes although the definitions of h and k are different it is known that the estimated model almost surely coincides with the true model as nrarrinfin if dn n 1 infin 2loglogn n 1 infin and that it does not if dn n 1 infin 2loglogn n 1 infin hannan and quinn the problem whether the same property is true for classification was open this paper solves the problem in the affirmative

a simple framework for nonparametric specification testing this paper presents a simple framework for testing the specification of parametric conditional means the test statistics are based on quadratic forms in the residuals of the null model under general assumptions the test statistics are asymptotically normal under the null with an appropriate choice of the weight matrix the tests are shown to be consistent and to have good local power specific implementations involving matrices of bin and kernel weights are discussed finite sample properties are explored in simulations

error exponents for ar order testing this paper is concerned with error exponents in testing problems raised by autoregressive ar modeling the tests to be considered are variants of generalized likelihood ratio testing corresponding to traditional approaches to autoregressive moving average arma modeling estimation in several related problems such as markov order or hidden markov model order estimation optimal error exponents have been determined thanks to large deviations theory ar order testing is specially challenging since the natural tests rely on quadratic forms of gaussian processes in sharp contrast with empirical measures of markov chains the large deviation principles ldps satisfied by gaussian quadratic forms do not always admit an information theoretic representation despite this impediment we prove the existence of nontrivial error exponents for gaussian ar order testing and furthermore we exhibit situations where the exponents are optimal these results are obtained by showing that the log likelihood process indexed by ar models of a given order satisfy an ldp upper bound with a weakened information theoretic representation

comparing nonparametric versus parametric regression fits in general there will be visible differences between a parametric and a nonparametric curve estimate it is therefore quite natural to compare these in order to decide whether the parametric model could be justified an asymptotic quantification is the distribution of the integrated squared difference between these curves we show that the standard way of bootstrapping this statistic fails we use and analyse a different form of bootstrapping for this task we call this method the wild bootstrap and apply it to fitting engel curves in expenditure data analysis

semiparametric comparison of regression curves the comparison of nonparametric regression curves is considered it is assumed that there are parametric possibly nonlinear transformations of the axes which map one curve into the other estimation and testing of the parameters in the transformations are studied the rate of convergence is n 1 2 although the nonparametric components of the model typically have a rate slower than that a statistic is provided for testing the validity of a given completely parametric model

nonparametric model checks for time series this paper studies a class of tests useful for testing the goodness of fit of an autoregressive model these tests are based on a class of empirical processes marked by certain residuals the paper first gives their large sample behavior under null hypotheses then a martingale transformation of the underlying process is given that makes tests based on it asymptotically distribution free consistency of these tests is also discussed briefly

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

selecting the order of autoregressive models from small samples the weak parameter criterion wpc is introduced as a means for model order selection it is based on the same principles as mallows c p and the fpe and aic criteria of akaike according to the wpc parameters are weak and should be removed if the squares of their estimates are less than twice the expectation for a white noise signal roughly speaking the square of an estimate must exceed twice its variance due to the conceptual simplicity this criterion remains useful for small samples where the asymptotical properties are no longer valid if the maximum order considered is sqrt n or less the difference between akaike s fpe and aic criteria on one hand and the wpc on the other hand remains small and the use of aic or fpe may be justified however it is advised to use the wpc for higher maximum orders by using different variances in the wpc for yule walker and for burg estimates it is achieved that the average selected wpc order in small samples depends mainly on the given data and no longer on the method of parameter estimation

testing the goodness of fit of a linear model via nonparametric regression techniques abstract this article investigates the use of nonparametric regression methodology to test the adequacy of a parametric linear model the large sample properties of parametric goodness of fit tests for linearity are considered the inadequacies of such tests lead to the proposal of new tests that are constructed from nonparametric regression fits to the residuals from linear regression large sample theory is derived for two variants of this type of statistic the results demonstrate that such tests are consistent against all fixed smooth alternatives to linearity but are incapable of detecting local alternatives converging to a linear model at the parametric rate n 1 2 simulation experiments involving a test based on fitting cubic smoothing splines to residuals reveals that this test has good power properties against several reasonable alternatives

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

constistent specification testing via nonparametric series regression this paper proposes two consistent one sided specification tests for parametric regression models one based on the sample covariance between the residual from the parametric model and the discrepancy between the parametric and nonparametric fitted values the other based on the difference in sums of squared residuals between the parametric and nonparametric models we estimate the nonparametric model by series regression the new test statistics converge in distribution to a unit normal under correct specification and grow to infinity faster than the parametric rate n 1 2 under misspecification while avoiding weighting sample splitting and non nested testing procedures used elsewhere in the literature asymptotically our tests can be viewed as a test of the joint hypothesis that the true parameters of a series regression model are zero where the dependent variable is the residual from the parametric model and the series terms are functions of the explanatory variables chosen so as to support nonparametric estimation of a conditional expectation we specifically consider fourier series and regression splines and present a monte carlo study of the finite sample performance of the new tests in comparison to consistent tests of bierens 1990 eubank and spiegelman 1990 jayasuriya 1990 wooldridge 1992 and yatchew 1992 the results show the new tests have good power performing quite well in some situations we suggest a joint bonferroni procedure that combines a new test with those of bierens and wooldridge to capture the best features of the three approaches

a simple consistent bootstrap test for a parametric regression function abstract a simple consistent test is considered and a bootstrap method is proposed for testing a parametric regression functional form it is shown that the bootstrap method gives a more accurate approximation to the null distribution of the test than the asymptotic normal theory result we also propose a consistent test for testing a parametric partially linear model versus a semiparametric partially linear alternative monte carlo simulations suggest that the bootstrap test performs well based on wild bootstrap critical values

consistent hypothesis testing in semiparametric and nonparametric models for econometric time series abstract in this paper we modify the general hypothesis studied by robinson 1989 for semi nonparametric time series models and present a consistent testing procedure for the modified hypothesis as examples we provide consistent tests for the portfolio conditional mean variance efficiency hypothesis for theomitted variables in a multivariate nonparametric time series regression model and for the two original examples in robinson the asymptotic distributions under the null and pitman local alternatives are established by invoking central limit theorems for hilbert valued dependent random arrays to approximate the critical values of the general test we modify the conditional monte carlo approach of hansen 1996 and the stationary bootstrap of politis and romano 1994a b and show that both work asymptotically

order estimation for a special class of hidden markov sources and binary renewal processes we consider the estimation of the order i e the number of hidden states of a special class of discrete time finite alphabet hidden markov sources this class can be characterized in terms of equivalent renewal processes no a priori bound is assumed on the maximum permissible order an order estimator based on renewal types is constructed and is shown to be strongly consistent by computing the precise asymptotics of the probability of estimation error the probability of underestimation of the true order decays exponentially in the number of observations while the probability of overestimation goes to zero sufficiently fast it is further shown that this estimator has the best possible error exponent in a large class of estimators our results are also valid for the general class of binary independent renewal processes with finite mean renewal times

tests of specification for parametric and semiparametric models abstract this paper provides a general framework for constructing specification tests for parametric and semiparametric models the paper develops new specification tests using the general framework in particular specification tests for semiparametric partially linear regression and sample selection models are introduced the results apply in time series and cross sectional contexts the method of proof exploits results concerning the stochastic equicontinuity or weak convergence of normalized sums of stochastic processes

cluster validation for unsupervised stochastic model based image segmentation image segmentation is an important and early processing stage in many image analysis problems often this must be done in an unsupervised fashion in that training data is not available and the class conditioned feature vectors must be estimated directly from the data a major problem in such applications is the determination of the number of classes actually present in an image this problem called the cluster validation problem remains essentially unsolved we investigate the cluster validation problem associated with the use of a previously developed unsupervised segmentation algorithm based upon the expectation maximization em algorithm more specifically we consider several well known information theoretic criteria ics as candidate solutions to the validation problem when used in conjunction with this em based segmentation scheme we show that these criteria generally provide inappropriate solutions due to the domination of the penalty term by the associated log likelihood function as an alternative we propose a model fitting technique in which the complete data log likelihood functional is modeled as an exponential function in the number of classes acting the estimated number of classes are then determined in a manner similar to finding the rise time of the exponential function this new validation technique is shown to be robust and outperform the ics in our experiments experimental results for both synthetic and real world imagery are detailed

kazhdan lusztig representations and whittaker space of some genuine representations we prove a formula for the dimension of whittaker functionals of irreducible constituents of a regular unramified genuine principal series for covering groups the formula explicitly relates such dimension to the kazhdan lusztig representations associated with certain right cells of the weyl group we also state a refined version of the formula which is proved under some natural assumption the refined formula is also verified unconditionally in several important cases

optimal watermark embedding and detection strategies under limited detection resources an information theoretic approach is proposed to watermark embedding and detection under limited detector resources first the attack free scenario is considered under which asymptotically optimal decision regions in the neyman pearson sense are proposed along with the optimal embedding rule later the case of zero mean independent and identically distributed i i d gaussian covertext distribution is explored with unknown variance under the attack free scenario for this case a lower bound on the exponential decay rate of the false negative probability is proposed it is proven that the optimal embedding and detecting strategy is superior to the customary linear additive embedding strategy in the exponential sense finally these results are extended to the case of memoryless attacks and general worst case attacks optimal decision regions and embedding rules are offered and the worst attack channel is identified

order estimation and sequential universal data compression of a hidden markov source by the method of mixtures we consider first the estimation of the order i e the number of states of a discrete time finite alphabet stationary ergodic hidden markov source hms our estimator uses a description of the observed data in terms of a uniquely decodable code with respect to a mixture distribution obtained by suitably mixing a parametric family of distributions on the observation space this procedure avoids maximum likelihood calculations the order estimator is shown to be strongly consistent with the probability of underestimation decaying exponentially fast in the number n of observations while the probability of overestimation does not exceed cn sup 3 where c is a constant next we present a sequential algorithm for the uniquely decodable universal data compression of the hms which performs an on line estimation of source order followed by arithmetic coding this code asymptotically attains optimum average redundancy

a metaplectic casselman shalika formula for gl r we provide formulas for various bases of spherical whittaker functions on the n fold metaplectic cover of rm gl r over a p adic field and show that there is a basis of symmetric functions in the complex parameter in addition we relate a specific spherical whittaker function to the p power part of the weyl group multiple dirichlet series for the root system of type a r 1 constructed from n th order gauss sums we also show that the zonal spherical functions can be computed explicitly in terms of hall littlewood polynomials as in macdonald s formula for rm gl r

empirical likelihood methods with weakly dependent processes this paper studies the method of empirical likelihood in models with weakly dependent processes in such cases if the likelihood function is formulated as if the data process were independent obviously empirical likelihood fails we propose to use empirical likelihood of blocks of observations to solve this problem in a nonparametric manner this method of blockwise empirical likelihood preserves the dependence of data and the resulting likelihood ratios can be used to construct asymptotically valid confidence intervals we consider general estimating equations for which an efficient estimator is derived by maximizing blockwise empirical likelihood we also introduce blocks of blocks empirical likelihood to conduct inference for parameters of the infinite dimensional joint distribution of data the smooth function model is used for such cases we show that blockwise empirical likelihood of the smooth function model with weakly dependent processes is bartlett correctable a wide variety of problems such as time series regressions and spectral densities can be treated using our methodology

goodness of fit tests for spectral distributions abstract the spectral distribution function of a stationary stochastic process standardized by dividing by the variance of the process is a linear function of the autocorrelations the integral of the sample standardized spectral density periodogram is a similar linear function of the autocorrelations as the sample size increases the difference of these two functions multiplied by the square root of the sample size converges is weakly to a gaussian stochastic process with a continuous time parameter a monotonic transformation of this parameter yields a brownian bridge plus an independent radom term the distributions of functionals of this process are the limiting distributions of goodness of fit criteria that are used for testing hypotheses about the process autocorrelations an application is to tests of independence flat spectrum the characteristic function of the cramer von miese statistic is obtained inequalities for the kolmogorow smirnov criterion are given confidence regions for unspecified process distributions are found

exact correct decoding exponent of the wiretap channel decoder the performance of the achievability scheme for wyner s wiretap channel model is examined from the perspective of the probability of correct decoding pc at the wiretap channel decoder in particular for finite alphabet memoryless channels the exact random coding exponent of pc is derived as a function of the total coding rate r1 and the rate of each subcode r2 two different representations are given for this function and its basic properties are provided we also characterize the region of pairs of rates r1 r2 of full security in the sense of the random coding exponent of pc in other words the region where the exponent of this achievability scheme is the same as that of blind guessing at the eavesdropper side finally an analogous derivation of the correct decoding exponent is outlined for the case of the gaussian channel

efficiency bounds for semiparametric regression efficiency bounds for conditional moment restrictions with a nonparametric component are derived there is a given function of the data a random sample from a distribution f and a parameter the restriction is that a conditional expectation of this function is zero at some point in the parameter space the parameter has two parts a finite dimensional component and a general function evaluated at a subset of the conditioning variables an example is a regression function that is additive in parametric and nonparametric component as arises in sample selection models copyright 1992 by the econometric society

local shimura correspondence it splits over the maximal compact subgroup let t be the corresponding lift of i the iwahori subgroup of g now fix a faithful character of n f let r be the category of smooth representations of which are generated by its t fixed vectors and such that n f acts via also let h be the hecke algebra of i biinvariant compactly supported functions on satisfying f gq f g for z v obj r let v be the space of i fixed vectors then f f l v is a representation of h t according to bernstein and borel 2 this gives the equivalence of r and the category of representations of h in particular this is the case for g whose hecke algebra will be denoted by h g and category by ri g in this paper we describe h in terms of generators and relations as a consequence in the case of simple group for example we find a group g related to g such that h t h g in particular we get the equivalence of r t and

a nonparametric test of serial independence based on the empirical distribution function the blum kiefer rosenblatt 1961 statistic for testing independence is considered in a time series setting this test is under mild conditions shown to be consistent against lag one dependent alternatives the null distribution of the test statistic is established both when the marginal distribution is continuous and when it is discrete simulation results giving information on the size and the power of the test are provided and comparisons are made with other tests of serial dependence an extension of the test is made to detect higher lag dependence and finally the test is applied to a real data example

testing conditional moment restrictions let x z be a pair of observable random vectors we construct a new smoothed empirical likelihood based test for the hypothesis e g z x 0 w p 1 where g is a vector of known functions and an unknown finite dimensional parameter we show that the test statistic is asymptotically normal under the null hypothesis and derive its asymptotic distribution under a sequence of local alternatives furthermore the test is shown to possess an optimality property in large samples simulation evidence suggests that it also behaves well in small samples

significance testing in nonparametric regression based on the bootstrap this paper proposes a test for selecting explanatory variables in nonparametric regression the test does not need to estimate the conditional expectation function given all the variables but only those which are significant under the null hypothesis this feature is computationally convenient and solves in part the problem of the curse of dimensionality when selecting regressors in a nonparametric context the proposed test statistic is based on functionals of a u process contiguous alternatives converging to the null at a rate n 1 2 can be detected the asymptotic null distribution of the statistic depends on certain features of the data generating process and asymptotic tests are difficult to implement except in rare circumstances we justify the consistency of two easy to implement bootstrap tests which exhibit good level accuracy for fairly small samples according to the reported monte carlo simulations these results are also applicable to test other interesting restrictions on nonparametric curves like partial linearity and conditional independence

bootstrap procedures under some non i i d models it is shown in this article that the classical i i d bootstrap remains a valid procedure for estimating the sampling distributions of certain symmetric estimators of location as long as the random observations are independently drawn from distributions with essentially a common location this may be viewed as a robust property of the classical i i d bootstrap also included is a study of the second order properties of a different bootstrap procedure proposed by wu in the context of heteroscedasticity in regression

on iwahori whittaker functions for metaplectic groups abstract we relate iwahori whittaker functions on metaplectic covers to certain demazure lusztig operators the latter of which are built from a weyl group action previously considered by g chinta and p gunnells using a certain combinatorial identity for the sum of these demazure lusztig operators we obtain an analogue of the casselman shalika formula for spherical whittaker functions in this context