optimal control for partially observed diffusions stochastic control problems are considered in which a state process x t and an observation process y t are governed by ito sense stochastic differential equations driven by independent brownian motions the control u t enters linearly in the dynamics of x t a separated control problem is introduced in which the state at any time t is a measure lambda t representing an unnormalized conditional distribution for x t given y s u s for s leqq t the method depends on introducing a pathwise version of lambda t which depends continuously on observation and control trajectories y u existence of an optimal control is obtained in a suitable class larger than the usual class of controls admissible in the strict sense that u t is measurable on the sigma algebra mathcal f t y generated by observations y s s leqq t the dynamics of lambda t are studied using a method of forward and backward partial differential equations under a suitable nondegeneracy condition the m

tree structured classification via generalized discriminant analysis abstract the problem of constructing classification rules that can be represented as decision trees is considered each object to be classified has an associated x vector containing possibly incomplete covariate information tree construction is based on the information provided in a learning sample of objects with known class identities the x vectors in the learning sample may have missing values as well procedures are proposed for each of the components of classifier construction such as split selection tree size determination treatment of missing values and ranking of variables the main idea is recursive application of linear discriminant analysis with the variables at each stage being appropriately chosen according to the data and the type of splits desired standard statistical techniques used as basic building blocks include analysis of variance linear and canonical discriminant analysis and principal component analysis a new method of tree structured classification is obtained by assem

on factor maps that send markov measures to gibbs measures let x and y be mixing shifts of finite type let be a factor map from x to y that is fiber mixing i e given x bar x in x with pi x pi bar x y in y there is z 1 y that is left asymptotic to x and right asymptotic to bar x we show that any markov measure on x projects to a gibbs measure on y under for a holder continuous potential in other words all hidden markov chains i e sofic measures realized by are gibbs measures in 2003 chazottes and ugalde gave a sufficient condition for a sofic measure to be a gibbs measure our sufficient condition generalizes their condition and is invariant under conjugacy and time reversal we provide examples demonstrating our result

sliced inverse regression for dimension reduction abstract modern advances in computing power have greatly widened scientists scope in gathering and investigating information from many variables information which might have been ignored in the past yet to effectively scan a large pool of variables is not an easy task although our ability to interact with data has been much enhanced by recent innovations in dynamic graphics in this article we propose a novel data analytic tool sliced inverse regression sir for reducing the dimension of the input variable x without going through any parametric or nonparametric model fitting process this method explores the simplicity of the inverse view of regression that is instead of regressing the univariate output variable y against the multivariate x we regress x against y forward regression and inverse regression are connected by a theorem that motivates this method the theoretical properties of sir are investigated under a model of the form y f 1 x k x e where the k s are the unknown

on measuring internal dependence in a set of random variables on considere un analogue multivariable de la correlation maximale qui consiste a transformer chacune des variables de telle sorte que les plus grandes sommes partielles de valeurs propres de la matrice de correlation resultante soient maximisees

an admissible systems approach to separation in partially observed stochastic control problems abstract stochastic optimal control of systems subject to noisy measurements of the states is considered the formulation is based on the concept of admissible systems it is shown that the costs achieved in the class of wide sense admissible systems and in the class of separated admissible systems are equal over a fixed discretization of the time interval it is also shown that strongly separated controls can be used to achieve e optimality

semiparametric estimates of the relation between weather and electricity sales abstract a nonlinear relationship between electricity sales and temperature is estimated using a semiparametric regression procedure that easily allows linear transformations of the data this accommodates introduction of covariates timing adjustments due to the actual billing schedules and serial correlation the procedure is an extension of smoothing splines with the smoothness parameter estimated from minimization of the generalized cross validation criterion introduced by craven and wahba 1979 estimates are presented for residential sales for four electric utilities and are compared with models that represent the weather using only heating and cooling degree days or with piecewise linear splines

research in statistical graphics abstract three active areas of research in statistical graphics are methodology computing and graphical perception the five articles in this special section provide a good representation of these areas dynamic graphical methods which involve a tight weaving of methodological and computing issues are a particularly exciting topic of research dynamic graphics will soon have a major impact on how data are analyzed evaluation of graphical inventions is difficult certain visualization issues can be evaluated by studies in graphical perception at the moment however the performance of most graphical methods can be studied only by rigorous field testing in which the methods are used to analyze a large number of data sets a bibliography is provided to allow readers to begin a study of any of the major areas of statistical graphics

spline smoothing in a partly linear model on donne des estimations qui minimisent la somme des sommes residuelles des carres et une penalite de difficulte

diagnostics for heteroscedasticity in regression summary for the usual regression model without replication we provide a diagnostic test for heteroscedasticity based on the score statistic a graphical procedure to complement the score test is also presented some key u ords influence linear model residual score test diagnostic methods in linear regression are used to examine the appropriateness of assumptions underlying the modelling process and to locate unusual characteristics of the data that may influence conclusions the recent literature on diagnostics is dominated by studies of methods for the detection of influential observations cook weisberg 1982 provide a review diagnostics for the relevance of specific assumptions however have not received the same degree of attention even though these may be of equal importance our purpose here is to provide appropriate diagnostic techniques to aid in an assessment of the validity of the usual assumption of homoscedasticity when little or no replication is present available methods for studying this assumption include both graphical and nongraphical procedures the usual graphical procedure consists of plotting the ordinary least squares residuals against fitted values or an explanatory variable a megaphone shaped pattern is taken as evidence that the variance depends on the quantity plotted on tlle abscissa weisberg 1980 chapter 6 in 3 we suggest several ways in which this

a characterization of e optimal controls for stochastic systems with partial observations via the unnormalized conditional density abstract the paper considers optimal control for continuous time stochastic systems with noisy measurements of the state it is known that the optimum coat for this problem may not be achieved within the class of strict sense controls however allowing for tolerances of size e a characterization is given for e optimal controls in terms of a semigroup formulation involving the unnormalized conditional density of the distribution of the state given the observations

exploratory projection pursuit abstract a new projection pursuit algorithm for exploring multivariate data is presented that has both statistical and computational advantages over previous methods a number of practical issues concerning its application are addressed a connection to multivariate density estimation is established and its properties are investigated through simulation studies and application to real data the goal of exploratory projection pursuit is to use the data to find low one two or three dimensional projections that provide the most revealing views of the full dimensional data with these views the human gift for pattern recognition can be applied to help discover effects that may not have been anticipated in advance since linear effects are directly captured by the covariance structure of the variable pairs which are straightforward to estimate the emphasis here is on the discovery of nonlinear effects such as clustering or other general nonlinear associations among the variables although arbitrary

projections of gibbs states for holder potentials we give a short proof that the projection of a gibbs state for a holder continuous potential on a mixing shift of finite type under a 1 block fiber wise mixing factor map has a holder continuous g function this improves a number of previous results the key insight in the proof is to realize the measure of a cylinder set in terms of positive operators and use cone techniques

asymptotic behavior of m estimators of p regression parameters when p 2 n is large ii normal approximation in a general linear model y x beta r with y and r n dimensional x a n times p matrix and beta p dimensional let hat beta be an m estimator of beta satisfying 0 sum x i psi y i x i beta let p rightarrow infty such that p log n 3 2 n rightarrow 0 then max i x i hat beta beta rightarrow p 0 and it is possible to find a uniform normal approximation for the distribution of hat beta under which arbitrary linear combinations a n hat beta beta are asymptotically normal when appropriately normalized and hat beta beta x x hat beta beta is approximately chi 2 p

projection pursuit approach to robust dispersion matrices and principal components primary theory and monte carlo abstract this article proposes and discusses a type of new robust estimators for covariance correlation matrices and principal components via projection pursuit techniques the most attractive advantage of the new procedures is that they are of both rotational equivariance and high breakdown point besides they are qualitatively robust and consistent at elliptic underlying distributions the monte carlo study shows that the best of the new estimators compare favorably with other robust methods they provide as good a performance as m estimators and somewhat better empirical breakdown properties

projection of markov measures may be gibbsian we study the induced measure obtained from a 1 step markov measure supported by a topological markov chain after the mapping of the original alphabet onto another one we give sufficient conditions for the induced measure to be a gibbs measure in the sense of bowen when the factor system is again a topological markov chain this amounts to constructing when it does exist the induced potential and proving its holder continuity this is achieved through a matrix method we provide examples and counterexamples to illustrate our results

asymptotic inference for eigenvectors abstract asymptotic procedures are given for testing certain hypotheses concerning eigenvectors and for constructing confidence regions for eigenvectors these asymptotic procedures are derived under fairly general conditions on the estimates of the matrix whose eigenvectors are of interest applications of the general results to principal components analysis and canonical variate analysis are given author

convergence rates for parametric components in a partly linear model consider the regression model y i x i beta g t i e i for i 1 cdots n here g is an unknown holder continuous function of known order p in r beta is a k times 1 parameter vector to be estimated and e i is an unobserved disturbance such a model is often encountered in situations in which there is little real knowledge about the nature of g a piecewise polynomial g n is proposed to approximate g the least squares estimator hat beta is obtained based on the model y i x i beta g n t i e i it is shown that hat beta can achieve the usual parametric rates n 1 2 with the smallest possible asymptotic variance for the case that x and t are correlated

kernel smoothing in partial linear models on considere deux methodes d estimation l une reliee aux splines de lissage partiels l autre motivee par une analyse de residus partielle

decay of correlations dedicated to micheline ishay i would like to thank p boyland l chierchia v donnay g de martino c gole j l lebowitz m lyubich m rychlik i g schwarz s vaienti and especially g gallavotti for helpful and enlightening discussions particularly warm thanks go to n chernov for carefully reading and finding a mistake in an early version the present paper benefits from several improvements due to his sharp criticism in addition i am indebted to p collet and most of all m wojtkowski for introducing me to the magical world of cones finally i thank j milnor director of the institute for mathematical sciences at stony brook university where i was visiting during part of this work and the italian c n r gnfm for providing travel funds

on projection pursuit measures of multivariate location and dispersion 0 introduction projection pursuit pp techniques for the analysis of high dimensional data were introduced by kruskal 1972 and switzer 1970 switzer and wright 1971 and friedman and tukey 1974 and later applied by friedman and stuetzle to a variety of problems including regression 1980a classification 1980b and density estimation 1981 the idea underlying pp is to select interesting low dimensional projections by iteratively maximizing an appropriate projection index usually with the aid of a computer huber 1981b and li and chen 1981 have proposed the use of pp to construct and estimate measures of location and dispersion for multivariate distributions when is such a measure equivariant under affine tranformations in essence we show that a pp location dispersion measure is equivariant if and only if the univariate measure from which it is built is linear quadratic in an appropriate sense lemmas 1 4 this equivariance holds for all distributions only when the univariate measure is expectation standard deviation theorems 2 5 for a fixed multivariate distribution all pp location dispersion measures will be equivariant only when the distribution is symmetric through its center elliptically contoured theorems 3 6 we emphasize that these theorems pertain to functionals on probability distributions corresponding estimators are constructed in the usual way by evaluating these functionals at the empirical distribution thus pp measures of location and dispersion possess limited equivariance properties nevertheless for data generated from elliptically contoured distributions the pp dispersion estimators of li and chen 1981 perform promisingly our results are developed in section 1 location and 2 dispersion and proved in sections 4 and 5 respectively section 3 contains further comments and discussion of some implications for data analysis

slicing regression a link free regression method slicing regression a link free regression m e t h o d author s naihua duan and k e r c h a u l i s o u r c e the annals of statistics v o l 19 n o 2 t u n 1991 p p 5 0 5 5 3 0 p u b l i s h e d b y institute of mathematical statistics s t a b l e u r l http www jstor org stable 2242072 accessed 16 05 2011 your use of the jstor archive indicates your acceptance of jstor s terms and conditions of use available at http www jstor org page info about policies terms jsp jstor s terms and conditions of use provides in part that unless you have obtained prior permission you may not download an entire issue of a journal or multiple copies of articles and you may use content in the jstor archive only for your personal non commercial use please contact the publisher regarding any further use of this work publisher contact information may be obtained at http www jstor org action showpublisher publishercode ims each copy of any part of a jstor transmission must contain the same copyright notice that appears on the screen or printed page of such transmission jstor is a not for profit service that helps scholars researchers and students discover use and build upon a wide range of content in a trusted digital archive we use information technology and tools to increase productivity and facilitate new forms of scholarship for more information about jstor please contact support jstor org http www jstor org

sequential gibbs measures and factor maps we define the notion of sequential gibbs measures inspired by on the classical notion of gibbs measures and recent examples from the study of non uniform hyperbolic dynamics extending previous results of kempton and pollicott factors of gibbs measures for full shifts entropy of hidden markov processes and connections to dynamical systems cambridge university press cambridge 2011 and chazottes and ugalde on the preservation of gibbsianness under symbol amalgamation entropy of hidden markov processes and connections to dynamical systems cambridge university press cambridge 2011 we show that the images of one block factor maps of a sequential gibbs measure are also a sequential gibbs measure with the same sequence of gibbs times we obtain some estimates on the regularity of the potential of the image measure at almost every point

asymptotic optimality for c_p c_l cross validation and generalized cross validation discrete index set c p c l cross validation and generalized cross validation are useful data driven techniques for selecting a good estimate from a proposed class of linear estimates the asymptotic behaviors of these procedures are studied some easily interpretable conditions are derived to demonstrate the asymptotic optimality it is argued that cross validation and generalized cross validation can be viewed as some special ways of applying c l applications in nearest neighbor nonparametric regression and in model selection are discussed in detail