The Annals of Statistics

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• Multiscale maximum likelihood analysis of a semiparametric model, with applications AI翻译
  作者：Walther, G
  作者单位：Stanford University
  摘要：A special semiparametric model for a univariate density is introduced that allows analyzing a number of problems via appropriate transformations. Two problems treated in some detail are testing for the presence of a mixture and detecting a wear-out trend in a failure rate. The analysis of the semiparametric model leads to an approach that advances the maximum likelihood theory of the Grenander estimator to a multiscale analysis. The construction of the corresponding test statistic rests on an ...
• Least absolute deviation estimation for all-pass time series models AI翻译
  作者：Breidt, FJ; Davis, RA; Trindade, AA
  作者单位：Colorado State University System; Colorado State University Fort Collins; State University System of Florida; University of Florida
  摘要：An autoregressive moving average model in which all of the roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa is called an all-pass time series model. All-pass models generate uncorrelated (white noise) time series, but these series are not independent in the non-Gaussian case. An approximation to the likelihood of the model in the case of Laplacian (two-sided exponential) noise yields a modified absolute deviations criterion, which ...
• Control of error rates in adaptive analysis of orthogonal saturated designs AI翻译
  作者：Wang, WZ; Voss, DT
  作者单位：University System of Ohio; Wright State University Dayton
  摘要：Individual and simultaneous confidence intervals using the data adaptively are constructed for the effects in orthogonal saturated designs under the assumption of effect sparsity. The minimum coverage probabilities of the intervals are equal to the nominal level 1-alpha.
• Least squares estimators of the mode of a unimodal regression function AI翻译
  作者：Shoung, JM; Zhang, CH
  作者单位：Rutgers University System; Rutgers University New Brunswick
  摘要：In this paper, we consider nonparametric least squares estimators of the mode of an unknown unimodal regression function. We establish almost sure convergence of these estimators with nearly optimal convergence rates, under the assumption of the exponential tail for the error distributions.
• Structure adaptive approach for dimension reduction AI翻译
  作者：Hristache, M; Juditsky, A; Polzehl, J; Spokoiny, V
  作者单位：Ecole Nationale de la Statistique et de l'Analyse de l'Information (ENSAI); Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
  摘要：We propose a new method of effective dimension reduction for a multi-index model which is based on iterative improvement of the family of average derivative estimates. The procedure is computationally straightforward and does not require any prior information about the structure of the underlying model. We show that in the case when the effective dimension in of the index space does not exceed 3, this space can be estimated with the rate n (-1/2) under rather mild assumptions on the model.
• Bootstrapping nonparametric density estimators with empirically chosen bandwidths AI翻译
  作者：Hall, P; Kang, KH
  作者单位：Australian National University; Hankuk University Foreign Studies
  摘要：We examine the way in which empirical bandwidth choice affects distributional properties of nonparametric density estimators. Two bandwidth selection methods are considered in detail: local and global plug-in rules. Particular attention is focussed on whether the accuracy of distributional bootstrap approximations is appreciably influenced by using the resample version (h) over cap*, rather than the sample version (h) over cap, of an empirical bandwidth. It is shown theoretically that, in mark...
• Convex models, MLE and misspecification AI翻译
  作者：Patilea, V
  作者单位：Universite de Orleans
  摘要：We analyze the asymptotic behavior of maximum likelihood estimators (MLE) in convex dominated models when the true distribution generating the independent data does not necessarily belong to the model. Inspired by the Hellinger distance and its properties, we introduce a family of divergences (contrast functions) which allow a unified treatment of well- and misspecified convex models. Convergence and rates of convergence of the MLE with respect to our divergences are obtained from inequalities...
• Causal inference for complex longitudinal data: The continuous case AI翻译
  作者：Gill, RD; Robins, JM
  作者单位：Utrecht University; Harvard University; Harvard T.H. Chan School of Public Health
  摘要：We extend Robins' theory of causal inference for complex longitudinal data to the case of continuously varying as opposed to discrete covariates and treatments. In particular we establish versions of the key results of the discrete theory: the g-computation formula and a collection of powerful characterizations of the g-null hypothesis of no treatment effect. This is accomplished under natural continuity hypotheses concerning the conditional distributions of the outcome variable and of the cov...
• Consistent estimation of mixture complexity AI翻译
  作者：James, LF; Preibe, CE; Marchette, DJ
  作者单位：Johns Hopkins University; United States Department of Defense; United States Navy
  摘要：The consistent estimation of mixture complexity is of fundamental importance in many applications of finite mixture models. An enormous body of literature exists regarding the application, computational issues and theoretical aspects of mixture models when the number of components is known, but estimating the unknown number of components remains an area of intense research effort. This article presents a semiparametric methodology yielding almost sure convergence of the estimated number of com...
• Nonparametric kernel regression subject to monotonicity constraints AI翻译
  作者：Hall, P; Huang, LS
  作者单位：Australian National University; Commonwealth Scientific & Industrial Research Organisation (CSIRO)
  摘要：We suggest a method for monotonizing general kernel-type estimators, for example local linear estimators and Nadaraya-Watson estimators. Attributes of our approach include the fact that it produces smooth estimates, indeed with the same smoothness as the unconstrained estimate. The method is applicable to a particularly wide range of estimator types, it can be trivially modified to render an estimator strictly monotone and it can be employed after the smoothing step has been implemented. There...