The Annals of Statistics

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• Estimation for almost periodic processes AI翻译
  作者：Lii, Keh-Shin; Rosenblatt, Murray
  作者单位：University of California System; University of California Riverside; University of California System; University of California San Diego
  摘要：Processes with almost periodic covariance functions have spectral mass on lines parallel to the diagonal in the two-dimensional spectral plane. Methods have been given for estimation of spectral mass on the lines of spectral concentration if the locations of the lines are known. Here methods for estimating the intercepts of the lines of spectral concentration in the Gaussian case are given under appropriate conditions. The methods determine rates of convergence sufficiently fast as the sample ...
• Nonparametric quasi-maximum likelihood estimation for Gaussian locally stationary processes AI翻译
  作者：Dahlhaus, Rainer; Polonik, Wolfgang
  作者单位：Ruprecht Karls University Heidelberg; University of California System; University of California Davis
  摘要：This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing a frequency domain likelihood over a class of functions. The asymptotic behavior of the resulting estimator is studied. The results depend on the richness of the class of functions. Both sieve estimation and global estimation are considered. Our results apply, in particular, to estimation under shape constraints. As an example, autoregr...
• Poisson inverse problems AI翻译
  作者：Antoniadis, Anestis; Bigot, Jeremie
  作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Universite de Toulouse; Universite Toulouse III - Paul Sabatier
  摘要：In this paper we focus on nonparametric estimators in inverse problems for Poisson processes involving the use of wavelet decompositions. Adopting an adaptive wavelet Galerkin discretization, we find that our method combines the well-known theoretical advantages of wavelet-vaguelette decompositions for inverse problems in terms of optimally adapting to the unknown smoothness of the solution, together with the remarkably simple closed-form expressions of Galerkin inversion methods. Adapting the...
• Confidence regions for high quantiles of a heavy tailed distribution AI翻译
  作者：Peng, Liang; Qi, Yongcheng
  作者单位：University System of Georgia; Georgia Institute of Technology; University of Minnesota System; University of Minnesota Duluth
  摘要：Estimating high quantiles plays an important role in the context of risk management. This involves extrapolation of an unknown distribution function. In this paper we propose three methods, namely, the normal approximation method, the likelihood ratio method and the data tilting method, to construct confidence regions for high quantiles of a heavy tailed distribution. A simulation study prefers the data tilting method.
• Closed form expressions for Bayesian sample size AI翻译
  作者：Clarke, B.; Yuan, Ao
  作者单位：University of British Columbia; Howard University
  摘要：Sample size criteria are often expressed in terms of the concentration of the posterior density, as controlled by some sort of error bound. Since this is done pre-experimentally, one can regard the posterior density as a function of the data. Thus, when a sample size criterion is formalized in terms of a functional of the posterior, its value is a random variable. Generally, such functionals have means under the true distribution. We give asymptotic expressions for the expected value, under a ...
• Misspecification in infinite-dimensional Bayesian statistics AI翻译
  作者：Kleun, B. J. K.; Van der Wart, A. W.
  作者单位：Vrije Universiteit Amsterdam
  摘要：We consider the asymptotic behavior of posterior distributions if the model is misspecified. Given a prior distribution and a random sample from a distribution P-0, which may not be in the support of the prior, we show that the posterior concentrates its mass near the points in the support of the prior that minimize the Kullback-Leibler divergence with respect to P0. An entropy condition and a prior-mass condition determine the rate of convergence. The method is applied to several examples, wi...
• Frequentist optimality of Bayesian wavelet shrinkage rules for Gaussian and non-Gaussian noise AI翻译
  作者：Pensky, Marianna
  作者单位：State University System of Florida; University of Central Florida
  摘要：The present paper investigates theoretical performance of various Bayesian wavelet shrinkage rules in a nonparametric regression model with i.i.d. errors which are not necessarily normally distributed. The main purpose is comparison of various Bayesian models in terms of their frequentist asymptotic optimality in Sobolev and Besov spaces. We establish a relationship between hyperparameters, verify that the majority of Bayesian models studied so far achieve theoretical optimality, state which B...
• Inference for covariate adjusted regression via varying coefficient models AI翻译
  作者：Senturk, Damla; Muller, Hans-Georg
  作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University of California System; University of California Davis
  摘要：We consider covariate adjusted regression (CAR), a regression method for situations where predictors and response are observed after being distorted by a multiplicative factor. The distorting factors are unknown functions of an observable covariate, where one specific distorting function is associated with each predictor or response. The dependence of both response and predictors on the same confounding covariate may alter the underlying regression relation between undistorted but unobserved p...
• Adaptive nonparametric confidence sets AI翻译
  作者：Robins, James; Van der Vaart, Aad
  作者单位：Harvard University; Harvard T.H. Chan School of Public Health; Vrije Universiteit Amsterdam
  摘要：We construct honest confidence regions for a Hilbert space-valued parameter in various statistical models. The confidence sets can be centered at arbitrary adaptive estimators, and have diameter which adapts optimally to a given selection of models. The latter adaptation is necessarily limited in scope. We review the notion of adaptive confidence regions, and relate the optimal rates of the diameter of adaptive confidence regions to the minimax rates for testing and estimation. Applications in...
• Semiparametric estimation of fractional cointegrating subspaces AI翻译
  作者：Chen, Willa W.; Hurvich, Clifford M.
  作者单位：Texas A&M University System; Texas A&M University College Station; New York University
  摘要：We consider a common-components model for multivariate fractional cointegration, in which the s >= 1 components have different memory parameters. The cointegrating rank may exceed 1. We decompose the true cointegrating vectors into orthogonal fractional cointegrating subspaces such that vectors from distinct subspaces yield cointegrating errors with distinct memory parameters. We estimate each cointegrating subspace separately, using appropriate sets of eigenvectors of an averaged periodogram ...