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作者：Lucas Bali, Juan; Boente, Graciela; Tyler, David E.; Wang, Jane-Ling
作者单位：University of Buenos Aires; University of California System; University of California Davis; Rutgers University System; Rutgers University New Brunswick
摘要：In many situations, data are recorded over a period of time and may be regarded as realizations of a stochastic process. In this paper, robust estimators for the principal components are considered by adapting the projection pursuit approach to the functional data setting. Our approach combines robust projection-pursuit with different smoothing methods. Consistency of the estimators are shown under mild assumptions. The performance of the classical and robust procedures are compared in a simul...
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作者：Stein, Michael L.
作者单位：University of Chicago
摘要：When using optimal linear prediction to interpolate point observations of a mean square continuous stationary spatial process, one often finds that the interpolant mostly depends on those observations located nearest to the predictand. This phenomenon is called the screening effect. However, there are situations in which a screening effect does not hold in a reasonable asymptotic sense, and theoretical support for the screening effect is limited to some rather specialized settings for the obse...
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作者：Liao, Yuan; Jiang, Wenxin
作者单位：Princeton University; Northwestern University
摘要：This paper addresses the estimation of the nonparametric conditional moment restricted model that involves an infinite-dimensional parameter g(0). We estimate it in a quasi-Bayesian way, based on the limited information likelihood, and investigate the impact of three types of priors on the posterior consistency: (i) truncated prior (priors supported on a bounded set), (ii) thin-tail prior (a prior that has very thin tail outside a growing bounded set) and (iii) normal prior with nonshrinking v...
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作者：Koltchinskii, Vladimir
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：We study a problem of estimation of a Hermitian nonnegatively definite matrix rho of unit trace (e. g., a density matrix of a quantum system) based on n i.i.d. measurements (X-1, Y-1), ... , (X-n, Y-n), where Y-j = tr(rho X-j)+ xi(j), j = 1, ... , n, {X-j} being random i.i.d. Hermitian matrices and {xi(j)} being i.i.d. random variables with E(xi(j) vertical bar X-j) = 0. The estimator (rho) over cap (epsilon) := S is an element of S-argmin [n(-1) Sigma(n)(j=1) (Y-j - tr(SXj))(2) + epsilon tr(S...
