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作者：Schick, Anton; Wefelmeyer, Wolfgang
作者单位：State University of New York (SUNY) System; Binghamton University, SUNY; University of Cologne
摘要：Convergence rates of kernel density estimators for stationary time series are well studied. For invertible linear processes, we construct a new density estimator that converges, in the supremum norm, at the better, parametric, rate n(-1/2). Our estimator is a convolution of two different residual-based kernel estimators. We obtain in particular convergence rates for such residual-based kernel estimators; these results are of independent interest.
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作者：Koltchinskii, Vladimir; Sakhanenk, Lyudmila; Cai, Songhe
作者单位：University of New Mexico; University System of Georgia; Georgia Institute of Technology; Michigan State University
摘要：Let nu be a vector field in a bounded open set G subset of R-d. Suppose that nu is observed with a random noise at random points X-i, i = 1,..., n, that are independent and uniformly distributed in G. The problem is to estimate the integral curve of the differential equation dx(t)/dt = nu(x(t)), t >= 0, x(0) = x(0) epsilon G, starting at a given point x(0) = x0 epsilon G and to develop statistical tests for the hypothesis that the integral curve reaches a specified set Gamma subset of G. We de...
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作者：Ing, Ching-Kang
作者单位：Academia Sinica - Taiwan; National Taiwan University
摘要：The predictive capability of a modification of Rissanen's accumulated prediction error (APE) criterion, APES,, is investigated in infinite-order autoregressive (AR(infinity)) models. Instead of accumulating squares of sequential prediction errors from the beginning, APES, is obtained by summing these squared errors from stage n delta(n), where n is the sample size and 1/n <= delta(n) <= 1 - (1/1n) may depend on n. Under certain regularity conditions, an asymptotic expression is derived for the...
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作者：Ling, Shiqing
作者单位：Hong Kong University of Science & Technology
摘要：This paper first establishes a strong law of large numbers and a strong invariance principle for forward and backward sums of near-epoch dependent sequences. Using these limiting theorems, we develop a general asymptotic theory on the Wald test for change points in a general class of time series models under the no change-point hypothesis. As an application, we verify our assumptions for the long-memory fractional ARIMA model.
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作者：Wu, Samuel S.; Wang, Weizhen
作者单位：State University System of Florida; University of Florida; University System of Ohio; Wright State University Dayton
摘要：A sequence of null hypotheses regarding the number of negligible effects (zero effects) in orthogonal saturated designs is formulated. Two step-up simultaneous testing procedures are proposed to identify active effects (nonzero effects) under the commonly used assumption of effect sparsity. It is shown that each procedure controls the experimentwise error rate at a given alpha level in the strong sense.
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作者：Balabdaoui, Fadoua; Wellner, Jon A.
作者单位：University of Gottingen; University of Washington; University of Washington Seattle
摘要：We study the asymptotic behavior of the Maximum Likelihood and Least Squares Estimators of a k-monotone density go at a fixed point x(0) when k > 2. We find that the jib derivative of the estimators at x(0) converges at the rate n(-(k-j)/(2k+1)) for j = 0.... k - 1. The limiting distribution depends on an almost surely uniquely defined stochastic process H-k that stays above (below) the k-fold integral of Brownian motion plus a deterministic drift when k is even (odd). Both the MLE and LSE are...
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作者：Durot, Cecile
作者单位：Universite Paris Saclay
摘要：We aim at estimating a function lambda : [0, 1] -> R, subject to the constraint that it is decreasing (or increasing). We provide a unified approach for studying the L-p-loss of an estimator defined as the slope of a concave (or convex) approximation of an estimator of a primitive of., based on n observations. Our main task is to prove that the Lp-loss is asymptotically Gaussian with explicit (though unknown) asymptotic mean and variance. We also prove that the local L-p-risk at a fixed point ...
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作者：Gine, Evarist; Mason, David M.
作者单位：University of Connecticut; University of Delaware
摘要：A notion of local U-statistic process is introduced and central limit theorems in various norms are obtained for it. This involves the development of several inequalities for U-processes that may be useful in other contexts. This local U-statistic process is based on an estimator of the density of a function of several sample variables proposed by Frees [J. Amer Statist. Assoc. 89 (1994) 517-525] and, as a consequence, uniform in bandwidth central limit theorems in the sup and in the L-p norms...
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作者：Delaigle, Aurore; Hall, Peter; Mueller, Hans-Georg
作者单位：University of Bristol; University of Melbourne; University of California System; University of California Davis
摘要：We consider nonparametric estimation of a regression function for a situation where precisely measured predictors are used to estimate the regression curve for coarsened, that is, less precise or contaminated predictors. Specifically, while one has available a sample (W(1), Y(1)),..., (W(n) ,Y(n)) of independent and identically distributed data, representing observations with precisely measured predictors, where E(Y(i)/W(i)) = g (W(i)), instead of the smooth regression function g, the target o...
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作者：Ritov, Ya'acov
作者单位：Hebrew University of Jerusalem
