-
作者：Jing, BY; Wang, QY
作者单位：Hong Kong University of Science & Technology
摘要：Berry-Esseen bounds for U-statistics under the optimal moment conditions were derived by Koroljuk and Borovskich and Friedrich. Under the same optimal moment assumptions with an additional nonlattice condition, we establish a one-term Edgeworth expansion with remainder o(n(-1/2)) for U-statistics.
-
作者：Dippon, J
作者单位：University of Stuttgart
摘要：We propose a general class of randomized gradient estimates to be employed in a recursive search for the minimum of an unknown multivariate regression function. Here only two observations per iteration step are used. Special cases include random direction stochastic approximation (Kushner and Clark), simultaneous perturbation stochastic approximation (Spall) and a special kernel based stochastic approximation method (Polyak and Tsybakov). If the unknown regression is p-smooth (p greater than o...
-
作者：Bickel, PJ; Ritov, Y
作者单位：University of California System; University of California Berkeley; Hebrew University of Jerusalem
摘要：We consider nonparametric estimation of an object such as a probability density or a regression function. Can such an estimator achieve the ratewise minimax rate of convergence on suitable function spaces, while, at the same time, when plugged-in, estimate efficiently (at a rate of n(-1/2) with the best constant) many functionals of the object? For example, can we have a density estimator whose definite integrals are efficient estimators of the cumulative distribution function? We show that th...
-
作者：Loh, WL
作者单位：National University of Singapore
摘要：Recently, in a series of articles, Owen proposed the use of scrambled (t, m, s) nets and (t, s) sequences in high-dimensional numerical integration. These scrambled nets and sequences achieve the superior accuracy of equidistribution methods while allowing for the simpler error estimation techniques of Monte Carlo methods. The main aim of this article is to use Stein's method to study the asymptotic distribution of the scrambled (0, m, s) net integral estimate. In particular, it is shown that,...
-
作者：Giraitis, L; Robinson, PM
作者单位：University of London; London School Economics & Political Science
摘要：The semiparametric local Whittle or Gaussian estimate of the long memory parameter is known to have especially nice limiting distributional properties, being asymptotically normal with a limiting variance that is completely known. However in moderate samples the normal approximation may not be very good, so we consider a refined, Edgeworth, approximation, for both a tapered estimate and the original untapered one. For the tapered estimate, our higher-order correction involves two terms, one of...
-
作者：Hössjer, O
作者单位：Stockholm University
摘要：We consider estimation of a disease susceptibility locus tau at a chromosome. With perfect marker data available, the estimator (tau) over cap (N) of r based on N pedigrees has a rate of convergence N-1 under mild regularity conditions. The limiting distribution is the arg max of a certain compound Poisson process. Our approach is conditional on observed phenotypes, and therefore treats parametric and nonparametric linkage, as well as quantitative trait loci methods within a unified framework....
-
作者：Buchmann, B; Grübel, AR
作者单位：Technical University of Munich; Leibniz University Hannover
摘要：Given a sample from a compound Poisson distribution, we consider estimation of the corresponding rate parameter and base distribution. This has applications in insurance mathematics and queueing theory. We propose a plug-in type estimator that is based on a suitable inversion of the compounding operation. Asymptotic results for this estimator are obtained via a local analysis of the decompounding functional.
-
作者：Kozek, AS
作者单位：Macquarie University
摘要：This paper explores a class of robust estimators of normal quantiles filling the gap between maximum likelihood estimators and empirical quantiles. Our estimators are linear combinations of M-estimators. Their asymptotic variances can be arbitrarily close to variances of the maximum likelihood estimators. Compared with empirical quantiles, the new estimators offer considerable reduction of variance at near normal probability distributions.
-
作者：Ren, JJ
作者单位：State University System of Florida; University of Central Florida
摘要：Considering the linear regression model with fixed design, the usual M-estimator with a complete sample of the response variables is expressed as a functional of a generalized weighted bivariate empirical process, and its asymptotic normality is directly derived through the Hadamard differentiability property of this functional and the weak convergence of this generalized weighted empirical process. The result reveals the direct relationship between the M-estimator and the distribution functio...
-
作者：Robinson, J; Ronchetti, E; Young, GA
作者单位：University of Sydney; University of Geneva; University of Cambridge
摘要：We consider multidimensional M-functional parameters defined by expectations of score functions associated with multivariate M-estimators and tests for hypotheses concerning multidimensional smooth functions of these parameters. We propose a test statistic suggested by the exponent in the saddlepoint approximation to the density of the function of the M-estimates. This statistic is analogous to the log likelihood ratio in the parametric case. We show that this statistic is approximately distri...
