-
作者：Chen, DC; Huang, P; Cheng, XZ
作者单位：Uniformed Services University of the Health Sciences - USA; Medical University of South Carolina; George Washington University
摘要：The method of stochastic discrimination (SD) introduced by Kleinberg is a new method in statistical pattern recognition. It works by producing many weak classifiers and then combining them to form a strong classifier. However, the strict mathematical assumptions in Kleinberg [The Annals of Statistics 24 (1996) 2319-2349] are rarely met in practice. This paper provides an applicable way to realize the SD algorithm. We recast SD in a probability-space framework and present a concrete statistical...
-
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：Hall, P; Yao, QW
作者单位：Australian National University; University of London; London School Economics & Political Science
摘要：in components of variance models the data are viewed as arising through a sum of two random variables, representing between- and within-group variation, respectively. The former is generally interpreted as a group effect, and the latter as error. It is assumed that these variables are stochastically independent and that the distributions of the group effect and the error do not vary from one instance to another. If each group effect can be replicated a large number of times, then standard meth...
-
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：Janssen, A; Pauls, T
作者单位：Heinrich Heine University Dusseldorf
摘要：Resampling methods are frequently used in practice to adjust critical values of nonparametric tests. In the present paper a comprehensive and unified approach for the conditional and unconditional analysis of linear resampling statistics is presented. Under fairly mild assumptions we prove tightness and an asymptotic series representation for their weak accumulation points. From this series it becomes clear which part of the resampling statistic is responsible for asymptotic normality. The res...
-
作者：Zhu, Y
作者单位：Purdue University System; Purdue University
摘要：A general approach to studying fractional factorial designs with multiple groups of factors is proposed. A structure function is generated by the defining contrasts among different groups of factors and the remaining columns. The structure function satisfies a first-order partial differential equation. By solving this equation, general results about the structures and properties of the designs are obtained. As an important application, practical rules for the selection of optimal single arrays...
-
作者：Linton, OB; Nielsen, JP; Van de Geer, S
作者单位：University of London; London School Economics & Political Science; Leiden University - Excl LUMC; Leiden University
摘要：We propose new procedures for estimating the component functions in both additive and multiplicative nonparametric marker-dependent hazard models. We work with a full counting process framework that allows for left truncation and right censoring and time-varying covariates. Our procedures are based on kernel hazard estimation as developed by Nielsen and Linton and on the idea of marginal integration. We provide a central limit theorem for the marginal integration estimator. We then define esti...
-
作者：Hall, P; Zhou, XH
作者单位：Australian National University; US Department of Veterans Affairs; Veterans Health Administration (VHA); Vet Affairs Puget Sound Health Care System; University of Washington; University of Washington Seattle
摘要：Suppose k-variate data are drawn from a mixture of two distributions, each having independent components. It is desired to estimate the univariate marginal distributions in each of the products, as well as the mixing proportion. This is the setting of two-class, fully parametrized latent models that has been proposed for estimating the distributions of medical test results when disease status is unavailable. The problem is one of inference in a mixture of distributions without training data, a...
-
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,...
