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作者：Nicoleris, T; Yatracos, YG
作者单位：Universite de Montreal
摘要：L-1-optimal minimum distance estimators are provided for a projection pursuit regression type function with smooth functional components that are either additive or multiplicative, in the presence of or without interactions. The obtained rates of convergence of the estimate to the true parameter depend on Kolmogorov's entropy of the assumed model and confirm Stone's heuristic dimensionality reduction principle. Rates of convergence are also obtained for the error in estimating the derivatives ...
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作者：Cuevas, A; Fraiman, R
作者单位：Autonomous University of Madrid; Universidad de la Republica, Uruguay
摘要：We suggest a new approach, based on the use of density estimators, for the problem of estimating the (compact) support of a multivariate density. This subject (motivated in terms of pattern analysis by Grenander) has interesting connections with detection and clustering. A natural class of density-based estimators is defined. Universal consistency results and convergence rates are established for these estimators, with respect to the usual measure-based metric d(mu) between sets. Further conve...
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作者：Brown, LD; Low, MG; Zhao, LH
作者单位：University of Pennsylvania
摘要：Fixed parameter asymptotic statements are often used in the context of nonparametric curve estimation problems (e.g., nonparametric density or regression estimation). In this context several forms of superefficiency can occur. In contrast to what can happen in regular parametric problems, here every parameter point (e.g., unknown density or regression function) can be a point of superefficiency. We begin with an example which shows how fixed parameter asymptotic statements have often appeared ...
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作者：Takemura, A; Kuriki, S
作者单位：University of Tokyo; Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan
摘要：We study the problem of testing a simple null hypothesis about the multivariate normal mean vector against smooth or piecewise smooth cone alternatives. We show that the mixture weights of the (chi)over-bar(2) distribution of the likelihood ratio test can be characterized as mixed volumes of the cone and its dual. The weights can be calculated by integration involving the second fundamental form on the boundary of the cone. We illustrate our technique by examples involving a spherical cone and...
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作者：Cabaña, A; Cabaña, EM
作者单位：Venezuelan Institute Science Research; Universidad de la Republica, Uruguay
摘要：A general way of constructing classes of goodness-of-fit tests for multivariate samples is presented. These tests are based on a random signed measure that plays the same role as the empirical process in the construction of the classical Kolmogorov-Smirnov tests. The resulting tests are consistent against any fixed alternative, and, for each sequence of contiguous alternatives, a test in each class can be chosen so as to optimize the discrimination of those alternatives.
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作者：Riedel, KS
作者单位：New York University
摘要：Given noisy data, function estimation is considered when the unknown function is known a priori to be either convex or concave on each of a small number of regions where the function. When the number of regions is unknown, the model selection problem is to determine the number of convexity change points. For kernel estimates in Gaussian noise, the number of false change points is evaluated as a function of the smoothing parameter. To insure that the number of false convexity change points tend...
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作者：Nakayama, MK
作者单位：New Jersey Institute of Technology
摘要：Suppose that there are k greater than or equal to 2 different systems (i.e., stochastic processes), where each system has an unknown steady-state mean performance and unknown asymptotic variance. We allow for the asymptotic variances to be unequal and for the distributions of the k systems to be different. We consider the problem of running independent, single-stage simulations to make multiple comparisons of the steady-state means of the different systems. We derive asymptotically valid (as t...
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作者：Shen, XT
作者单位：University System of Ohio; Ohio State University
摘要：We develop a general theory which provides a unified treatment for the asymptotic normality and efficiency of the maximum likelihood estimates (MLE's) in parametric, semiparametric and nonparametric models. We find that the asymptotic behavior of substitution estimates for estimating smooth functionals are essentially governed by two indices: the degree of smoothness of the functional and the local size of the underlying parameter space. We show that when the local size of the parameter space ...
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作者：Haussler, D; Opper, M
作者单位：University of California System; University of California Santa Cruz; University of Wurzburg
摘要：Assume (P-theta: theta epsilon Theta) is a set of probability distributions with a common dominating measure on a complete separable metric space Y. A state theta* epsilon Theta is chosen by Nature. A statistician obtains n independent observations Y-1,...,Y-n from Y distributed according to P-theta.. For each time t between 1 and n, based on the observations Y-1,...,Yt-1, the statistician produces an estimated distribution (P) over cap(t) for P-theta* and suffers a loss L(P-theta., (P) over c...
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作者：Riccomagno, E; Schwabe, R; Wynn, HP
作者单位：University of Warwick; Technical University of Darmstadt
摘要：A theory of optimum orthogonal fractions is developed for Fourier regression models using integer lattice designs. These provide alternatives to simple grids (product designs) in the case when specified main effects and interaction terms are required to be analyzed. The challenge is to obtain sample sizes which are polynomial in the dimension rather than exponential. This is achieved for certain models with special algorithms based on both algebraic generation and more direct sequential search.
