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作者：BURMAN, P
摘要：We consider here spline estimates of the optimal transformations of variables for multiple correlation and regression as dealt with in a recent paper by Breiman and friedman. We show that we can construct estimates of the optimal transformations which have the same optimal rate of convergence as in the usual nonparametric estimation of a univariate function.
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作者：CALVIN, JA; DYKSTRA, RL
摘要：The problem of maximum likelihood estimation of Lowner ordered covariance matrices is considered. It is shown that a dual formulation of this problem is tractable and important in its own right. The interplay between the primal and dual problems suggests a general algorithm for computing the solutions to these problems. This algorithm has application to some estimation problems in balanced multivariate variance components models. The speed of convergence is also discussed for the variance comp...
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作者：CHEN, JH; WU, CFJ
摘要：The minimum aberration criterion is commonly used for selecting good fractional factorial designs. In this paper we obtain minimum aberration 2n-k designs for k = 3,4 and any n. For k > 4 analogous results are not available for general n since the resolution criterion is not periodic for general n and k > 4. However, it can be shown that for any fixed k, both the resolution criterion and the minimum aberration criterion have a periodicity property in n for s(n-k) designs with large n. Furtherm...
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作者：DONOHO, DL; LIU, RC
摘要：We establish upper and lower bounds on the asymptotic minimax risk in estimating (1) a density at a point when the density is known to be decreasing with a Lipschitz condition; (2) a density at a point when the density satisfies a local second-order smoothness (Sacks-Ylvisaker) condition; and (3) the k th derivative of the density at a point, when the density satisfies a local L(p) constraint on the m th derivative. In (1), (2) and (3) the upper and lower bounds differ asymptotically by less t...
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作者：PROSCHAN, M
作者单位：National Institutes of Health (NIH) - USA; NIH National Heart Lung & Blood Institute (NHLBI)
摘要：The papers of Blackwell and Hodges (1957) and Diaconis and Graham (1981) contain an error concerning the asymptotic distribution of the number of returns to the origin of a constrained random walk. The correct distribution is given.
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作者：YANG, S
摘要：This paper discusses the minimum Hellinger distance estimation (MHDE) of the parameter that gives the best fit of a parametric family to a density when the data are randomly censored. In studying the MHDE, the tail behavior of the product-limit (P-L) process is investigated, and the weak convergence of the process on the real line is established. An upper bound on the mean square increment of the normalized P-L process is also obtained. With these results, the asymptotic behavior of the MHDE i...
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作者：DONOHO, DL; LIU, RC
摘要：Consider estimating a functional T(F) of an unknown distribution F member-of F from data X1,...,X(n) i.i.d. F. Let omega(epsilon) denote the modulus of continuity of the functional T over F, computed with respect to Hellinger distance. For well-behaved loss functions l(t), we show that inf(T)n sup(F) E(F)l(T(n) - T(F)) is equivalent to l(omega(n-1/2)) to within constants, whenever T is linear and F is convex. The same conclusion holds in three nonlinear cases: estimating the rate of decay of a...
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作者：BARINGHAUS, L
摘要：Rotationally invariant tests based on test statistics of the von Mises type are proposed under the hypothesis of spherical symmetry of a multivariate distribution. The tests are distribution-free when the hypothesis of spherical symmetry is true. The asymptotic distributions of the test statistics are derived under the null hypothesis and under any fixed alternative. A simple criterion for consistency is given. The results are illustrated by numerous examples of test statistics which give rise...
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作者：DYKSTRA, R; KOCHAR, S; ROBERTSON, T
摘要：Stochastic ordering between probability distributions is a widely studied concept. It arises in numerous settings and has useful applications. Since it is often easy to make value judgments when such orderings exist, it is desirable to recognize their occurrence and to model distributional structure under such orderings. Unfortunately, the necessary theory for statistical inference procedures has not been developed for many problems involving stochastic ordering and this development seems to b...
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作者：HARDLE, W; MARRON, JS
作者单位：University of Bonn; Universite Catholique Louvain
摘要：Simultaneous error bars are constructed for nonparametric kernel estimates of regression functions. The method is based on the bootstrap, where resampling is done from a suitably estimated residual distribution. The error bars are seen to give asymptotically correct coverage probabilities uniformly over any number of gridpoints. Applications to an economic problem are given and comparison to both pointwise and Bonferroni-type bars is presented through a simulation study.
