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作者：JOHNSTONE, IM; MACGIBBON, KB
作者单位：University of Quebec; University of Quebec Montreal
摘要：Suppose that the mean-tau of a vector of Poisson variates is known to lie in a bounded domain T in [0, infinity)p. How much does this a priori information increase precision of estimation of tau? Using error measure SIGMA(i)(tau(i) - tau(i))2/tau(i) and minimax risk rho(T), we give analytical and numerical results for small intervals when p = 1. Usually, however, approximations are needed. If T is rectangulary convex at 0, there exist linear estimators with risk at most 1.26-rho(T). For genera...
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作者：ROEDER, K
摘要：A semiparametric method for estimating densities of normal mean mixtures is presented. This consistent data-driven method of estimation is based on probability spacings. The estimation technique involves iteratively fixing the standard deviation of the normal kernel that serves as a smoothing parameter, and then maximizing a function of the probability spacings over all mixing distributions. Based on the distribution of uniform spacings, a distribution free goodness-of-fit criterion is develop...
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作者：CHENG, QS
作者单位：Peking University
摘要：In this paper, we prove the uniqueness of linear i.i.d. representations of non-Gaussian linear processes on a countable abelian group under a basic invertibility condition, without requiring the existence of higher than second moments.
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作者：BERAN, R
摘要：Suppose the variable X to be predicted and the learning sample Y(n) that was observed are independent, with a joint distribution that depends on an unknown parameter-theta. A prediction region D(n) for X is a random set, depending on Y(n), that contains X with prescribed probability-alpha. In sufficiently regular models, D(n) can be constructed so that overall coverage probability converges to alpha at rate n(-r), where r is any positive integer. This paper shows that the conditional coverage ...
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作者：HSING, TL; CARROLL, RJ
摘要：Sliced inverse regression [Li (1989), (1991) and Duan and Li (1991)] is a nonparametric method for achieving dimension reduction in regression problems. It is widely applicable, extremely easy to implement on a computer and requires no nonparametric smoothing devices such as kernel regression. If Y is the response and X is-an-element-of R(p) is the predictor, in order to implement sliced inverse regression, one requires an estimate of LAMBDA = E{cov(X\Y)} = cov(X) - cov{E(X\Y)}. The inverse re...
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作者：LO, SH
作者单位：Harvard University
摘要：A basic interpretation is given which provides a new way of understanding the structure of the species problem and which leads to the popular Turing-Good-Robbins estimator. Through this interpretation we provide an explanation why the Turing-Good-Robbins estimators are always biased. An iterative procedure is suggested and applied to these estimators, which leads to new estimators whose biases are reduced. Using this basic construction we are able to generalize our discussion to a much broader...
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作者：MARTINSEK, AT
摘要：Suppose X1, X2,..., X(n) are i.i.d. with unknown density f. There is a well-known expression for the asymptotic mean integrated squared error (MISE) in estimating f by a kernel estimate f(n), under certain conditions on f, the kernel and the bandwidth. Suppose that one would like to choose a sample size so that the MISE is smaller than some preassigned positive number w. Based on the asymptotic expression for the MISE, one can identify an appropriate sample size to solve this problem. However,...
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作者：CHAUDHURI, P
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：We consider a class of U-statistics type estimates for multivariate location. The estimates extend some R-estimates to multivariate data. In particular, the class of estimates includes the multivariate median considered by Gini and Galvani (1929) and Haldane (1948) and a multivariate extension of the well-known Hodges-Lehmann (1963) estimate. We explore large sample behavior of these estimates by deriving a Bahadur type representation for them. In the process of developing these asymptotic res...
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作者：CUZICK, J
摘要：Several authors have shown how to efficiently estimate-beta in the semiparametric additive model y = x'-beta + g(t) + error, g(t) smooth but unknown when the error distribution is normal. However, the general theory suggests that efficient estimation should be possible for general error distributions with finite Fisher information even when the error distribution is unknown. In this note we construct a sequence of estimators which achieves this goal under technical assumptions.
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作者：DONOHO, DL; LOW, MG
作者单位：University of Pennsylvania
摘要：Simple renormalization arguments can often be used to calculate optimal rates of convergence for estimating linear functionals from indirect measurements contaminated with white noise. This allows one to quickly identify optimal rates for certain problems of density estimation, nonparametric regression, signal recovery and tomography. Optimal kernels may also be derived from renormalization; we give examples for deconvolution and tomography.
