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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：TAKADA, Y
摘要：A sequential procedure for estimating the mean of a normal distribution is proposed. The procedure is shown to have a negative regret at the origin and the same regret as the usual procedure at the other point asymptotically.
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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：DONOHO, DL; GASKO, M
作者单位：University of California System; University of California Berkeley; California State University System; San Jose State University
摘要：We describe multivariate generalizations of the median, trimmed mean and W estimates. The estimates are based on a geometric construction related to ''projection pursuit.'' They are both affine equivariant (coordinate-free) and have high breakdown point. The generalization of the median has a breakdown point of at least 1/(d + 1) in dimension d and the breakdown point can be as high as 1/3 under symmetry. In contrast, various estimators based on rejecting apparent outliers and taking the mean ...
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作者：MASON, DM; NEWTON, MA
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：A general notion of a bootstrapped mean constructed by exchangeably weighting sample points is introduced. Consistency of this generalized bootstrapped mean, which includes proposals of Efron and Rubin among others, is proved by classical linear rank statistics theory. The consistency of generalized bootstrapped empirical and quantile processes is also established.
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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：FAN, JQ; GIJBELS, I
作者单位：Hasselt University
摘要：In this paper we introduce an appealing nonparametric method for estimating the mean regression function. The proposed method combines the ideas of local linear smoothers and variable bandwidth. Hence, it also inherits the advantages of both approaches. We give expressions for the conditional MSE and MISE of the estimator. Minimization of the MISE leads to an explicit formula for an optimal choice of the variable bandwidth. Moreover, the merits of considering a variable bandwidth are discussed...
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作者：GOUTIS, C; CASELLA, G
作者单位：Cornell University; Cornell University
摘要：The usual confidence interval, based on Student's t distribution, has conditional confidence that is larger than the nominal confidence level. Although this fact is known, along with the fact that increased conditional confidence can be used to improve a confidence assertion, the confidence assertion of Student's t interval has never been critically examined. We do so here, and construct a confidence estimator that allows uniformly higher confidence in the interval and is closer (than 1 - alph...
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作者：MAULDIN, RD; SUDDERTH, WD; WILLIAMS, SC
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Utah System of Higher Education; Utah State University
摘要：Trees of Polya urns are used to generate sequences of exchangeable random variables. By a theorem of de Finetti each such sequence is a mixture of independent, identically distributed variables and the mixing measure can be viewed as a prior on distribution functions. The collection of these Polya tree priors forms a convenient conjugate family which was mentioned by Ferguson and includes the Dirichlet processes of Ferguson. Unlike Dirichlet processes, Polya tree priors can assign probability ...
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作者：LOW, MG
作者单位：University of California System; University of California Berkeley
摘要：A strong adaptive criteria is defined for density estimation problems. In a particular case it is shown that there is no strongly adaptive sequence of estimators. In contrast Woodroofe has shown that a weakly adaptive result holds.
