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作者：Neumann, MH
摘要：In the present paper we combine the issues of bandwidth choice and construction of confidence intervals in nonparametric regression. Main emphasis is put on fully data-driven methods. We modify the root n-consistent bandwidth selector of Hardle, Hall and Marron such that it is appropriate for heteroscedastic data, and we show how one can optimally choose the bandwidth g of the pilot estimator <(m)over cap(g)>. Then we consider classical confidence intervals based on kernel estimators with data...
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作者：Richards, DSP
摘要：Let M be a compact, smooth, orientable manifold without boundary, and let f: M --> R be a smooth function. Let dm be a volume form on M with total volume 1, and denote by X the corresponding random variable. Using a theorem of Kirwan, we obtain necessary conditions under which the method of stationary phase returns an exact evaluation of the characteristic function of f(X). As an application to the Langevin distribution on the sphere S-d-1, We deduce that the method of stationary phase provide...
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作者：BASU, S; DASGUPTA, A
作者单位：Purdue University System; Purdue University
摘要：Let X(i) = theta + sigma Z(i) where Z(i) are i.i.d. from a distribution F, and -infinity < theta < infinity and sigma > 0 are unknown parameters. If F is N(0, 1), a standard confidence interval for the unknown mean theta is the t-interval (X) over bar +/- t(alpha/2)s/root n. The question of conservatism of this interval under nonnormality is considered by evaluating the infimum of its coverage probability when F belongs to a suitably chosen class of distributions F. Some rather surprising phen...
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作者：NYCHKA, D
摘要：A smoothing spline is a nonparametric curve estimate that is defined as the solution to a minimization problem. One problem with this representation is that it obscures the fact that a spline, like most other nonparametric estimates, is a local, weighted average of the observed data. This property has been used extensively to study the limiting properties of kernel estimates and it is advantageous to apply similar techniques to spline estimates. Although equivalent kernels have been identified...
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作者：MCKEAGUE, IW; NIKABADZE, AM; SUN, YQ
作者单位：University of Rochester
摘要：It has been over 60 years since Kolmogorov introduced a distribution-free omnibus test for the simple null hypothesis that a distribution function coincides with a given distribution function. Doob subsequently observed that Kolmogorov's approach could be simplified by transforming the empirical process to an empirical process based on uniform random variables. Recent use of more sophisticated transformations has led, to the construction of asymptotically distribution-free omnibus tests when u...
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作者：WU, CO
摘要：This paper considers efficient estimation of the Euclidean parameter theta in the proportional odds model G(1 - G)(-1) = theta F(1 - F)(-1) when two independent i.i.d. samples with distributions F and G, respectively, are observed. The Fisher information I(theta) is calculated based on the solution of a pair of integral equations which are derived from a class of more general semiparametric models. A one-step estimate is constructed using an initial root N-consistent estimate and shown to be a...
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作者：CARROLL, RJ; KNICKERBOCKER, RK; WANG, CY
作者单位：Eli Lilly; Lilly Research Laboratories; Fred Hutchinson Cancer Center
摘要：We consider a semiparametric estimation method for general regression models when some of the predictors are measured with error. The technique relies on a kernel regression of the ''true'' covariate on all the observed covariates and surrogates. This requires a nonparametric regression in as many dimensions as there are covariates and surrogates. The usual theory copes with such higher-dimensional problems by using higher-order kernels, but this is unrealistic for most problems. We show that ...
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作者：HJORT, NL; GLAD, IK
作者单位：Norwegian University of Science & Technology (NTNU)
摘要：The traditional kernel density estimator of an unknown density is by construction completely nonparametric in the sense that it has no preferences and will work reasonably well for all shapes. The present paper develops a class of semiparametric methods that are designed to work better than the kernel estimator in a broad nonparametric neighbourhood of a given parametric class of densities, for example, the normal, while not losing much in precision when the true density is far from the parame...
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作者：FOURDRINIER, D; WELLS, MT
作者单位：Cornell University
摘要：This paper is concerned with estimating the loss of a point estimator when sampling from a spherically symmetric distribution. We examine the canonical setting of a general linear model where the dimension of the parameter space is greater than 4 and less than the dimension of the sampling space. We consider two location estimators-the least squares estimator and a shrinkage estimator-and we compare their unbiased loss estimator with an improved loss estimator. The domination results are valid...
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作者：STUTE, W
摘要：Let ($) over cap F-n be the Kaplan-Meier estimator of a distribution function F computed from randomly censored data. We show that under optimal integrability assumptions on a function phi, the Kaplan-Meier integral integral phi d ($) over cap F-n, when properly standardized, is asymptotically normal.
