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作者：Ling, SQ
作者单位：University of Hong Kong; University of Western Australia
摘要：This paper establishes the weak convergence of the sequential empirical process (K) over bar(n) of the estimated residuals in nonstationary autoregressive models. Under some regular conditions, it is shown that (K) over bar(n) converges weakly to a Kiefer process when the characteristic polynomial does not include the unit root 1; otherwise (K) over bar(n) converges weakly to a Kiefer process plus a functional of stochastic integrals in terms of the standard Brownian motion. The latter differs...
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作者：Golubev, GK; Levit, BY
作者单位：Russian Academy of Sciences; Utrecht University
摘要：We consider the classical Wicksell problem of estimating an unknown distribution function G of the radii of balls, based on their observed cross-sections. It is assumed that the underlying distribution function G belongs to a Holder class of smoothness gamma > 1/2. We prove that, for a suitable choice of the smoothing parameters, kernel-type estimators are asymptotically efficient for a large class of symmetric bowl-shaped loss functions.
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作者：Robinson, J; Skovgaard, IM
作者单位：University of Sydney; University of Copenhagen
摘要：To obtain test probabilities based on empirical approximations to the distribution of a Studentized function of a mean, we need the approximations to be accurate with sufficiently high probability. In particular, when these test probabilities are small it is best to consider relative errors. Here we show that in the case of univariate standardized means and in the general case of tests based on smooth functions of means, the empirical approximations have asymptotically small relative errors on...
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作者：Neumann, MH
作者单位：Humboldt University of Berlin; Universite Catholique Louvain
摘要：We derive an approximation of a density estimator based on weakly dependent random vectors by a density estimator built from independent random vectors. We construct, on a sufficiently rich probability space, such a pairing of the random variables of both experiments that the set of observations (X-1,..., X-n) from the time series model is nearly the same as the set of observations (Y-1,..., Y-n) from the i.i.d. model. With a high probability, all sets of the form ((X-1,..., X-n)Delta(Y-1,...,...
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作者：He, SY; Yang, GL
作者单位：Peking University; University System of Maryland; University of Maryland College Park
摘要：Under random truncation, a pair of independent random variables X and Y is observable only if X is larger than Y. The resulting model is the conditional probability distribution H(x, y) = P[X less than or equal to x, Y less than or equal to y\X greater than or equal to Y]. For the truncation probability alpha = P[X greater than or equal to Y], a proper estimate is not the sample proportion but alpha(n) = integral G(n)(s)dF(n)(s) where F-n and G(n) are product limit estimates of the distributio...
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作者：Snapp, RR; Venkatesh, SS
作者单位：University of Vermont; University of Pennsylvania
摘要：The finite-sample risk of the k nearest neighbor classifier that uses a weighted L-p-metric as a measure of class similarity is examined. For a family of classification problems with smooth distributions in R-n, an asymptotic expansion for the risk is obtained in decreasing fractional powers of the reference sample size. An analysis of the leading expansion coefficients reveals that the optimal weighted L-p-metric, that is, the metric that minimizes the finite-sample risk, tends to a weighted ...
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作者：Koo, JY; Chung, HY
作者单位：Hallym University
摘要：We estimate a probability density function p which is related by a linear operator K to a density function q in sequences of regular exponential families based on a random sample from q. In this paper deconvolution and positron emission tomography are considered. The logarithm of the density Function is approximated by basis functions consisting of singular functions of K. While direct maximum likelihood (or minimum Kullback-Leibler) density estimation in exponential families selects the param...
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作者：Munk, A; Dette, H
作者单位：Ruhr University Bochum; Ruhr University Bochum
摘要：A new test is proposed for the comparison of two regression curves f and g. We prove an asymptotic normal law under fixed alternatives which can be applied for power calculations, for constructing confidence regions and for testing precise hypotheses of a weighted L-2 distance between f and g. In particular, the problem of nonequal sample sizes is treated, which is related to a peculiar formula of the area between two step functions. These results are extended in various directions, such as th...
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作者：Qiu, PH
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We suggest a three-stage procedure to recover discontinuous regression surfaces when noisy data are present. In the first stage, jump candidate points are detected using a jump detection criterion. A local principal component line is then fitted through these points in a neighborhood of a design point. This line provides a first-order approximation to the true jump location curve in that neighborhood. In the third stage, observations on the same side of the line as the given point are combined...
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作者：Beran, R; Fisher, NI
作者单位：University of California System; University of California Berkeley; Commonwealth Scientific & Industrial Research Organisation (CSIRO)
摘要：Samples of directional or axial measurements arise in geophysical, biological and econometric contexts. We represent the rotational difference between two mean directions (or two mean axes) as a direction (or axis). We then construct nonparametric simultaneous confidence sets for all pairwise rotational differences among the mean directions or mean axes of s samples. By specialization, this methodology yields nonparametric simultaneous tests for pairwise equality of directional means or axes.
