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作者：CHAUDHURI, P
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：Let (X,Y) be a random vector such that X is d-dimensional, Y is real valued and Y = theta-(X) + epsilon, where X and epsilon-are independent and the alpha-th quantile of epsilon-is 0 (alpha-is fixed such that 0 < alpha < 1). Assume that theta-is a smooth function with order of smoothness p > 0, and set r = (p - m)/(2p + d), where m is a nonnegative integer smaller than p. Let T(theta) denote a derivative of theta-of order m. It is proved that there exists a pointwise estimate T triple-over-dot...
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作者：ALBERS, W
摘要：In this paper we present a rank analogue to Stein's two-stage procedure. We analyze its behavior to second order using existing asymptotic expansions for fixed sample size rank tests and recent results on combinations of independent rank statistics.
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作者：MAMMEN, E
摘要：The problem of estimating a smooth monotone regression function m will be studied. We will consider the estimator m(SI) consisting of a smoothing step (application of a kernel estimator based on a kernel K) and of a isotonisation step (application of the pool adjacent violator algorithm). The estimator m(SI) will be compared with the estimator m(IS) where these two steps are interchanged. A higher order stochastic expansion of these estimators will be given which show that m(SI) and m(IS) are ...
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作者：VANZUIJLEN, MCA
作者单位：Radboud University Nijmegen
摘要：Under minimal conditions precise bounds are obtained for the expectation of the supremum of the weighted empirical process over the interval (0, 1/(n(log n)d-1)), where d is the dimension of the underlying random vectors. The allowed growth of the weight function is optimal in the iid case. The results will have broad applications in the theory of all kinds of nonstandard weighted empirical processes, such as empirical processes based on uniform spacings or U-statistics, where it is often not ...
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作者：WONG, WH; SEVERINI, TA
作者单位：Northwestern University
摘要：An approximate maximum likelihood estimate is known to be consistent under some compactness and integrability conditions. In this paper we study its convergence rate and its asymptotic efficiency in estimating smooth functionals of the parameter. We provide conditions under which the rate of convergence can be established. This rate is essentially governed by the size of the space of score functions as measured by an entropy index. We also show that, for a large class of smooth functionals, th...
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作者：BUCKLEW, JA; NEY, PE
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：The binary hypothesis testing problem of deciding between two Markov chains is formulated under memory constraints. The optimality criterion used is the exponential rate with which the probability of error approaches zero as the sample size tends to infinity. The optimal memory constrained test is shown to be the solution of a set of equations derived from suitable large deviation twistings of the transition matrices under the two hypotheses. A computational algorithm and some examples are giv...
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作者：GHOSH, BK; HUANG, WM
摘要：Bickel and Rosenblatt proposed a procedure for testing the goodness of fit of a specified density to observed data. The test statistic is based on the distance between the kernel density estimate and the hypothesized density, and it depends on a kernel K, a bandwidth b(n) and an arbitrary weight function a. We study the behavior of the asymptotic power of the test and show that a uniform kernel maximizes the power when a > 0.
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作者：BICKEL, PJ; RITOV, J
作者单位：Hebrew University of Jerusalem; Nokia Corporation; Nokia Bell Labs; AT&T; New York University
摘要：Biased sampling regression models were introduced by Jewell, generalizing the truncated regression model studied by Bhattacharya, Chernoff and Yang. If the independent variable takes on only a finite number of values (as does the stratum variable), we show: 1. That if the slope of the underlying regression model is assumed known, then the nonparametric maximum likelihood estimates of the distribution of the independent and dependent variables (a) can be calculated from ordinary M estimates; (b...
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作者：HALL, P
摘要：We derive Bahadur-type representations for quantile estimates obtained from two different types of nonparametric bootstrap resampling-the commonly used uniform resampling method, where each sample value is drawn with the same probability, and importance resampling, where different sample values are assigned different resampling weights. These results are applied to obtain the relative efficiency of uniform resampling and importance resampling and to derive exact convergence rates, both weakly ...
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作者：MAMMEN, E
摘要：We propose a new nonparametric regression estimate. In contrast to the traditional approach of considering regression functions whose m th derivatives lie in a ball in the L-infinity or L2 norm, we consider the class of functions whose (m - 1)st derivative consists of at most k monotone pieces. For many applications this class seems more natural than the classical ones. The least squares estimator of this class is studied. It is shown that the speed of convergence is as fast as in the classica...
