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作者：TERRELL, GR; SCOTT, DW
作者单位：Rice University
摘要：We investigate some of the possibilities for improvement of univariate and multivariate kernel density estimates by varying the window over the domain of estimation, pointwise and globally. Two general approaches are to vary the window width by the point of estimation and by point of the sample observation. The first possibility is shown to be of little efficacy in one variable. In particular, nearest-neighbor estimators in all versions perform poorly in one and two dimensions, but begin to be...
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作者：GUTENBRUNNER, C; JURECKOVA, J
作者单位：Charles University Prague
摘要：We show that regression quantiles, which could be computed as solutions of a linear programming problem, and the solutions of the corresponding dual problem, which we call the regression rank-scores, generalize the duality of order statistics and of ranks from the location to the linear model. Noting this fact, we study the regression quantile and regression rank-score processes in the heteroscedastic linear regression model, obtaining some new estimators and interesting comparisons with exist...
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作者：SHAKED, M; TONG, YL
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：In this note we study comparison of experiments via the positive dependence of normal variables with a common univariate marginal distribution. We show that positive dependence has an adverse effect on the information concerning the common mean theta, and give a partial ordering of the information via a majorization ordering of the correlation matrices. In the special case when the random variables are equally correlated, the main theorem yields a result for the comparison of experiments for p...
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作者：DATTA, S
摘要：In this paper we obtain uniform upper bounds for the L1 error of kernel estimators in estimating monotone densities and densities of bounded variation. The bounds are nonasymptotic and optimal in n, the sample size. For the bounded variation class, it is also optimal wrt an upper bound of the total variation. The proofs employ a one-sided kernel technique and are extremely simple.
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作者：KIM, SJ
作者单位：University of California System; University of California Berkeley
摘要：The metrically trimmed mean is defined as the average of observations remaining after a fixed number of outlying observations have been removed. A metric, the distance from the median, is used to determine which points are outlying. The influence curve and the asymptotic normality of the metrically trimmed mean are derived using von Mises expansions. The relative merits of the median, the trimmed mean and the metrically trimmed mean are discussed in neighborhoods of nonparametric models with n...
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作者：MARRON, JS; WAND, MP
作者单位：Rice University
摘要：An exact and easily computable expression for the mean integrated squared error (MISE) for the kernel estimator of a general normal mixture density, is given for Gaussian kernels of arbitrary order. This provides a powerful new way of understanding density estimation which complements the usual tools of simulation and asymptotic analysis. The family of normal mixture densities is very flexible and the formulae derived allow simple exact analysis for a wide variety of density shapes. A number o...
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作者：KANAZAWA, Y
摘要：Suppose we wish to construct a variable k-cell histogram based on an independent identically distributed sample of size n - 1 from an unknown density f on the interval of finite length. A variable cell histogram requires cutpoints and heights of all of its cells to be specified. We propose the following procedure: (i) choose from the order statistics corresponding to the sample a set of k + 1 cutpoints that maximize a criterion, a function of the sample spacings; (ii) compute heights of the k ...
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作者：HALL, P
摘要：The bootstrap is a poor estimator of bias in problems of curve estimation, and so bias must be corrected by other means when the bootstrap is used to construct confidence intervals for a probability density. Bias may either be estimated explicitly, or allowed for by undersmoothing the curve estimator. Which of these two approaches is to be preferred? In the present paper we address this question from the viewpoint of coverage accuracy, assuming a given number of derivatives of the unknown dens...
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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...
