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作者：Díaz-García, JA; Jáimez, RG
作者单位：University of Granada
摘要：Uhlig proposes two conjectures. The first concerns the Jacobian of the transformation Y = B X B' where B is the matrix m x m and m and X, Y belong to the class of positive semidefinite matrices of the order of m X m of rank n < m, S-m,n(+). The second is concerned with the singular multivariate Beta distribution. This article seeks to prove the two conjectures. The latter result is then extended to the case of the singular multivariate F distribution, and the respective density functions are l...
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作者：Koshevoy, G; Mosler, K
作者单位：Russian Academy of Sciences; Central Economics & Mathematics Institute RAS; University of Cologne
摘要：A family of trimmed regions is introduced for a probability distribution in Euclidean d-space. The regions decrease with their parameter Lu, from the closed convex hull of support (at alpha = 0) to the expectation vector (at alpha = 1). The family determines the underlying distribution uniquely. For every cu the region is affine equivariant and continuous with respect to weak convergence of distributions. The behavior under mixture and dilation is studied. A new concept of data depth is introd...
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作者：Kitamura, Y
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：This paper studies the method of empirical likelihood in models with weakly dependent processes. In such cases, if the likelihood function is formulated as if the data process were independent, obviously empirical likelihood fails. We propose to use empirical likelihood of blocks of observations to solve this problem in a nonparametric manner. This method of blockwise empirical likelihood preserves the dependence of data, and the resulting likelihood ratios can be used to construct asymptotica...
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作者：Hedayat, S; Stufken, J; Su, GQ
作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Iowa State University
摘要：We study the construction of orthogonal arrays with three levels and index 1 and the existence of orthogonal arrays with three levels and index 2. For strength greater than or equal to 2, we show that orthogonal arrays with three levels and index 1 are unique, and we establish the maximum number of factors for orthogonal arrays with three levels and index 2.
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作者：Lindsay, BG; Li, B
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：The realized error of an estimate is determined not only by the efficiency of the estimator, but also by chance. For example, suppose that we have observed a bivariate normal vector whose expectation is known to be on a circle. Then, intuitively, the longer that vector happens to be, the more accurately its angle is likely to be estimated. Yet this chance, though its information is contained in the data, cannot be accounted for by the variance of the estimate. One way to capture it is by the d...
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作者：Gather, U; Hilker, T
作者单位：Dortmund University of Technology
摘要：In 1994 Tyler proposed a modification of the MAD in order to achieve the maximal possible finite sample breakdown point for the Stahel-Donoho estimator based upon the median and the modified MAD. A proof is not given, however, and as far as we know has not been published yet. Moreover there seems to be an error concerning the exact definition of the modified MAD which is needed to achieve this goal. For the sake of theoretical completeness and in order to correct this error we calculate the fi...
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作者：Liu, W
作者单位：University of Southampton
摘要：A new sequential sampling scheme is proposed in which, after an initial batch sample, sampling is continued in batches of data-dependent sizes (at most k such batches), and then one-at-a-time with a data-dependent stopping rule. This new scheme requires about the same sample size as the fully sequential Anscombe-Chow-Robbins (ACR) sampling scheme but substantially fewer sampling operations. The problem of constructing fixed-width confidence intervals for the mean of a normal population with un...
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作者：Robinson, PM
作者单位：University of London; London School Economics & Political Science
摘要：A central limit theorem is given for certain weighted partial sums of a covariance stationary process, assuming it is linear in martingale differences, but without any restriction on its spectrum. We apply the result to kernel nonparametric fixed-design regression, giving a single central limit theorem which indicates how error spectral behavior at only zero frequency influences the asymptotic distribution and covers long-range, short-range and negative dependence. We show how the regression e...
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作者：Walther, G
作者单位：Stanford University
摘要：The Kolmogorov-Smirnov distance is an important tool for constructing confidence sets and tests in univariate problems. In multivariate settings, an analogous role is played by the halfspace distance, which has the merit of being invariant under linear transformations. However, the evaluation of the halfspace distance between two samples is a computationally very intensive combinatorial problem even in moderate dimensions, which severely restricts the use of the halfspace distance, especially ...
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作者：Yakir, B
作者单位：Hebrew University of Jerusalem
摘要：Suppose X-1, X-2,..., Xv-1 are lid random variables with distribution F-0, and X-v, Xv+1,... are are lid with distributed F-1. The change point v is unknown. The problem is to raise an alarm as soon as possible after the distribution changes from F-0 to F-1 (detect the change), but to avoid false alarms. Pollak found a version of the Shiryayev-Roberts procedure to be asymptotically optimal for the problem of minimizing the average run length to detection over all stopping times which satisfy a...
