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作者：MURPHY, SA
摘要：The frailty model is a generalization of Cox's proportional hazards model which includes a random effect. Nielsen, Gill, Andersen and Sorensen (1992) proposed an EM algorithm to estimate the cumulative baseline hazard and the variance of the random effect. Here the asymptotic distribution of the estimators is given along with a consistent estimator of the asymptotic variance.
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作者：DETTE, H; HEILIGERS, B; STUDDEN, WJ
作者单位：University of Augsburg; Purdue University System; Purdue University; University of Gottingen
摘要：In the usual linear regression model we investigate the geometric structure of a class of minimax optimality criteria containing Elfving's minimax and Kiefer's phi(p)-criteria as special cases. It is shown that the optimal designs with respect to these criteria are also optimal for A'theta, where A is any inball vector (in an appropriate norm) of a generalized Elfving set. The results explain the particular role of the A- and E-optimality criterion and are applied for determining the optimal d...
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作者：HALL, P; HU, TC; MARRON, JS
作者单位：National Tsing Hua University; University of North Carolina; University of North Carolina Chapel Hill
摘要：Variable window width kernel density estimators, with the width varying proportionally to the square root of the density, have been thought to have superior asymptotic properties. The rate of convergence has been claimed to be as good as those typical for higher-order kernels, which makes the variable width estimators more attractive because no adjustment is needed to handle the negativity usually entailed by the latter. However, in a recent paper, Terrell and Scott show that these results can...
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作者：CHENG, CS
摘要：In 1987 Cheng determined phi(p)-optimal designs for linear regression (without intercept) over the n-dimensional unit cube [0, 1](n) for -infinity less than or equal to p less than or equal to 1. These are uniform distributions on the vertices with a fixed number of entries equal to unity, and mixtures of neighboring such designs. In 1989 Pukelsheim showed that this class of designs is essentially complete and that the corresponding class of moment matrices is minimally complete, with respect ...
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作者：HASTIE, T; BUJA, A; TIBSHIRANI, R
作者单位：AT&T; Nokia Corporation; Nokia Bell Labs; University of Toronto; University of Toronto; Telcordia Technologies
摘要：Fisher's linear discriminant analysis (LDA) is a popular data-analytic tool for studying the relationship between a set of predictors and a categorical response. In this paper we describe a penalized version of LDA. It is designed for situations in which there are many highly correlated predictors, such as those obtained by discretizing a function, or the grey-scale values of the pixels in a series of images. In cases such as these it is natural, efficient and sometimes essential to impose a s...
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作者：YAKIR, B
作者单位：University of Rochester
摘要：A new proof is given to a known result on the average run length to false alarm of the Shiryayev-Roberts change-point detection policy when the observations are nonlattice. Via the approach of this new proof, the average run length to false alarm can be calculated in the lattice case and for the mixed-type Shiryayev-Roberts scheme.
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作者：GREENWOOD, PE; WEFELMEYER, W
作者单位：Universitat Siegen
摘要：Suppose we observe a uniformly ergodic Markov chain with unknown transition distribution. The empirical estimator for a linear functional of the (invariant) joint distribution of two successive observations is defined using the pairs of successive observations. Its efficiency is proved using a martingale approximation. As a corollary we show efficiency of the empirical joint distribution function in the sense of a functional convolution theorem.
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作者：BIRGE, L; MASSART, P
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
摘要：Let phi be a smooth function of k + 2 variables. We shall investigate in this paper the rates of convergence of estimators of T(f) = integral phi(f(x), f'(x),..., f((k))(x), x) dx when f belongs to some class of densities of smoothness s. We prove that, when s greater than or equal to 2k + 1/4, one can define an estimator (T) over cap(n) of T(f), based on n i.i.d. observations of density f on the real line, which converges at the semiparametric rate 1/root n. On the other hand, when s < 2k + 1...
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作者：EGGERMONT, PPB; LARICCIA, VN
摘要：We consider the problem of estimating a pdf f from samples X(1), X(2), ..., X(n) of a random variable with pdf Kf, where K is a compact integral operator. We employ a maximum smoothed likelihood formalism inspired by a nonlinearly smoothed version of the EMS algorithm of Silverman, Jones, Wilson and Nychka. We show that this nonlinearly smoothed algorithm is itself an EM algorithm, which helps explain the strong convergence properties of the algorithm. For the case of(standard) density estimat...
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作者：SIEGMUND, D; VENKATRAMAN, ES
作者单位：Memorial Sloan Kettering Cancer Center
摘要：We study sequential detection of a change-point using the generalized likelihood ratio statistic. For the special case of detecting a change in a normal mean with known variance, we give approximations to the average run lengths and compare our procedure to standard CUSUM tests and combined CUSUM-Shewhart tests. Several examples indicating extensions to problems involving multiple parameters are discussed.
