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作者：Stein, ML
摘要：For a stationary random field Z on R(d), this work studies the asymptotic behavior of predictors of integral v(x)Z(x) dx based on observations on a lattice as the distance between neighbors in the lattice tends to 0. Under a mild condition on the spectral density of Z, an asymptotic expression for the mean-squared error of a predictor of integral v(x)Z(x) dx based on observations on an infinite lattice is derived. For predicting integrals over the unit cube, a simple predictor based just on ob...
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作者：LOW, MG
摘要：It is shown in infinite-dimensional Gaussian problems that affine estimators minimax the variance among all estimators of a linear functional subject to a constraint on the bias. Likewise, affine estimators also minimax the square of the bias among all estimates of a linear functional subject to a constraint on the variance.
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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：ZHANG, CH
摘要：This paper concerns estimating a mixing density function g and its derivatives based on lid observations from f(x) = integral f(x \ theta)g(theta) d theta, where f(x \ theta) is a known exponential family of density functions with respect to the counting measure on the set of nonnegative integers. Fourier methods are used to derive kernel estimators, upper bounds for their rate of convergence and lower bounds for the optimal rate of convergence. If f(x \ theta(o)) greater than or equal to epsi...
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作者：MAMMEN, E; TSYBAKOV, AB
作者单位：Sorbonne Universite
摘要：In this paper optimal rates of convergence are derived for estimates of sets in N-dimensional ''black and white'' pictures under smoothness conditions. It is assumed that the boundaries of the ''black'' regions have a smooth parameterisation, that is, that the boundaries are given by smooth functions from the sphere S-N-1 into R(N). Furthermore, classes of convex regions are considered. Two models are studied: edge estimation models motivated by image segmentation problems and density support ...
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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：Nielsen, JP; Linton, OB
作者单位：Yale University
摘要：We introduce a new kernel hazard estimator in a nonparametric model where the stochastic hazard depends on the current value of time and on the current value of a time dependent covariate or marker. We establish the pointwise and global convergence of our estimator.
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作者：VandeGeer, S
摘要：We obtain an exponential probability inequality for martingales and a uniform probability inequality for the process integral gdN, where N is a counting process and where g varies within a class of predictable functions g. For the latter, we use techniques from empirical process theory. The uniform inequality is shown to hold under certain entropy conditions on g. As an application, we consider rates of convergence for (nonparametric) maximum likelihood estimators for counting processes. A sim...
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作者：SIEGMUND, DO; WORSLEY, KJ
作者单位：McGill University
摘要：We suppose that our observations can be decomposed into a fixed signal plus random noise, where the noise is modelled as a particular stationary Gaussian random field in N-dimensional Euclidean space. The signal has the form of a known function centered at an unknown location and multiplied by an unknown amplitude, and we are primarily interested in a test to detect such a signal. There are many examples where the signal scale or width is assumed known, and the test is based on maximising a Ga...
