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作者：Robinson, J; Skovgaard, IM
作者单位：University of Sydney; University of Copenhagen
摘要：To obtain test probabilities based on empirical approximations to the distribution of a Studentized function of a mean, we need the approximations to be accurate with sufficiently high probability. In particular, when these test probabilities are small it is best to consider relative errors. Here we show that in the case of univariate standardized means and in the general case of tests based on smooth functions of means, the empirical approximations have asymptotically small relative errors on...
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作者：Munk, A; Dette, H
作者单位：Ruhr University Bochum; Ruhr University Bochum
摘要：A new test is proposed for the comparison of two regression curves f and g. We prove an asymptotic normal law under fixed alternatives which can be applied for power calculations, for constructing confidence regions and for testing precise hypotheses of a weighted L-2 distance between f and g. In particular, the problem of nonequal sample sizes is treated, which is related to a peculiar formula of the area between two step functions. These results are extended in various directions, such as th...
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作者：Qiu, PH
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We suggest a three-stage procedure to recover discontinuous regression surfaces when noisy data are present. In the first stage, jump candidate points are detected using a jump detection criterion. A local principal component line is then fitted through these points in a neighborhood of a design point. This line provides a first-order approximation to the true jump location curve in that neighborhood. In the third stage, observations on the same side of the line as the given point are combined...
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作者：Tsybakov, AB
作者单位：Sorbonne Universite
摘要：The problem of nonparametric function estimation in the Gaussian white noise model is considered. It is assumed that the unknown function belongs to one of the Sobolev classes, with an unknown regularity parameter. Asymptotically exact adaptive estimators of functions are proposed on the scale of Sobolev classes, with respect to pointwise and sup-norm risks. It is shown that, unlike the case of L-2-risk, a loss of efficiency under adaptation is inevitable here. Bounds on the value of the loss ...
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作者：Hall, P; Raimondo, M
作者单位：Australian National University
摘要：Approximating boundaries using data recorded on a regular grid induces discrete rounding errors in both vertical and horizontal directions. In cases where grid points exhibit at least some degree of randomness, an extensive theory has been developed for local-polynomial boundary estimators. It is inapplicable to regular grids, however. In this paper we impose strict regularity of the grid and describe the performance of local linear estimators in this context. Unlike the case of classical curv...
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作者：Adrover, JG
作者单位：National University of Cordoba
摘要：Maronna defines affine equivariant M-estimators for multivariate location and scatter. They are particularly suited for estimating the pseudo-covariance or scatter matrix of an elliptical population. By defining the bias of a dispersion matrix properly, we consider the maximum bias of an M-estimator over an E-neighborhood of the underlying elliptical distribution (location known). We find that Tyler's estimator minimizes the maximum bias.
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作者：Niu, XF
作者单位：State University System of Florida; Florida State University
摘要：Consider a space-time stochastic process Z(t)(x) = S(x)+ xi(t)(x) where S(x) is a signal process defined on R-d and xi(t)(x) represents measurement errors at time t. For a known measurable function v(x) on R-d and a fixed cube D subset of R-d, this paper proposes a linear estimator for the stochastic integral integral(D) v(x)S(x)dx based on space-time observations {Z(t)(x(i)): i = 1,..., n; t = 1,..., T}. Under mild conditions, the asymptotic properties of the mean squared error of the estimat...
