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作者：Neumann, MH
摘要：In the present paper we combine the issues of bandwidth choice and construction of confidence intervals in nonparametric regression. Main emphasis is put on fully data-driven methods. We modify the root n-consistent bandwidth selector of Hardle, Hall and Marron such that it is appropriate for heteroscedastic data, and we show how one can optimally choose the bandwidth g of the pilot estimator <(m)over cap(g)>. Then we consider classical confidence intervals based on kernel estimators with data...
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作者：Eubank, RL; Hart, JD; Simpson, DG; Stefanski, LA
作者单位：North Carolina State University; University of Illinois System; University of Illinois Urbana-Champaign
摘要：Additive models are one means of assuaging the curse of dimensionality when nonparametric smoothing methods are used to estimate multivariable regression functions. It is important to have methods for testing the fit of such models, especially in high dimensions where visual assessment of fit becomes difficult. New tests of additivity are proposed in this paper that derive from Fourier series estimators with data-driven smoothing parameters. Other tests related to the classical Tukey test for ...
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作者：Ghosal, S; Ghosh, JK; Samanta, T
作者单位：Indian Statistical Institute; Indian Statistical Institute Kolkata
摘要：A general (asymptotic) theory of estimation was developed by Ibragimov and Has'minskii under certain conditions on the normalized likelihood ratios. In an earlier work, the present authors studied the limiting behaviour of the posterior distributions under the general setup of Ibragimov and Has'minskii. In particular, they obtained a necessary condition for the convergence of a suitably centered (and normalized) posterior to a constant limit in terms of the limiting likelihood ratio process. I...
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作者：Seidenfeld, T; Schervish, MJ; Kadane, JB
作者单位：Carnegie Mellon University
摘要：This essay considers decision-theoretic foundations for robust Bayesian statistics. We modify the approach of Ramsey, de Finetti, Savage and Anscombe and Aumann in giving axioms for a theory of robust preferences. We establish that preferences which satisfy axioms for robust preferences can be represented by a set of expected utilities. Tn the presence of two axioms relating to state-independent utility, robust preferences are represented by a set of probability/utility pairs, where the utilit...
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作者：Wahba, G; Wang, YD; Gu, C; Klein, R; Klein, B
作者单位：Purdue University System; Purdue University; University of Michigan System; University of Michigan; University of Wisconsin System; University of Wisconsin Madison
摘要：Let y(i), i = 1, ..., n, be independent observations with the density of y(i) of the form h(y(i), f(i)) = exp[y(i)f(i) - b(f(i)) + c(y(i))], where b and c are given functions and b is twice continuously differentiable and bounded away from 0. Let f(i) = f(t(i)), where t = (t(1), ..., t(d)) is an element of J((1)) x ... x J((d)) = J, the J((alpha)) are measurable spaces of rather general form and f is an unknown function on J with some assumed ''smoothness'' properties. Given {y(i), t(i), i = 1...
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作者：Wei, XY
摘要：We propose a conditional MLE of the index of regular variation when the functional form of a slowly varying function is assumed known in the tail, and we study its asymptotic properties. We prove asymptotic normality of P-theta(kn), a probability measure whose density is the product of the joint conditional density of the k(n) largest order statistics from F-theta(x) given Z(n - k), the (n - k)th order statistic, and a density of Z(n - k) with parameter theta. Based on this result, we shore th...
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作者：Hall, P; Lahiri, SN; Truong, YK
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Iowa State University
摘要：We address the empirical bandwidth choice problem in cases where the range of dependence may be virtually arbitrarily long. Assuming that the observed data derive from an unknown function of a Gaussian process, it is argued that, unlike more traditional contexts of statistical inference, in density estimation there is no clear role for the classical distinction between short- and long-range dependence. Indeed, the ''boundaries'' that separate different modes of behaviour for optimal bandwidths...
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作者：Menendez, JA; Salvador, B
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作者：Mukerjee, R; Wu, CFJ
作者单位：University of Michigan System; University of Michigan
摘要：We develop a combinatorial condition necessary for the existence of a saturated asymmetrical orthogonal array of strength 2. This condition Limits the choice of integral solutions to the system of equations in the Bose-Bush approach and can thus strengthen considerably the Bose-Bush approach as applied to a symmetrical part of such an array. As a consequence, several nonexistence results follow for saturated and nearly saturated orthogonal arrays of strength 2. One of these leads to a partial ...
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作者：Xu, Y; Martinsek, AT
摘要：This paper proposes a fully sequential procedure for constructing a fixed-width confidence band for an unknown density on a finite interval and shows the procedure has the desired coverage probability asymptotically as the width of the band approaches zero. The procedure is based on a result-of Bickel and Rosenblatt. Its implementation in the sequential setting cannot be obtained using Anscombe's theorem, because the normalized maximal deviations between the kernel estimate and the true densit...
