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作者：Johnstone, IM
作者单位：Stanford University
摘要：Let x((1)) denote the square of the largest singular value of an n x p matrix X, all of whose entries are independent standard Gaussian variates. Equivalently, x((1)) is the largest principal component variance of the covariance matrix X'X, or the largest eigenvalue of a p-variate Wishart distribution on n degrees of freedom with identity covariance. Consider the limit of large p and n with n/p = gamma greater than or equal to 1. When centered by mu (p) = (rootn - 1 + rootp)(2) and scaled by s...
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作者：Kuriki, S; Takemura, A
作者单位：Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan; University of Tokyo
摘要：Let Z be a k-way array consisting of independent standard normal variables. For column vectors h(1), ..., h(k), define a multilinear form of deg-ree k by (h(1) circle times . . . circle times h(k))'vec(Z). We derive formulas for upper tail probabilities of the maximum of a multilinear form with respect to the h(i)'s under the condition that the h(i)'s are unit vectors, and of its standardized statistic obtained by dividing by the norm of Z. We also give formulas for the maximum of a symmetric ...
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作者：Xu, HQ; Wu, CFJ
作者单位：University of Michigan System; University of Michigan
摘要：By studying treatment contrasts and ANOVA models, we propose a generalized minimum aberration criterion for comparing asymmetrical fractional factorial designs. The criterion is independent of the choice of treatment contrasts and thus model-free. It works for symmetrical and asymmetrical designs, regular and nonregular designs. In particular, it reduces to the minimum aberration criterion for regular designs and the minimum G(2)-aberration criterion for two-level nonregular designs. In additi...
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作者：Bagchi, B; Bagchi, S
作者单位：Indian Statistical Institute; Indian Statistical Institute Bangalore
摘要：We find a sufficient condition on the spectrum of a partial geometric design d* such that, when d* satisfies this condition, it is better (with respect to all convex decreasing optimality criteria) than all unequally replicated designs (binary or not) with the same parameters b, v, h as d*. Combining this with existing results, we obtain the following results: (i) For any q greater than or equal to 3, a linked block design with parameters b = q(2), = q(2)+q, k = q(2)-1 is optimal with respect ...
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作者：Goldenshluger, A; Zeevi, A
作者单位：University of Haifa; Stanford University
摘要：The subject of this paper is autoregressive (AR) modeling of a stationary, Gaussian discrete time process, based on a finite sequence of observations. The process is assumed to admit an AR(co) representation with exponentially decaying coefficients. We adopt the nonparametric minimax framework and study how well the process can be approximated by a finite-order AR model. A lower bound on the accuracy of AR approximations is derived, and a nonasymptotic upper bound on the accuracy of the regula...
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作者：Cheng, CS; Mukerjee, R
作者单位：University of California System; University of California Berkeley; Indian Institute of Management (IIM System); Indian Institute of Management Calcutta
摘要：In this paper, the problem of constructing optimal blocked regular fractional factorial designs is considered. The concept of minimum aberration due to Fries and Hunter is a well-accepted criterion for selecting good unblocked fractional factorial designs. Cheng, Steinberg and Sun showed that a minimum aberration design of resolution three or higher maximizes the number of two-factor interactions which are not aliases of main effects and also tends to distribute these interactions over the ali...
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作者：Horváth, L; Kokoszka, P; Teyssière, G
作者单位：Utah System of Higher Education; University of Utah; European Commission Joint Research Centre; EC JRC ISPRA Site; University of Liverpool
摘要：We derive the asymptotic distribution of the sequential empirical process of the squared residuals of an ARCH(p) sequence. Unlike the residuals of an ARMA process, these residuals do not behave in this context like asymptotically independent random variables, and the asymptotic distribution involves a term depending on the parameters of the model. We show that in certain applications, including the detection of changes in the distribution of the unobservable innovations, our result leads to as...
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作者：Karlsen, HA; Tjostheim, D
作者单位：University of Bergen
摘要：We develop a nonparametric estimation theory in a nonstationary environment, more precisely in the framework of null recurrent Markov chains. An essential tool is the split chain, which makes it possible to decompose the times series under consideration into independent and identical parts. A tail condition on the distribution of the recurrence time is introduced. This condition makes it possible to prove weak convergence results for sums of functions of the process depending on a smoothing pa...
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作者：Efron, B
作者单位：Stanford University
摘要：Scatterplot smoothers estimate a regression function y = f(x) by local averaging of the observed data points (x(i), y(i)). In using a smoother, the statistician must choose a window width, a crucial smoothing parameter that says just how locally the averaging is done. This paper concerns the data-based choice of a smoothing parameter for splinelike smoothers, focusing on the comparison of two popular methods, C-p and generalized maximum likelihood. The latter is the MLE within a normal-theory ...
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作者：Geiger, D; Heckerman, D; King, H; Meek, C
作者单位：Technion Israel Institute of Technology; University System of Maryland; University of Maryland College Park
摘要：We describe a hierarchy of exponential families which is useful for distinguishing types of graphical models. Undirected graphical models with no hidden variables are linear exponential families (LEFs). Directed acyclic graphical (DAG) models and chain graphs with no hidden variables, including DAG models with several families of local distributions, are curved exponential families (CEFs). Graphical models with hidden variables are what we term stratified exponential families (SEFs). A SEF is ...
