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作者：Lin, Y
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：To deal with the curse of dimensionality in high-dimensional nonparametric problems, we consider using tensor product space ANOVA models, which extend the popular additive models and are able to capture interactions of any order. The multivariate function is given an ANOVA decomposition, that is, it is expressed as a constant plus the sum of functions of one variable (main effects), plus the sum of functions of two variables (two-factor interactions) and so on. We assume the interactions to be...
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作者：Bartolucci, F; Forcina, A
作者单位：University of Perugia
摘要：Multivariate Totally Positive (MTP2) binary distributions have been studied in many fields, such as statistical mechanics, computer storage and latent variable models. We show that MTP2 is equivalent to the requirement that the parameters of a saturated log-linear model belong to a convex cone, and we provide a Fisher-scoring algorithm for maximum likelihood estimation. We also show that the asymptotic distribution of the log-likelihood ratio is a mixture of chi-squares (a distribution known a...
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作者：Meyer, M; Woodroofe, M
作者单位：University System of Georgia; University of Georgia; University of Michigan System; University of Michigan
摘要：For the problem of estimating a regression function, mu say, subject to shape constraints, like monotonicity or convexity it is argued that the divergence of the maximum likelihood estimator provides a useful measure of the effective dimension of the model. Inequalities are derived for the expected mean squared error of the maximum likelihood estimator and the expected residual sum of squares. These generalize equalities from the case of linear regression. As an application, it is shown that t...
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作者：Picard, D; Tribouley, K
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：We present a procedure associated with nonlinear wavelet methods that provides adaptive confidence intervals around f(x(0)), in either a white noise model or a regression setting. A suitable modification in the truncation rule for wavelets allows construction of confidence intervals that achieve optimal coverage accuracy up to a logarithmic factor. The procedure does not require knowledge of the regularity of the unknown function f; it is also efficient for functions with a low degree of regul...
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作者：Loh, WL; Lam, TK
作者单位：National University of Singapore; Dell Incorporated; Dell EMC
摘要：This article considers the estimation of structured correlation matrices in infinitely differentiable Gaussian random field models. The problem is essentially motivated by the stochastic modeling of smooth deterministic responses in computer experiments. In particular, the log-likelihood function is determined explicitly in closed-form and the sieve maximum likelihood estimators are shown to be strongly consistent under mild conditions.
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作者：Chen, K
作者单位：Hong Kong University of Science & Technology
摘要：Fixed case-control studies separately collect a case sample and a control sample with the two sample sizes being fixed prior to studies and sometimes arbitrarily chosen. This often results in loss of efficiency of case-control designs in terms of cost-saving or time-saving of the studies. We study sequential case-control designs and, in connection with treatment allocation and stochastic approximation, derive a simple sampling rule that leads to optimal case-control designs. Some important iss...
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作者：Hall, P; Rau, C
作者单位：Australian National University; Commonwealth Scientific & Industrial Research Organisation (CSIRO)
摘要：We suggest a sequential, or tracking, algorithm for estimating a smooth fault line in a response surface. The method starts with an approximation to a point on the line, and from there the line is tracked as it meanders through the plane. The technique differs from recent approaches in that it does not require a large part of the plane to be searched for evidence of a fault line. This offers potential computational savings, and produces a method that is invariant under rotations of coordinate ...
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作者：Knight, K; Fu, WJ
作者单位：University of Toronto; Michigan State University
摘要：We consider the asymptotic behavior of regression estimators that minimize the residual sum of squares plus a penalty proportional to Sigma\beta (j)\(gamma) for some gamma > 0. These estimators include the Lasso as a special case when gamma = 1. Under appropriate conditions, we show that the limiting distributions can have positive probability mass at 0 when the true value of the parameter is 0. We also consider asymptotics for nearly singular designs.
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作者：Politis, K; Pitts, SM
作者单位：University of Southampton; University of Cambridge
摘要：Nonparametric estimators of solutions of renewal-type equations are proposed in terms of the empirical renewal function. Using the approach of Grubel and Pitts [Ann. Stat. 21 1431-1451(1993)], who studied asymptotic properties of the empirical renewal function, a number of properties of our estimators are established, including strong consistency, asymptotic normality and efficiency, and asymptotic validity of bootstrap confidence bounds. The results are illustrated by some particular examples.
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作者：Xiong, MM; Guo, SW
作者单位：University of Texas System; University of Texas Health Science Center Houston; Medical College of Wisconsin
摘要：The interval mapping method has been shown to be a powerful tool for mapping QTL. However, it is still a challenge to perform a simultaneous analysis of several linked QTLs, and to isolate multiple linked QTLs. To circumvent these problems, multiple regression analysis has been suggested for experimental species. In this paper, the multiple regression approach is extended to human sib-pair data through multiple regression of the squared difference in trait values between two sibs on the propor...
