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作者：Efron, Bradley
作者单位：Stanford University
摘要：Modern scientific technology has provided a new class of large-scale simultaneous inference problems, with thousands of hypothesis tests to consider at the same time. Microarrays epitomize this type of technology, but similar situations arise in proteomics, spectroscopy, imaging, and social science surveys. This paper uses false discovery rate methods to carry out both size and power calculations on large-scale problems. A simple empirical Bayes approach allows the false discovery rate (fdr) a...
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作者：Horowitz, Joel L.; Mammen, Enno
作者单位：Northwestern University; University of Mannheim
摘要：This paper discusses a nonparametric regression model that naturally generalizes neural network models. The model is based on a finite number of one-dimensional transformations and can be estimated with a one-dimensional rate of convergence. The model contains the generalized additive model with unknown link function as a special case. For this case, it is shown that the additive components and link function can be estimated with the optimal rate by a smoothing spline that is the solution of a...
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作者：He, Heping; Severini, Thomas A.
作者单位：Northwestern University; University of Melbourne
摘要：Approximations to the modified signed likelihood ratio statistic are asymptotically standard normal with error of order n(-1), where n is the sample size. Proofs of this fact generally require that the sufficient statistic of the model be written as ((theta) over cap, a), where theta is the maximum likelihood estimator of the parameter theta of the model and a is an ancillary statistic. This condition is very difficult or impossible to verify for many models. However, calculation of the statis...
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作者：Wu, Wei Biao
作者单位：University of Chicago
摘要：We study asymptotic properties of M-estimates of regression parameters in linear models in which errors are dependent. Weak and strong Bahadur representations of the M-estimates are derived and a central limit theorem is established. The results are applied to linear models with errors being short-range dependent linear processes, heavy-tailed linear processes and some widely used nonlinear time series.
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作者：Efromovich, Sam
作者单位：University of Texas System; University of Texas Dallas
摘要：Regression problems are traditionally analyzed via univariate characteristics like the regression function, scale function and marginal density of regression errors. These characteristics are useful and informative whenever the association between the predictor and the response is relatively simple. More detailed information about the association can be provided by the conditional density of the response given the predictor. For the first time in the literature, this article develops the theor...
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作者：Banerjee, Moulinath
作者单位：University of Michigan System; University of Michigan
摘要：The behavior of maximum likelihood estimates (MLEs) and the likelihood ratio statistic in a family of problems involving pointwise nonparametric estimation of a monotone function is studied. This class of problems differs radically from the usual parametric or semiparametric situations in that the MLE of the monotone function at a point converges to the truth at rate n(1/3) (slower than the usual root n rate) with a non-Gaussian limit distribution. A framework for likelihood based estimation o...
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作者：Hu, Zhishui; Robinson, John; Wang, Qiying
作者单位：University of Sydney
摘要：Cramer-type large deviations for means of samples from a finite population are established under weak conditions. The results are comparable to results for the so-called self-normalized large deviation for independent random variables. Cramer-type large deviations for the finite population Student t-statistic are also investigated.
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作者：Szekely, Gabor J.; Rizzo, Maria L.; Bakirov, Nail K.
作者单位：University System of Ohio; Bowling Green State University; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Hungarian Academy of Sciences; Russian Academy of Sciences
摘要：Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation, distance correlation is zero only if the random vectors are independent. The empirical distance dependence measures are based on certain Euclidean distances between sample elements rather than sample moments, yet have a compact representation analogous to the class...
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作者：Merkl, Franz; Mohammadi, Leila
作者单位：University of Munich; Leiden University; Leiden University Medical Center (LUMC); Leiden University - Excl LUMC
摘要：This paper is concerned with estimating the intersection point of two densities, given a sample of both of the densities. This problem arises in classification theory. The main results provide lower bounds for the probability of the estimation errors to be large on a scale determined by the inverse cube root of the sample size. As corollaries, we obtain probabilistic bounds for the prediction error in a classification problem. The key to the proof is an entropy estimate. The lower bounds are b...
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作者：Wang, Xiao; Woodroofe, Michael
作者单位：University System of Maryland; University of Maryland Baltimore County; University of Michigan System; University of Michigan
摘要：We extend the isotonic analysis for Wicksell's problem to estimate a regression function, which is motivated by the problem of estimating dark matter distribution in astronomy. The main result is a version of the Kiefer-Wolfowitz theorem comparing the empirical distribution to its least concave majorant, but with a convergence rate n(-1) log n faster than n(-2/3) log n. The main result is useful in obtaining asymptotic distributions for estimators, such as isotonic and smooth estimators.
