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作者：Hong, Han; Li, Jessie
作者单位：Stanford University; University of California System; University of California Santa Cruz
摘要：This paper proposes a numerical bootstrap method that is consistent in many cases where the standard bootstrap is known to fail and where the m-out-of-n bootstrap and subsampling have been the most commonly used inference approaches. We provide asymptotic analysis under both fixed and drifting parameter sequences, and we compare the approximation error of the numerical bootstrap with that of the m-out-of-n bootstrap and subsampling. Finally, we discuss applications of the numerical bootstrap, ...
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作者：Deng, Hang; Zhang, Cun-Hui
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：In this paper, we study minimax and adaptation rates in general isotonic regression. For uniform deterministic and random designs in [0, 1](d) with d >= 2 and N(0, 1) noise, the minimax rate for the l(2) risk is known to be bounded from below by n(-1/d) when the unknown mean function f is non-decreasing and its range is bounded by a constant, while the least squares estimator (LSE) is known to nearly achieve the minimax rate up to a factor (log n)(gamma) where n is the sample size, gamma = 4 i...
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作者：Patilea, Valentin; Van Keilegom, Ingrid
作者单位：Universite de Rennes; Ecole Nationale de la Statistique et de l'Analyse de l'Information (ENSAI); KU Leuven
摘要：In survival analysis it often happens that some subjects under study do not experience the event of interest; they are considered to be cured. The population is thus a mixture of two subpopulations, one of cured subjects and one of susceptible subjects. We propose a novel approach to estimate a mixture cure model when covariates are present and the lifetime is subject to random right censoring. We work with a parametric model for the cure proportion, while the conditional survival function of ...
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作者：Wu, Yihong; Yang, Pengkun
作者单位：Yale University; Princeton University
摘要：The method of moments (Philos. Trans. R. Soc. Lond. Ser. A 185 (1894) 71-110) is one of the most widely used methods in statistics for parameter estimation, by means of solving the system of equations that match the population and estimated moments. However, in practice and especially for the important case of mixture models, one frequently needs to contend with the difficulties of non-existence or nonuniqueness of statistically meaningful solutions, as well as the high computational cost of s...
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作者：Saha, Sujayam; Guntuboyina, Adityanand
作者单位：University of California System; University of California Berkeley
摘要：We study the nonparametric maximum likelihood estimator (NPMLE) for estimating Gaussian location mixture densities in d-dimensions from independent observations. Unlike usual likelihood-based methods for fitting mixtures, NPMLEs are based on convex optimization. We prove finite sample results on the Hellinger accuracy of every NPMLE. Our results imply, in particular, that every NPMLE achieves near parametric risk (up to logarithmic multiplicative factors) when the true density is a discrete Ga...
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作者：Tang, Niansheng; Yan, Xiaodong; Zhao, Xingqiu
作者单位：Yunnan University; Shandong University; Hong Kong Polytechnic University
摘要：This article considers simultaneous variable selection and parameter estimation as well as hypothesis testing in censored survival models where a parametric likelihood is not available. For the problem, we utilize certain growing dimensional general estimating equations and propose a penalized generalized empirical likelihood, where the general estimating equations are constructed based on the semiparametric efficiency bound of estimation with given moment conditions. The proposed penalized ge...
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作者：Han, Qiyang; Zhang, Cun-Hui
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：We study limit distributions for the tuning-free max-min block estimator originally proposed in (Fokianos, Leucht and Neumann (2017)) in the problem of multiple isotonic regression, under both fixed lattice design and random design settings. We show that, if the regression function f(0) admits vanishing derivatives up to order alpha(k) along the kth dimension (k = 1, ..., d) at a fixed point x(0) is an element of (0, 1)(d), and the errors have variance sigma(2), then the max-min block estimato...
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作者：Bagchi, Pramita; Dette, Holger
作者单位：George Mason University; Ruhr University Bochum
摘要：The assumption of separability is a simplifying and very popular assumption in the analysis of spatiotemporal or hypersurface data structures. It is often made in situations where the covariance structure cannot be easily estimated, for example, because of a small sample size or because of computational storage problems. In this paper we propose a new and very simple test to validate this assumption. Our approach is based on a measure of separability which is zero in the case of separability a...
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作者：Fang, Xiao; Li, Jian; Siegmund, David
作者单位：Chinese University of Hong Kong; Adobe Systems Inc.; Stanford University
摘要：To segment a sequence of independent random variables at an unknown number of change-points, we introduce new procedures that are based on thresholding the likelihood ratio statistic, and give approximations for the probability of a false positive error when there are no change-points. We also study confidence regions based on the likelihood ratio statistic for the change-points and joint confidence regions for the change-points and the parameter values. Applications to segment array CGH data ...
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作者：Xi, Haokai; Yang, Fan; Yin, Jun
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of California System; University of California Los Angeles
摘要：The eigenvector empirical spectral distribution (VESD) is a useful tool in studying the limiting behavior of eigenvalues and eigenvectors of covariance matrices. In this paper, we study the convergence rate of the VESD of sample covariance matrices to the deformed Marcenko-Pastur (MP) distribution. Consider sample covariance matrices of the form Sigma(XX)-X-1/2* Sigma(1/2), where X = (x(ij)) is an M x N random matrix whose entries are independent random variables with mean zero and variance N-...
