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作者：Zhao, Tianqi; Cheng, Guang; Liu, Han
作者单位：Princeton University; Purdue University System; Purdue University
摘要：We consider a partially linear framework for modeling massive heterogeneous data. The major goal is to extract common features across all subpopulations while exploring heterogeneity of each subpopulation. In particular, we propose an aggregation type estimator for the commonality parameter that possesses the (nonasymptotic) minimax optimal bound and asymptotic distribution as if there were no heterogeneity. This oracle result holds when the number of subpopulations does not grow too fast. A p...
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作者：Fissler, Tobias; Ziegel, Johanna F.
作者单位：University of Bern
摘要：A statistical functional, such as the mean or the median, is called elicitable if there is a scoring function or loss function such that the correct forecast of the functional is the unique minimizer of the expected score. Such scoring functions are called strictly consistent for the functional. The elicitability of a functional opens the possibility to compare competing forecasts and to rank them in terms of their realized scores. In this paper, we explore the notion of elicitability for mult...
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作者：Joseph, Antony; Yu, Bin
作者单位：University of California System; University of California Berkeley
摘要：The performance of spectral clustering can be considerably improved via regularization, as demonstrated empirically in Amini et al. [Ann. Statist. 41 (2013) 2097-2122]. Here, we provide an attempt at quantifying this improvement through theoretical analysis. Under the stochastic block model (SBM), and its extensions, previous results on spectral clustering relied on the minimum degree of the graph being sufficiently large for its good performance. By examining the scenario where the regulariza...
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作者：Cai, T. Tony; Liang, Tengyuan; Rakhlin, Alexander
作者单位：University of Pennsylvania
摘要：This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix estimation and noisy matrix completion. We propose computationally feasible convex programs for statistical inference including estimation, confidence intervals and hypothesis testing. A theoretical framework is developed to characterize the local estimation ...
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作者：Chen, Xiaohong; Shao, Qi-Man; Wu, Wei Biao; Xu, Lihu
作者单位：Yale University; Chinese University of Hong Kong; University of Chicago; University of Macau
摘要：We establish a Cramer-type moderate deviation result for self-normalized sums of weakly dependent random variables, where the moment requirement is much weaker than the non-self-normalized counterpart. The range of the moderate deviation is shown to depend on the moment condition and the degree of dependence of the underlying processes. We consider three types of self-normalization: the equal-block scheme, the big-block-small-block scheme and the interlacing scheme. Simulation study shows that...
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作者：Cavaliere, Giuseppe; Georgiev, Iliyan; Taylor, A. M. Robert
作者单位：University of Bologna; Universidade Nova de Lisboa; University of Essex
摘要：We extend the available asymptotic theory for autoregressive sieve estimators to cover the case of stationary and invertible linear processes driven by independent identically distributed (i.i.d.) infinite variance (IV) innovations. We show that the ordinary least squares sieve estimates, together with estimates of the impulse responses derived from these, obtained from an autoregression whose order is an increasing function of the sample size, are consistent and exhibit asymptotic properties ...
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作者：Lei, Huang; Xia, Yingcun; Qin, Xu
作者单位：Southwest Jiaotong University; National University of Singapore; University of Electronic Science & Technology of China
摘要：Serial correlation in the residuals of time series models can cause bias in both model estimation and prediction. However, models with such serially correlated residuals are difficult to estimate, especially when the regression function is nonlinear. Existing estimation methods require strong assumption for the relation between the residuals and the regressors, which excludes the commonly used autoregressive models in time series analysis. By extending the Whittle likelihood estimation, this p...
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作者：Dieuleveut, Aymeric; Bach, Francis
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS)
摘要：We consider the random-design least-squares regression problem within the reproducing kernel Hilbert space (RKHS) framework. Given a stream of independent and identically distributed input/output data, we aim to learn a regression function within an RKHS H, even if the optimal predictor (i.e., the conditional expectation) is not in H. In a stochastic approximation framework where the estimator is updated after each observation, we show that the averaged unregularized least-mean-square algorith...
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作者：Qu, Simeng; Wang, Jane-Ling; Wang, Xiao
作者单位：Purdue University System; Purdue University; University of California System; University of California Davis
摘要：Functional covariates are common in many medical, biodemographic and neuroimaging studies. The aim of this paper is to study functional Cox models with right-censored data in the presence of both functional and scalar covariates. We study the asymptotic properties of the maximum partial likelihood estimator and establish the asymptotic normality and efficiency of the estimator of the finite-dimensional estimator. Under the framework of reproducing kernel Hilbert space, the estimator of the coe...
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作者：Hayashi, Masahito; Watanabe, Shun
作者单位：Nagoya University; National University of Singapore; Tokyo University of Agriculture & Technology
摘要：We consider the parameter estimation of Markov chain when the unknown transition matrix belongs to an exponential family of transition matrices. Then we show that the sample mean of the generator of the exponential family is an asymptotically efficient estimator. Further, we also define a curved exponential family of transition matrices. Using a transition matrix version of the Pythagorean theorem, we give an asymptotically efficient estimator for a curved exponential family.
