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作者：Akritas, Michael G.
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：For a response variable Y, and a d dimensional vector of covariates X, the first projective direction, V, is defined as the direction that accounts for the most variability in Y. The asymptotic distribution of an estimator of a trimmed version of V has been characterized only under the assumption of the single index model (SIM). This paper proposes the use of a flexible trimming function in the objective function, which results in the consistent estimation of V. It also derives the asymptotic ...
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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：Perchet, Vianney; Rigollet, Philippe; Chassang, Sylvain; Snowberg, Erik
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite; Inria; Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); Princeton University; California Institute of Technology; National Bureau of Economic Research
摘要：Motivated by practical applications, chiefly clinical trials, we study the regret achievable for stochastic bandits under the constraint that the employed policy must split trials into a small number of batches. We propose a simple policy, and show that a very small number of batches gives close to minimax optimal regret bounds. As a byproduct, we derive optimal policies with low switching cost for stochastic bandits.
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作者：Fan, Jianqing; Liao, Yuan; Wang, Weichen
作者单位：Princeton University; University System of Maryland; University of Maryland College Park
摘要：This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employs principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to high-dimensional factor analysis, the projection removes noise components. We show that the unobserved latent factors can be more accurately estimated than the conventional PCA if the projection is genuine, or more precisely, when the factor loading matrices are rela...
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作者：Bailey, R. A.; Brien, C. J.
作者单位：University of St Andrews; University of London; Queen Mary University London; University of South Australia; Australian Centre for Plant Functional Genomics; University of Adelaide
摘要：We derive randomization-based models for experiments with a chain of randomizations. Estimation theory for these models leads to formulae for the estimators of treatment effects, their standard errors and expected mean squares in the analysis of variance. We discuss the practicalities in fitting these models and outline the difficulties that can occur, many of which do not arise in two-tiered experiments.
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作者：Bertsimas, Dimitris; King, Angela; Mazumder, Rahul
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
摘要：In the period 1991-2015, algorithmic advances in Mixed Integer Optimization (MIO) coupled with hardware improvements have resulted in an astonishing 450 billion factor speedup in solving MIO problems. We present a MIO approach for solving the classical best subset selection problem of choosing k out of p features in linear regression given n observations. We develop a discrete extension of modern first-order continuous optimization methods to find high quality feasible solutions that we use as...
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作者：Bhattacharjee, Monika; Bose, Arup
作者单位：Indian Statistical Institute; Indian Statistical Institute Kolkata
摘要：The existence of limiting spectral distribution (LSD) of (Gamma) over cap (u) + (Gamma) over cap (u)*, the symmetric sum of the sample autocovariance matrix (Gamma) over cap (u) of order u, is known when the observations are from an infinite dimensional vector linear process with appropriate (strong) assumptions on the coefficient matrices. Under significantly weaker conditions, we prove, in a unified way, that the LSD of any symmetric polynomial in these matrices such as (Gamma) over cap (u) ...
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作者：Patschkowski, Tim; Rohde, Angelika
作者单位：Ruhr University Bochum
摘要：A scheme for locally adaptive bandwidth selection is proposed which sensitively shrinks the bandwidth of a kernel estimator at lowest density regions such as the support boundary which are unknown to the statistician. In case of a Holder continuous density, this locally minimax-optimal bandwidth is shown to be smaller than the usual rate, even in case of homogeneous smoothness. Some new type of risk bound with respect to a density-dependent standardized loss of this estimator is established. T...
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作者：Li, Degui; Tjostheim, Dag; Gao, Jiti
作者单位：University of York - UK; University of Bergen; Monash University
摘要：In this paper, we study parametric nonlinear regression under the Harris recurrent Markov chain framework. We first consider the nonlinear least squares estimators of the parameters in the homoskedastic case, and establish asymptotic theory for the proposed estimators. Our results show that the convergence rates for the estimators rely not only on the properties of the nonlinear regression function, but also on the number of regenerations for the Harris recurrent Markov chain. Furthermore, we ...
