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作者：Hjort, Nils Lid; Walker, Stephen G.
作者单位：University of Oslo; University of Kent
摘要：Polya trees fix partitions and use random probabilities in order to construct random probability measures. With quantile pyramids we instead fix probabilities and use random partitions. For nonparametric Bayesian inference we use a prior which supports piecewise linear quantile functions, based on the need to work with a finite set of partitions, yet we show that the limiting version of the prior exists. We also discuss and investigate an alternative model based on the so-called substitute lik...
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作者：Allman, Elizabeth S.; Matias, Catherine; Rhode, John A.
作者单位：University of Alaska System; University of Alaska Fairbanks; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
摘要：While hidden class models of various types arise in many statistical applications, it is often difficult to establish the identifiability of their parameters. Focusing on models in which there is some structure of independence of some of the observed variables conditioned on hidden ones, we demonstrate,I general approach for establishing identifiability utilizing algebraic arguments. A theorem of J. Kruskal for a simple latent-class model with finite state space lies at the core of our results...
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作者：Jung, Sungkyu; Marron, J. S.
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：Principal Component Analysis (PCA) is an important tool of dimension reduction especially when the dimension (or the number of variables) is very high. Asymptotic studies where the sample size is fixed, and the dimension grows [i.e., High Dimension, Low Sample Size (HDLSS)] are becoming increasingly relevant. We investigate the asymptotic behavior of the Principal Component (PC) directions. HDLSS asymptotics are used to study consistency, strong inconsistency and subspace consistency. We show ...
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作者：Khmaladze, Estate V.; Koul, Hira L.
作者单位：Victoria University Wellington; Michigan State University
摘要：This paper discusses asymptotically distribution free tests for the classical goodness-of-fit hypothesis of all error distribution in nonparametric regression models. These tests are based on the same martingale transform of the residual empirical process as used in the one sample location model. This transformation eliminates extra randomization due to covariates but not due the errors, which is intrinsically present in the estimators of the regression function. Thus, tests based on the trans...
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作者：Kulik, Rafal; Raimondo, Marc
作者单位：University of Ottawa; University of Sydney
摘要：We investigate function estimation in nonparametric regression models with random design and heteroscedastic correlated noise. Adaptive properties of warped wavelet nonlinear approximations are studied over a wide range of Besov scales, f is an element of B-pi,r(S), and for a variety of L-P error measures. We consider error distributions with Long-Range-Dependence parameter alpha, 0 < alpha <= 1; heteroscedasticity is modeled with a design dependent function a. We prescribe a tuning paradigm, ...
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作者：Moreira, Marcelo J.
作者单位：Columbia University
摘要：This paper uses the invariance principle to solve the incidental parameter problem of [Econometrica 16 (1948) 1-32]. We seek group actions that preserve the structural parameter and yield a maximal invariant in the parameter space with fixed dimension. M-estimation from the likelihood of the maximal invariant statistic yields the maximum invariant likelihood estimator (MILE). Consistency of MILE for cases in which the likelihood of the maximal invariant is the product of marginal likelihoods i...
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作者：Nishiyama, Yoichi
作者单位：Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan
摘要：This paper generalizes a part of the theory of Z-estimation which has been developed mainly in the context of modern empirical processes to the case of stochastic processes, typically, semimartingales. We present a general theorem to derive the asymptotic behavior of the solution to an estimating equation theta (sic) Psi(n) (theta, (h) over cap (n)) = 0 with an abstract nuisance parameter h when the compensator of Psi(n) is random. As its application, we consider the estimation problem in an e...
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作者：Panaretos, Victor M.
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We formulate and investigate a statistical inverse problem of a random tomographic nature, where a probability density function on R-3 is to be recovered from observation of finitely many of its two-dimensional projections in random and unobservable directions. Such a problem is distinct from the classic problem of tomography where both the projections and the unit vectors normal to the projection plane are observable. The problem arises in single particle electron microscopy, a powerful metho...
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作者：Zhao, Peng; Rocha, Guilherme; Yu, Bin
作者单位：University of California System; University of California Berkeley
摘要：Extracting useful information from high-dimensional data is an important focus of today's statistical research and practice. Penalized loss function minimization has been shown to be effective for this task both theoretically and empirically. With the virtues of both regularization and sparsity, the L-1-penalized squared error minimization method Lasso has been popular in regression models and beyond. In this paper, we combine different norms including L-1 to form an intelligent penalty in ord...
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作者：Amini, Arash A.; Wainwright, Martin J.
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：Principal component analysis (PCA) is a classical method for dimensionality reduction based oil extracting the dominant eigenvectors of the Sample covariance matrix. However, PCA is well known to behave poorly inw the large p, small n setting, in which the problem dimension p is comparable to or larger than the sample size n. This paper studies PICA ill this high-dimensional regime, but under the additional assumption that the maximal eigenvector is sparse, say, with at most k nonzero componen...
