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作者：Koenker, Roger; Mizera, Ivan
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; University of Alberta
摘要：Maximum likelihood estimation of a log-concave probability density is formulated as a convex optimization problem and shown to have an equivalent dual formulation as a constrained maximum Shannon entropy problem. Closely related maximum Renyi entropy estimators that impose weaker concavity restrictions on the fitted density are also considered, notably a minimum Hellinger discrepancy estimator that constrains the reciprocal of the square-root of the density to be concave. A limiting form of th...
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作者：Ait-Sahalia, Yacine; Jacod, Jean
作者单位：Princeton University; National Bureau of Economic Research; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：This paper considers the problem of testing for the presence of a continuous part in a semimartingale sampled at high frequency. We provide two tests, one where the null hypothesis is that a continuous component is present, the other where the continuous component is absent, and the model is then driven by a pure jump process. When applied to high-frequency individual stock data, both tests point toward the need to include a continuous component in the model.
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作者：Reynaud-Bouret, Patricia; Schbath, Sophie
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur; Universite Paris Saclay; INRAE
摘要：The aim of this paper is to provide a new method for the detection of either favored or avoided distances between genomic events along DNA sequences. These events are modeled by a Hawkes process. The biological problem is actually complex enough to need a nonasymptotic penalized model selection approach. We provide a theoretical penalty that satisfies an oracle inequality even for quite complex families of models. The consecutive theoretical estimator is shown to be adaptive minimax for Holder...
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作者：Ait-Sahalia, Yacine; Fan, Jianqing; Jiang, Jiancheng
作者单位：Princeton University; National Bureau of Economic Research; Princeton University; University of North Carolina; University of North Carolina Charlotte
摘要：We propose several statistics to test the Markov hypothesis for beta-mixing stationary processes sampled at discrete time intervals. Our tests are based on the Chapman Kolmogorov equation. We establish the asymptotic null distributions of the proposed test statistics, showing that Wilks's phenomenon holds. We compute the power of the test and provide simulations to investigate the finite sample performance of the test statistics when the null model is a diffusion process, with alternatives con...
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作者：Cheng, Guang; Huang, Jianhua Z.
作者单位：Purdue University System; Purdue University; Texas A&M University System; Texas A&M University College Station
摘要：Consider M-estimation in a semiparametric model that is characterized by a Euclidean parameter of interest and an infinite-dimensional nuisance parameter. As a general purpose approach to statistical inferences, the bootstrap has found wide applications in semiparametric M-estimation and, because of its simplicity, provides an attractive alternative to the inference approach based on the asymptotic distribution theory. The purpose of this paper is to provide theoretical justifications for the ...
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作者：Addario-Berry, Louigi; Broutin, Nicolas; Devroye, Luc; Lugosi, Gabor
作者单位：McGill University; McGill University; ICREA; Pompeu Fabra University; McGill University
摘要：We study a class of hypothesis testing problems in which, upon observing the realization of an n-dimensional Gaussian vector, one has to decide whether the vector was drawn from a standard normal distribution or, alternatively, whether there is a subset of the components belonging to a certain given class of sets whose elements have been contaminated, that is, have a mean different from zero. We establish some general conditions under which testing is possible and others under which testing is...
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作者：Brien, C. J.; Bailey, R. A.
作者单位：University of South Australia; University of London; Queen Mary University London
摘要：We investigate structure for pairs of randomizations that do not follow each other in a chain. These are unrandomized-inclusive, independent, coincident or double randomizations. This involves taking several structures that satisfy particular relations and combining them to form the appropriate orthogonal decomposition of the data space for the experiment. We show how to establish the decomposition table giving the sources of variation, their relationships and their degrees of freedom, so that...
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作者：Lang, Faming
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：The subject of stochastic approximation was founded by Robbins and Monro [Ann. Math. Statist. 22 (1951) 400-407]. After five decades of continual development, it has developed into an important area in systems control and optimization, and it has also served as a prototype for the development of adaptive algorithms for on-line estimation and control of stochastic systems. Recently, it has been used in statistics with Markov chain Monte Carlo for solving maximum likelihood estimation problems a...
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作者：Palma, Wilfredo; Olea, Ricardo
作者单位：Pontificia Universidad Catolica de Chile
摘要：This paper addresses the estimation of locally stationary long-range dependent processes, a methodology that allows the statistical analysis of time series data exhibiting both nonstationarity and strong dependency. A time-varying parametric formulation of these models is introduced and a Whittle likelihood technique is proposed for estimating the parameters involved. Large sample properties of these Whittle estimates such as consistency, normality and efficiency are established in this work. ...
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作者：Golubev, Yuri
作者单位：Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：This paper deals with recovering an unknown vector theta from the noisy data Y = A theta + sigma xi, where A is a known (m x n)-matrix and xi is a white Gaussian noise. It is assumed that n is large and A may be severely ill-posed. Therefore, in order to estimate theta, a spectral regularization method is used, and our goal is to choose its regularization parameter with the help of the data Y. For spectral regularization methods related to the so-called ordered smoothers [see Kneip Ann. Statis...
