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作者：Beskos, Alexandros; Papaspiliopoulos, Omiros; Roberts, Gareth
作者单位：University of Warwick
摘要：This paper introduces a Monte Carlo method for maximum likelihood inference in the context of discretely observed diffusion processes. The method gives unbiased and a.s. continuous estimators of the likelihood function for a family of diffusion models aid its performance in numerical examples is computationally efficient. It uses a recently developed technique for the exact simulation of diffusions, and involves no discretization error. We show that, under regularity conditions, the Monte Carl...
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作者：Goldenshluger, Alexander
作者单位：University of Haifa
摘要：In this paper we study the aggregation problem that can be formulated as follows. Assume that we have a family of estimators F built on the basis of available observations. The goal is to construct a new estimator whose risk is as close as possible to that of the best estimator in the family. We propose a general aggregation scheme that is universal in the following sense: it applies for families of arbitrary estimators and a wide variety of models and global risk measures. The procedure is ba...
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作者：Ait-Sahalia, Yacine; Jacod, Jean
作者单位：Princeton University; National Bureau of Economic Research; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite
摘要：We define a generalized index of jump activity, propose estimators of that index for a discretely sampled process and derive the estimators' properties. These estimators are applicable despite the presence of Brownian volatility in the process, which makes it more challenging to infer the characteristics of the small, infinite activity jumps. When the method is applied to high frequency stock returns, we find evidence of infinitely active jumps in the data and estimate their index of activity.
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作者：Spokoiny, Vladimir; Vial, Celine
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Humboldt University of Berlin; Ecole Nationale de la Statistique et de l'Analyse de l'Information (ENSAI)
摘要：This paper discusses the problem of adaptive estimation Of a univariate object like the value of a regression function at a given point or a linear functional in a linear inverse problem. We consider an adaptive procedure originated from Lepski [Theory Probab. Appl. 35 (1990) 454-466.] that selects in a data-driven way one estimate Out of a given class of estimates ordered by their variability. A serious problem with using this and similar procedures is the choice of some tuning parameters lik...
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作者：Jiang, Wenhua; Zhang, Cun-Hui
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：We propose a general maximum likelihood empirical Bayes (GMLEB) method for the estimation of a mean vector based on observations with i.i.d. normal errors. We prove that under mild moment conditions on the unknown means, the average mean squared error (MSE) of the GMLEB is within an infinitesimal fraction of the minimum average MSE among all separable estimators which use a single deterministic estimating function on individual observations, provided that the risk is of greater order than (log...
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作者：Zou, Hui; Zhang, Hao Helen
作者单位：University of Minnesota System; University of Minnesota Twin Cities; North Carolina State University
摘要：We consider the problem of model selection and estimation in situations where the number of parameters diverges with the sample size. When the dimension is high, an ideal method should have the oracle property [J Amer. Statist. Assoc. 96 (2001) 1348-1360] and [Ann. Statist. 32 (2004) 928-961] which ensures the optimal large sample performance. Furthermore, the high-dimensionality often induces the collinearity problem, which should be properly handled by the ideal method. Many existing variabl...
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作者：Wang, Huixia Judy; Fygenson, Mendel
作者单位：North Carolina State University; University of Southern California
摘要：We develop inference procedures for longitudinal data where some of the measurements are censored by fixed constants. We consider a semi-parametric quantile regression model that makes no distributional assumptions. Our research is motivated by the lack of proper inference procedures for data from biomedical studies where measurements are censored due to a fixed quantification limit. In such studies the focus is often on testing hypotheses about treatment equality. To this end, we propose a ra...
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作者：Chen, Jiahua; Li, Pengfei
作者单位：University of British Columbia; University of Alberta
摘要：Normal mixture distributions are arguably the most important mixture models. and also the most technically challenging. The likelihood function of the normal mixture model is unbounded based oil a set of random samples, unless an artificial bound is placed oil its component variance parameter. Moreover, the model is not strongly identifiable so it is hard to differentiate between over dispersion caused by the presence of a mixture and that caused by a large variance, and it has infinite Fisher...
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作者：De Blasi, Pierpaolo; Peccati, Giovanni; Prunster, Igor
作者单位：University of Turin; Universite Paris Nanterre; Universite Paris Saclay
摘要：An important issue in survival analysis is the investigation and the modeling of hazard rates. Within a Bayesian nonparametric framework, a natural and popular approach is to model hazard rates as kernel mixtures with respect to a completely random measure. In this paper we provide a comprehensive analysis of the asymptotic behavior of such models. We investigate consistency of the posterior distribution and derive fixed sample size central limit theorems for both linear and quadratic function...
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作者：Lan, Yan; Banerjee, Moulinath; Michailidis, George
作者单位：University of Michigan System; University of Michigan; Abbott Laboratories
摘要：We consider the problem of locating a jump discontinuity (chan-e-point) in a smooth parametric regression model with a bounded covariate. It is assumed that one can sample the covariate at different values and measure the corresponding responses. Budget constraints dictate that a total of n such measurements can be obtained. A multistage adaptive procedure is proposed, where at each stage an estimate of the change point is obtained and new points are sampled from its appropriately chosen neigh...
