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作者：Omelka, Marek; Gijbels, Irene; Veraverbeke, Noel
作者单位：Charles University Prague; KU Leuven; KU Leuven; Hasselt University
摘要：We reconsider the existing kernel estimators for a copula function. as proposed in Gijbels and Mielniczuk [Comm. Statist. Theory, Methods 19 (1990) 445-464] Fermaman, Radulovic and Wegkamp [Bernoulli 10 (2004) 847-860] and Chen and Huang [Canad. J. Statist. 35 (2007) 265-282]. All of these estimators have as a drawback that they can suffer from a corner bias problem. A way to deal with this is to impose rather stringent conditions on the copula, outruling as such many classical families of cop...
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作者：Spokoiny, Vladimir
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Humboldt University of Berlin
摘要：This paper offers a new approach to modeling and forecasting of nonstationary time series with applications to volatility modeling for financial data. The approach is based on the assumption of local homogeneity: for every time point, there exists a historical interval of homogeneity, in which the volatility parameter can be well approximated by a constant. The proposed procedure recovers this interval from the data using the local change point (LCP) analysis. Afterward, the estimate of the vo...
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作者：Chan, Hock Peng
作者单位：National University of Singapore
摘要：Generalized likelihood ratio (GLR) test statistics are often used in the detection of spatial clustering in case-control and case-population datasets to check for a significantly large proportion of cases within some scanning window. The traditional spatial scan test statistic takes the supremum GLR value over all windows, whereas the average likelihood ratio (ALR) test statistic that we consider here takes an average of the GLR values. Numerical experiments in the literature and in this paper...
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作者：Candes, Emmanuel J.; Plan, Yaniv
作者单位：California Institute of Technology
摘要：We consider the fundamental problem of estimating the mean of a vector y = X beta + 7, where X is an n x p design matrix in which one can have far more variables than observations, and z is a stochastic error term-the so-called p > n setup. When beta is sparse, or, more generally, when there is a sparse subset of covariates providing a close approximation to the unknown mean vector, we ask whether or not it is possible to accurately, estimate X beta using a computationally tractable algorithm....
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作者：Belloni, Alexandre; Chernozhukov, Victor
作者单位：Duke University; Massachusetts Institute of Technology (MIT)
摘要：In this paper we examine the implications of the statistical large sample theory for the computational complexity of Bayesian and quasi-Bayesian estimation carried out using Metropolis random walks. Our analysis is motivated by the Laplace-Bernstein-Von Mises central limit theorem, which states that in large samples the posterior or quasi-posterior approaches a. normal density. Using the conditions required for the central limit theorem to hold, we establish polynomial bounds on the computatio...
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作者：Koltchinskii, Vladimir
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：Let (X. Y) be a random couple in S x T with unknown distribution P and (X-1, Y-1),..., (X-n, Y-n,) be i.i.d. copies of (X, Y). Denote P-n the empirical distribution of (X-1, Y-1),..., (X-n, Y-n). Let h(1),..., h(N): S bar right arrow [-1, 1] be a dictionary that consists of N functions. For lambda is an element of R-N, denote f(lambda) := Sigma(N)(j=1) lambda(j)h(j). Let l: T x R bar right arrow R be a given loss function and suppose it is convex with respect to the second variable. Let (l cen...
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作者：Drton, Mathias
作者单位：University of Chicago
摘要：Many statistical hypotheses can be formulated in terms of polynomial equalities and inequalities in the unknown parameters and thus correspond to semi-algebraic Subsets of the parameter space. We consider large sample asymptotics for the likelihood ratio test of such hypotheses in models that satisfy standard probabilistic regularity conditions. We show that the assumptions of Chernoff's theorem hold for semi-algebraic sets such that the asymptotics are determined by the tangent cone at the tr...
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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.
