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作者：Muler, Nora; Pena, Daniel; Yohai, Victor J.
作者单位：Universidad Carlos III de Madrid
摘要：This paper introduces a new class of robust estimates for ARMA models. They are M-estimates, but the residuals are computed so the effect of one outlier is limited to the period where it occurs. These estimates are closely related to those based on a robust filter, but they have two important advantages: they are consistent and the asymptotic theory is tractable. We perform a Monte Carlo where we show that these estimates compare favorably with respect to standard M-estimates and to estimates ...
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作者：Nguyen, XuanLong; Wainwright, Martin J.; Jordan, Michael I.
作者单位：Duke University; University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：The goal of binary classification is to estimate a discriminant function gamma from observations of covariate vectors and corresponding binary labels. We consider an elaboration of this problem in which the covariates are not available directly but are transformed by a dimensionality-reducing quantizer Q. We present conditions on loss functions such that empirical risk minimization yields Bayes consistency when both the discriminant function and the quantizer are estimated. These conditions ar...
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作者：Dette, Holger; Holland-Letz, Tim
作者单位：Ruhr University Bochum; Ruhr University Bochum
摘要：We consider the common nonlinear regression model where the variance, as well as the mean, is a parametric function of the explanatory variables. The c-optimal design problem is investigated in the case when the parameters of both the mean and the variance function are of interest. A geometric characterization of c-optimal designs in this context is presented, which generalizes the classical result of Elfving [Ann. Math. Statist. 23 (1952) 255-262] for c-optimal designs. As in Elfving's famous...
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作者：van der Vaart, A. W.; van Zanten, J. H.
作者单位：Vrije Universiteit Amsterdam
摘要：We consider nonparametric Bayesian estimation inference using a rescaled smooth Gaussian field as a prior for a multidimensional function. The rescaling is achieved using a Gamma variable and the procedure can be viewed as choosing all inverse Gamma bandwidth. The procedure is studied from a frequentist perspective in three statistical settings involving replicated observations (density estimation, regression and classification). We prove that the resulting posterior distribution shrinks to th...
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作者：Zhang, Cun-Hui; Zhang, Zhiyi
作者单位：Rutgers University System; Rutgers University New Brunswick; University of North Carolina; University of North Carolina Charlotte
摘要：This paper establishes a necessary and sufficient condition for the asymptotic normality of the nonparametric estimator of sample coverage proposed by Good [Biometrica 40 (1953) 237-264]. This new necessary and sufficient condition extends the validity of the asymptotic normality beyond the previously proven cases.
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作者：Cui, Xia; Guo, Wensheng; Lin, Lu; Zhu, Lixing
作者单位：Shandong University; Hong Kong Baptist University; University of Pennsylvania; East China Normal University
摘要：In this paper, we propose a covariate-adjusted nonlinear regression model. In this model, both the response and predictors can only be observed after being distorted by some multiplicative factors. Because of nonlinearity, existing methods for the linear setting cannot be directly employed. To attack this problem, we propose estimating the distorting functions by nonparametrically regressing the predictors and response on the distorting covariate; then, nonlinear least squares estimators for t...
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作者：Shi, Tao; Belkin, Mikhail; Yu, Bin
作者单位：University System of Ohio; Ohio State University; University System of Ohio; Ohio State University; University of California System; University of California Berkeley
摘要：This paper focuses on obtaining clustering information about a distribution from its i.i.d. samples. We develop theoretical results to understand and use clustering information contained in the eigenvectors of data adjacency matrices based on a radial kernel function with a sufficiently fast tail decay. In particular, we provide population analyses to gain insights into which eigenvectors should be used and when the clustering information for the distribution can be recovered from the sample. ...
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作者：Wasserman, Larry; Roeder, Kathryn
作者单位：Carnegie Mellon University
摘要：This paper explores the following question: what kind of statistical guarantees can be given when doing variable selection in high-dimensional models? In particular, we look at the error rates and power of some multi-stage regression methods. In the first stage we fit a set of candidate models. In the second stage we select one model by cross-validation. In the third stage we use hypothesis testing to eliminate some variables. We refer to the first two stages as screening and the last stage as...
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作者：Brown, Lawrence D.; Greenshtein, Eitan
作者单位：University of Pennsylvania; Duke University
摘要：We consider the classical problem of estimating a vector mu = (mu(1,) ..., mu(n)) based on independent observations Yi similar to N(mu(i), 1), i = 1, ..., n. Suppose mu(i), i = 1, ..., n are independent realizations from a completely unknown G. We suggest an easily computed estimator (mu) over cap, such that the ratio of its risk E((mu) over cap - mu)(2) with that of the Bayes procedure approaches 1. A related compound decision result is also obtained. Our asymptotics is of a triangular array;...
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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：We propose a new test to determine whether jumps are present in asset returns or other discretely sampled processes. As the sampling interval tends to 0, our test statistic converges to I if there are jumps, and to another deterministic and known value (such as 2) if there are no jumps. The test is valid 4 for all Ito semi martingales, depends neither on the law of the process nor on the coefficients of the equation which it solves, does not require a preliminary estimation of these coefficien...
