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作者：Hardouin, Cecile; Yao, Jian-Feng
作者单位：heSam Universite; Universite Pantheon-Sorbonne; Universite de Rennes
摘要：Motivated by the modelling of non-Gaussian data or positively correlated data on a lattice, extensions of Besag's automodels to exponential families with multi-dimensional parameters have been proposed recently. We provide a multiple-parameter analogue of Besag's one-dimensional result that gives the necessary form of the exponential families for the Markov random field's conditional distributions. We propose estimation of parameters by maximum pseudolikelihood and give a proof of the consiste...
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作者：Stute, W.; Xu, W. L.; Zhu, L. X.
作者单位：Justus Liebig University Giessen; Renmin University of China; Hong Kong Baptist University
摘要：We study tools for checking the validity of a parametric regression model. When the dimension of the regressors is large, many of the existing tests face the curse of dimensionality or require some ordering of the data. Our tests are based on the residual empirical process marked by proper functions of the regressors. They are able to detect local alternatives converging to the null at parametric rates. Parametric and nonparametric alternatives are considered. In the latter case, through a pro...
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作者：Carroll, Raymond J.; Wang, Yuedong
作者单位：Texas A&M University System; Texas A&M University College Station; University of California System; University of California Santa Barbara
摘要：We investigate the effects of measurement error on the estimation of nonparametric variance functions. We show that either ignoring measurement error or direct application of the simulation extrapolation, SIMEX, method leads to inconsistent estimators. Nevertheless, the direct SIMEX method can reduce bias relative to a naive estimator. We further propose a permutation SIMEX method that leads to consistent estimators in theory. The performance of both the SIMEX methods depends on approximations...
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作者：Waagepetersen, Rasmus
作者单位：Aalborg University
摘要：The R package spatstat provides a very flexible and useful framework for analysing spatial point patterns. A fundamental feature is a procedure for fitting spatial point process models depending on covariates. However, in practice one often faces incomplete observation of the covariates and this leads to parameter estimation error which is difficult to quantify. In this paper, we introduce a Monte Carlo version of the estimating function used in spatstat for fitting inhomogeneous Poisson proce...
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作者：Li, Guodong; Li, Wai Keung
作者单位：University of Hong Kong
摘要：We consider a unified least absolute deviation estimator for stationary and nonstationary fractionally integrated autoregressive moving average models with conditional heteroscedasticity. Its asymptotic normality is established when the second moments of errors and innovations are finite. Several other alternative estimators are also discussed and are shown to be less efficient and less robust than the proposed approach. A diagnostic tool, consisting of two portmanteau tests, is designed to ch...
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作者：Meinshausen, Nicolai
作者单位：University of Oxford
摘要：A frequently encountered challenge in high-dimensional regression is the detection of relevant variables. Variable selection suffers from instability and the power to detect relevant variables is typically low if predictor variables are highly correlated. When taking the multiplicity of the testing problem into account, the power diminishes even further. To gain power and insight, it can be advantageous to look for influence not at the level of individual variables but rather at the level of c...
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作者：Li, Yingxing; Ruppert, David
作者单位：Cornell University; Cornell University
摘要：We study the asymptotic behaviour of penalized spline estimators in the univariate case. We use B-splines and a penalty is placed on mth-order differences of the coefficients. The number of knots is assumed to converge to infinity as the sample size increases. We show that penalized splines behave similarly to Nadaraya - Watson kernel estimators with 'equivalent' kernels depending upon m. The equivalent kernels we obtain for penalized splines are the same as those found by Silverman for smooth...
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作者：Neumann, Michael H.; Paparoditis, Efstathios
作者单位：Friedrich Schiller University of Jena; University of Cyprus
摘要：We propose a method for the construction of simultaneous confidence bands for a smoothed version of the spectral density of a Gaussian process based on nonparametric kernel estimators obtained by smoothing the periodogram. A studentized statistic is used to determine the width of the band at each frequency and a frequency-domain bootstrap approach is employed to estimate the distribution of the supremum of this statistic over all frequencies. We prove by means of strong approximations that the...
