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作者：Ait-Sahalia, Yacine
作者单位：Princeton University; National Bureau of Economic Research
摘要：This paper provides closed-form expansions for the log-likelihood function of multivariate diffusions sampled at discrete time intervals. The coefficients of the expansion are calculated explicitly by exploiting the special structure afforded by the diffusion model. Examples of interest in financial statistics and Monte Carlo evidence are included, along with the convergence of the expansion to the true likelihood function.
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作者：El Karoui, Noureddine
作者单位：University of California System; University of California Berkeley
摘要：Estimating covariance matrices is a problem of fundamental importance in multivariate statistics. In practice it is increasingly frequent to work with data matrices X of dimension if x p, where p and n are both large. Results from random matrix theory show very clearly that in this setting, standard estimators like the sample covariance matrix perform in general very poorly. In this large n, large p setting, it is sometimes the case that practitioners are willing to assume that many elements o...
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作者：Fryzlewicz, Piotr; Sapatinas, Theofanis; Rao, Suhasini Subba
作者单位：University of Bristol; University of Cyprus; Texas A&M University System; Texas A&M University College Station; Ruprecht Karls University Heidelberg
摘要：We investigate the time-varying ARCH (tvARCH) process. It is shown that it can be used to describe the slow decay of the sample autocorrelations of the squared returns often observed in financial time series, which warrants the further study of parameter estimation methods for the model. Since the parameters are changing over time, a successful estimator needs to perform well for small samples. We propose a kernel normalized-least-squares (kernel-NLS) estimator which has a closed form, and thu...
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作者：Lindsay, Bruce G.; Markatou, Marianthi; Ray, Surajit; Yang, Ke; Chen, Shu-Chuan
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Columbia University; Boston University; Cytokinetics, Inc.; Arizona State University; Arizona State University-Tempe; National Cheng Kung University
摘要：This work builds a unified framework for the study of quadratic form distance measures as they are used in assessing the goodness of fit of models. Many important procedures have this structure, but the theory for these methods is dispersed and incomplete. Central to the statistical analysis of these distances is the spectral decomposition of the kernel that generates the distance. We show how this determines the limiting distribution of natural goodness-of-fit tests. Additionally, we develop ...
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作者：Chen, Song Xi; Gao, Jiti; Tang, Cheng Yong
作者单位：Iowa State University; University of Western Australia
摘要：We propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process. The empirical likelihood is used to formulate a statistic, for each kernel smoothing bandwidth, which is effectively a Studentized L-2-distance between the kernel transitional density estimator and the parametric transitional density implied by the parametric process. To reduce the sensitivity of the test on smoothing bandwidth choice, the final t...
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作者：Linton, Oliver; Sperlich, Stefan; Van Keilegom, Ingrid
作者单位：University of London; London School Economics & Political Science; University of Gottingen; Universite Catholique Louvain
摘要：This paper proposes consistent estimators for transformation parameters in semiparametric models. The problem is to find the optimal transformation into the space of models with a predetermined regression structure like additive or multiplicative separability. We give results for the estimation of the transformation when the rest of the model is estimated non- or semi-parametrically and fulfills some consistency conditions. We propose two methods for the estimation of the transformation parame...
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作者：El Karoui, Noureddine
作者单位：University of California System; University of California Berkeley
摘要：Estimating the eigenvalues of a population covariance matrix from a sample covariance matrix is a problem of fundamental importance in multivariate statistics; the eigenvalues of covariance matrices play a key role in many widely used techniques, in particular in principal component analysis (PCA). In many modern data analysis problems, statisticians are faced with large datasets where the sample size, n, is of the same order of magnitude as the number of variables p. Random matrix theory pred...
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作者：Bellon, Alexandre; Didier, Gustavo
作者单位：Duke University; Tulane University
摘要：In this paper we provide a provably convergent algorithm for the multi-variate Gaussian Maximum Likelihood version of the Behrens-Fisher Problem. Our work builds upon a formulation of the log-likelihood function proposed by Buot and Richards [5]. Instead of focusing on the first order optimality conditions, the algorithm aims directly for the maximization of the log-likelihood function itself to achieve a global solution. Convergence proof and complexity estimates are provided for the algorith...
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作者：Hofmann, Thomas; Schoelkopf, Bernhard; Smola, Alexander J.
作者单位：Technical University of Darmstadt; Max Planck Society; NICTA
摘要：We review machine learning methods employing positive definite kernels. These methods formulate learning and estimation problems in a reproducing kernel Hilbert space (RKHS) of functions defined on the data domain, expanded in terms of a kernel. Working in linear spaces of function has the benefit of facilitating the construction and analysis of learning algorithms while at the same time allowing large classes of functions. The latter include nonlinear functions as well as functions defined on...
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作者：Rohde, Angelika
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：Within the nonparametric regression model with unknown regression function l and independent, symmetric errors, a new multiscale signed rank statistic is introduced and a conditional multiple test of the simple hypothesis l = 0 against a nonparametric alternative is proposed. This test is distribution-free and exact for finite samples even in the heteroscedastic case. It adapts in a certain sense to the unknown smoothness of the regression function under the alternative, and it is uniformly co...
