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In this paper, the problem of the robustness of the sample autocovariance function is addressed. We propose a new autocovariance estimator, based on a highly robust estimator of scale. Its robustness properties are studied by means of the in¯uence function, and a new concept of temporal breakdown point. As the theoretical variance of the estimator does not… (More)
Objectives Master classical and modern nonparametric modeling, estimation and inference methods.
Summarizing the effect of many covariates through a few linear combinations is an effective way of reducing covariate dimension and is the backbone of (sufficient) dimension reduction. Because the replacement of high-dimensional covariates by low-dimensional linear combinations is performed with a minimum assumption on the specific regression form, it… (More)
We develop an efficient estimation procedure for identifying and estimating the central subspace. Using a new way of parameterization, we convert the problem of identifying the central subspace to the problem of estimating a finite dimensional parameter in a semiparametric model. This conversion allows us to derive an efficient estimator which reaches the… (More)
We construct a semiparametric estimator in case-control studies where the gene and the environment are assumed to be independent. A discrete or continuous parametric distribution of the genes is assumed in the model. A discrete distribution of the genes can be used to model the mutation or presence of certain group of genes. A continuous distribution allows… (More)
We show that if an 11 X n Jordan block is perturbed by an O(E) upper k-Hessen-berg matrix (k subdiagonals including the main diagonal), then generically the eigenvalues split into p rings of size k and one of size T (if r f O), where n = pk + r. This generalizes the familiar result (k = n, p = 1, r = 0) that generically the eigenvalues split into a ring of… (More)
We provide a novel and completely different approach to dimension-reduction problems from the existing literature. We cast the dimension-reduction problem in a semiparametric estimation framework and derive estimating equations. Viewing this problem from the new angle allows us to derive a rich class of estimators, and obtain the classical dimension… (More)
We consider a class of generalized skew-normal distributions that is useful for selection modeling and robustness analysis and derive a class of semiparametric estimators for the location and scale parameters of the central part of the model. We show that these estimators are consistent and asymptotically normal. We present the semiparametric efficiency… (More)
A hierarchical Bayesian approach is developed to estimate parameters at both the individual and the population level in a HIV model, with the implementation carried out by Markov Chain Monte Carlo (MCMC) techniques. Sample numerical simulations and statistical results are provided to demonstrate the feasibility of this approach.
Treating matrices as points in n 2-dimensional space, we apply geometry to study and explain algorithms for the numerical determination of the Jordan structure of a matrix. Traditional notions such as sensitivity of subspaces are replaced with angles between tangent spaces of manifolds in n 2-dimensional space. We show that the subspace sensitivity is… (More)