Yuval Nardi

On the asymptotic properties of the group lasso estimator for linear models

We establish estimation and model selection consistency, pre- diction and estimation boundsand persistencefor the group-lassoestimator and model selectorproposed by Yuan and Lin (2006) for least squares prob- lems when the covariates have a natural grouping structure. We consider the case of a fixed-dimensionalparameter space with increasing sample size and the double asymptotic scenario where the model complexity changes with the sample size.

Autoregressive process modeling via the Lasso procedure

The Lasso is a popular model selection and estimation procedure for linear models that enjoys nice theoretical properties. In this paper, we study the Lasso estimator for fitting autoregressive time series models. We adopt a double asymptotic framework where the maximal lag may increase with the sample size. We derive theoretical results establishing various types of consistency. In particular, we derive conditions under which the Lasso estimator for the autoregressive coefficients is model selection consistent, estimation consistent and prediction consistent. Simulation study results are reported.

Valid Statistical Analysis for Logistic Regression with Multiple Sources

Considerable effort has gone into understanding issues of privacy protection of individual information in single databases, and various solutions have been proposed depending on the nature of the data, the ways in which the database will be used and the precise nature of the privacy protection being offered. Once data are merged across sources, however, the nature of the problem becomes far more complex and a number of privacy issues arise for the linked individual files that go well beyond those that are considered with regard to the data within individual sources. In the paper, we propose an approach that gives full statistical analysis on the combined database without actually combining it. We focus mainly on logistic regression, but the method and tools described may be applied essentially to other statistical models as well.

The log-linear group-lasso estimator and its asymptotic properties

We define the group-lasso estimator for the natural parameters of the exponential families of distributions representing hierarchical log-linear models under multinomial sampling scheme. Such estimator arises as the solution of a convex penalized likelihood optimization problem based on the group-lasso penalty. We illustrate how it is possible to construct an estimator of the underlying log-linear model using the blocks of nonzero coefficients recovered by the group-lasso procedure. We investigate the asymptotic properties of the group-lasso estimator as a model selection method in a double-asymptotic framework, in which both the sample size and the model complexity grow simultaneously. We provide conditions guaranteeing that the group-lasso estimator is model selection consistent, in the sense that, with overwhelming probability as the sample size increases, it correctly identifies all the sets of nonzero interactions among the variables. Provided the sequences of true underlying models is sparse enough, recovery is possible even if the number of cells grows larger than the sample size. Finally, we derive some central limit type of results for the log-linear group-lasso estimator.

Genetic considerations in human sex-mate selection: partners share human leukocyte antigen but not short-tandem-repeat identity markers.

Previous studies support a role for MHC on mating preference, yet it remains unsettled as to whether mating occurs preferentially between individuals sharing human leukocyte antigen (HLA) determinants or not. Investigating sex‐mate preferences in the contemporary Israeli population is of further curiosity being a population with distinct genetic characteristics, where multifaceted cultural considerations influence mate selection.