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Pre-validation is a way to build prediction model with two datasets of significantly different feature dimensions. Previous work showed that the asymptotic distribution of the resulting test statistic for the pre-validated predictor…
Cross-validation is a widely-used technique to estimate prediction error, but its behavior is complex and not fully understood. Ideally, one would like to think that cross-validation estimates the prediction error for the model at hand, fit…
Generalized extreme value (GEV) regression is often more adapted when we investigate a relationship between a binary response variable $Y$ which represents a rare event and potentiel predictors $\mathbf{X}$. In particular, we use the…
High-dimensional sparse generalized linear models (GLMs) have emerged in the setting that the number of samples and the dimension of variables are large, and even the dimension of variables grows faster than the number of samples. False…
De-biased lasso has emerged as a popular tool to draw statistical inference for high-dimensional regression models. However, simulations indicate that for generalized linear models (GLMs), de-biased lasso inadequately removes biases and…
In this article we propose a new variable selection method for analyzing data collected from longitudinal sample surveys. The procedure is based on the survey-weighted quadratic inference function, which was recently introduced as an…
Causal models are important tools to understand complex phenomena and predict the outcome of controlled experiments, also known as interventions. In this work, we present statistical rates of estimation for linear cyclic causal models under…
In this paper we develop inference for high dimensional linear models, with serially correlated errors. We examine Lasso under the assumption of strong mixing in the covariates and error process, allowing for fatter tails in their…
A new empirical Bayes approach to variable selection in the context of generalized linear models is developed. The proposed algorithm scales to situations in which the number of putative explanatory variables is very large, possibly much…
With regard to a three-step estimation procedure, proposed without theoretical discussion by Li and You in Journal of Applied Statistics and Management, for a nonparametric regression model with time-varying regression function, local…
We consider a high-dimensional mean estimation problem over a binary hidden Markov model, which illuminates the interplay between memory in data, sample size, dimension, and signal strength in statistical inference. In this model, an…
Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…
We propose the variable selection procedure incorporating prior constraint information into lasso. The proposed procedure combines the sample and prior information, and selects significant variables for responses in a narrower region where…
We consider high-dimensional inference for potentially misspecified Cox proportional hazard models based on low dimensional results by Lin and Wei [1989]. A de-sparsified Lasso estimator is proposed based on the log partial likelihood…
Shrinkage estimators that possess the ability to produce sparse solutions have become increasingly important to the analysis of today's complex datasets. Examples include the LASSO, the Elastic-Net and their adaptive counterparts.…
We consider regression problems where the number of predictors greatly exceeds the number of observations. We propose a method for variable selection that first estimates the regression function, yielding a "pre-conditioned" response…
Lasso-type estimators are routinely used to estimate high-dimensional time series models. The theoretical guarantees established for these estimators typically require the penalty level to be chosen in a suitable fashion often depending on…
This paper proposes a new method for estimating high-dimensional binary choice models. We consider a semiparametric model that places no distributional assumptions on the error term, allows for heteroskedastic errors, and permits endogenous…
Recently, many machine learning and statistical models such as non-linear regressions, the Single Index, Multi-index, Varying Coefficient Index Models and Two-layer Neural Networks can be reduced to or be seen as a special case of a new…
We investigate the accuracy of the two most common estimators for the maximum expected value of a general set of random variables: a generalization of the maximum sample average, and cross validation. No unbiased estimator exists and we…