Related papers: Robust variable selection for partially linear add…
Consider a logistic partially linear model, in which the logit of the mean of a binary response is related to a linear function of some covariates and a nonparametric function of other covariates. We derive simple, doubly robust estimators…
We consider the problems of variable selection and estimation in nonparametric additive regression models for high-dimensional data. In recent years, several methods have been proposed to model nonlinear relationships when the number of…
In this paper, we propose a model averaging approach for addressing model uncertainty in the context of partial linear functional additive models. These models are designed to describe the relation between a response and mixed-types of…
In semi-supervised learning, the prevailing understanding suggests that observing additional unlabeled samples improves estimation accuracy for linear parameters only in the case of model misspecification. In this work, we challenge such a…
This paper studies model selection consistency for high dimensional sparse regression when data exhibits both cross-sectional and serial dependency. Most commonly-used model selection methods fail to consistently recover the true model when…
We propose a new method for the simultaneous selection and estimation of multivariate sparse additive models with correlated errors. Our method called Covariance Assisted Multivariate Penalized Additive Regression (CoMPAdRe) simultaneously…
In multivariate nonparametric regression the additive models are very useful when a suitable parametric model is difficult to find. The backfitting algorithm is a powerful tool to estimate the additive components. However, due to complexity…
Traditional variable selection methods could fail to be sign consistent when irrepresentable conditions are violated. This is especially critical in high-dimensional settings when the number of predictors exceeds the sample size. In this…
It is widely admitted that structured nonparametric modeling that circumvents the curse of dimensionality is important in nonparametric estimation. In this paper we show that the same holds for semi-parametric estimation. We argue that…
This paper investigates the high-dimensional linear regression with highly correlated covariates. In this setup, the traditional sparsity assumption on the regression coefficients often fails to hold, and consequently many model selection…
Let $Y\in\R^n$ be a random vector with mean $s$ and covariance matrix $\sigma^2P_n\tra{P_n}$ where $P_n$ is some known $n\times n$-matrix. We construct a statistical procedure to estimate $s$ as well as under moment condition on $Y$ or…
Missing values in datasets are common in applied statistics. For regression problems, theoretical work thus far has largely considered the issue of missing covariates as distinct from missing responses. However, in practice, many datasets…
We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse…
Robustness to outliers is often a desirable property of statistical estimators. Indeed many well known estimators offer very good optimal performance in theory but are unusable in applied contexts because of their sensitivity to outliers.…
Many problems in signal processing require finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. When dealing with real-world data, the presence of outliers and impulsive noise must also be accounted…
Functional logistic regression is a popular model to capture a linear relationship between binary response and functional predictor variables. However, many methods used for parameter estimation in functional logistic regression are…
The scalar-on-function regression model has become a popular analysis tool to explore the relationship between a scalar response and multiple functional predictors. Most of the existing approaches to estimate this model are based on the…
In this paper we review existing methods for robust functional principal component analysis (FPCA) and propose a new method for FPCA that can be applied to longitudinal data where only a few observations per trajectory are available. This…
Ultra-high dimensional longitudinal data are increasingly common and the analysis is challenging both theoretically and methodologically. We offer a new automatic procedure for finding a sparse semivarying coefficient model, which is widely…
Statistical analysis on compositional data has gained a lot of attention due to their great potential of applications. A feature of these data is that they are multivariate vectors that lie in the simplex, that is, the components of each…