Related papers: The partial linear model in high dimensions

We consider a high-dimensional regression model with a possible change-point due to a covariate threshold and develop the Lasso estimator of regression coefficients as well as the threshold parameter. Our Lasso estimator not only selects…

Linear models that contain a time-dependent response and explanatory variables have attracted much interest in recent years. The most general form of the existing approaches is of a linear regression model with autoregressive moving average…

We consider high-dimensional binary classification by sparse logistic regression. We propose a model/feature selection procedure based on penalized maximum likelihood with a complexity penalty on the model size and derive the non-asymptotic…

We tackle estimation and prediction at non-visted sites in a spatial semi-functional linear regression model with derivatives that combines a functional linear model with a nonparametric regression one. The parametric part is estimated by a…

In this article, we develop a semiparametric Bayesian estimation and model selection approach for partially linear additive models in conditional quantile regression. The asymmetric Laplace distribution provides a mechanism for Bayesian…

We consider the theory for the high-dimensional generalized linear model with the Lasso. After a short review on theoretical results in literature, we present an extension of the oracle results to the case of quasi-likelihood loss. We prove…

Using a multiplicative reparametrization, I show that a subclass of $L_q$ penalties with $q\leq 1$ can be expressed as sums of $L_2$ penalties. It follows that the lasso and other norm-penalized regression estimates may be obtained using a…

We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases…

We propose an $\ell_1$-penalized estimation procedure for high-dimensional linear mixed-effects models. The models are useful whenever there is a grouping structure among high-dimensional observations, i.e. for clustered data. We prove a…

Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…

The partial linear Cox model for interval-censoring is well-studied under the additive assumption but is still under-investigated without this assumption. In this paper, we propose to use a deep ReLU neural network to estimate the…

We propose two semiparametric versions of the debiased Lasso procedure for the model $Y_i = X_i\beta_0 + g_0(Z_i) + \epsilon_i$, where $\beta_0$ is high dimensional but sparse (exactly or approximately). Both versions are shown to have the…

When predicting scalar responses in the situation where the explanatory variables are functions, it is sometimes the case that some functional variables are related to responses linearly while other variables have more complicated…

Confounding can lead to spurious associations. Typically, one must observe confounders in order to adjust for them, but in high-dimensional settings, recent research has shown that it becomes possible to adjust even for unobserved…

In this paper, we propose a new nonparametric estimator of time-varying forecast combination weights. When the number of individual forecasts is small, we study the asymptotic properties of the local linear estimator. When the number of…

In this paper we are interested in parameters estimation of linear model when number of parameters increases with sample size. Without any assumption about moments of the model error, we propose and study the seamless $L_0$ quantile…

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…

The paper considers a linear regression model with multiple change-points occurring at unknown times. The LASSO technique is very interesting since it allows the parametric estimation, including the change-points, and automatic variable…

We review recent results for high-dimensional sparse linear regression in the practical case of unknown variance. Different sparsity settings are covered, including coordinate-sparsity, group-sparsity and variation-sparsity. The emphasis is…

In this paper, utilizing recent theoretical results in high dimensional statistical modeling, we propose a model-free yet computationally simple approach to estimate the partially linear model $Y=X\beta+g(Z)+\varepsilon$. Motivated by the…