Related papers: Estimation of Partially Linear Regression Model un…
Statistical inference with nonresponse is quite challenging, especially when the response mechanism is nonignorable. In this case, the validity of statistical inference depends on untestable correct specification of the response model. To…
This paper analyzes a new regularized learning scheme for high dimensional partially linear support vector machine. The proposed approach consists of an empirical risk and the Lasso-type penalty for linear part, as well as the standard…
Traditional parametric econometric models often rely on rigid functional forms, while nonparametric techniques, despite their flexibility, frequently lack interpretability. This paper proposes a parsimonious alternative by modeling the…
In this paper, we introduce a novel method to generate interpretable regression function estimators. The idea is based on called data-dependent coverings. The aim is to extract from the data a covering of the feature space instead of a…
We consider a robust linear regression model $y=X\beta^* + \eta$, where an adversary oblivious to the design $X\in \mathbb{R}^{n\times d}$ may choose $\eta$ to corrupt all but an $\alpha$ fraction of the observations $y$ in an arbitrary…
In this article, we study a partially linear single-index model for longitudinal data under a general framework which includes both the sparse and dense longitudinal data cases. A semiparametric estimation method based on a combination of…
Regressing a function $F$ on $\mathbb{R}^d$ without the statistical and computational curse of dimensionality requires special statistical models, for example that impose geometric assumptions on the distribution of the data (e.g., that its…
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…
We address the issue of estimating the regression vector $\beta$ in the generic $s$-sparse linear model $y = X\beta+z$, with $\beta\in\R^{p}$, $y\in\R^{n}$, $z\sim\mathcal N(0,\sg^2 I)$ and $p> n$ when the variance $\sg^{2}$ is unknown. We…
We consider an additive partially linear framework for modelling massive heterogeneous data. The major goal is to extract multiple common features simultaneously across all sub-populations while exploring heterogeneity of each…
Partial linear models have been widely used as flexible method for modelling linear components in conjunction with non-parametric ones. Despite the presence of the non-parametric part, the linear, parametric part can under certain…
We consider a sparse linear regression model Y=X\beta^{*}+W where X has a Gaussian entries, W is the noise vector with mean zero Gaussian entries, and \beta^{*} is a binary vector with support size (sparsity) k. Using a novel conditional…
Having a regression model, we are interested in finding two-sided intervals that are guaranteed to contain at least a desired proportion of the conditional distribution of the response variable given a specific combination of predictors. We…
This paper introduces a new kind of seasonal fractional autoregressive process (SFAR) driven by fractional Gaussian noise (fGn). The new model includes a standard seasonal AR model and fGn. {The estimation of the parameters of this new…
In this paper, we propose an empirical likelihood-based weighted estimator of regression parameter in quantile regression model with nonignorable missing covariates. The proposed estimator is computationally simple and achieves…
We propose a partially linear additive Gaussian graphical model (PLA-GGM) for the estimation of associations between random variables distorted by observed confounders. Model parameters are estimated using an $L_1$-regularized maximal…
A regression method for proportional, or fractional, data with mixed effects is outlined, designed for analysis of datasets in which the outcomes have substantial weight at the bounds. In such cases a normal approximation is particularly…
This paper is concerned with inference on the regression function of a high-dimensional linear model when outcomes are missing at random. We propose an estimator which combines a Lasso pilot estimate of the regression function with a bias…
We focus on the high-dimensional linear regression problem, where the algorithmic goal is to efficiently infer an unknown feature vector $\beta^*\in\mathbb{R}^p$ from its linear measurements, using a small number $n$ of samples. Unlike most…
The partial least squares algorithm for dependent data realisations is considered. Consequences of ignoring the dependence for the algorithm performance are studied both theoretically and in simulations. It is shown that ignoring certain…