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Solving linear systems is often the computational bottleneck in real-life problems. Iterative solvers are the only option due to the complexity of direct algorithms or because the system matrix is not explicitly known. Here, we develop a…

Regression is one of the most fundamental statistical inference problems. A broad definition of regression problems is as estimation of the distribution of an outcome using a family of probability models indexed by covariates. Despite the…

Random matrix theory has become a widely useful tool in high-dimensional statistics and theoretical machine learning. However, random matrix theory is largely focused on the proportional asymptotics in which the number of columns grows…

In latent variable models the parameter estimation can be implemented by using the joint or the marginal likelihood, based on independence or conditional independence assumptions. The same dilemma occurs within the Bayesian framework with…

This paper develops an approach to inference in a linear regression model when the number of potential explanatory variables is larger than the sample size. The approach treats each regression coefficient in turn as the interest parameter,…

Most data sets comprise of measurements on continuous and categorical variables. In regression and classification Statistics literature, modeling high-dimensional mixed predictors has received limited attention. In this paper we study the…

Quantile regression provides a framework for modeling statistical quantities of interest other than the conditional mean. The regression methodology is well developed for linear models, but less so for nonparametric models. We consider…

Anomalies persist in the foundations of ridge regression as set forth in Hoerl and Kennard (1970) and subsequently. Conventional ridge estimators and their properties do not follow on constraining lengths of solution vectors using…

Predict a new response from a covariate is a challenging task in regression, which raises new question since the era of high-dimensional data. In this paper, we are interested in the inverse regression method from a theoretical viewpoint.…

We present a method to infer on joint regression coefficients obtained from marginal regressions using a reference panel. This type of scenario is common in genetic fine-mapping, where the estimated marginal associations are reported in…

Because of the advance in technologies, modern statistical studies often encounter linear models with the number of explanatory variables much larger than the sample size. Estimation and variable selection in these high-dimensional problems…

To address the problem of multicollinearity in the logistic regression model, in this paper we propose a new estimator called Stochastic restricted almost unbiased logistic Liu-estimator (SRAULLE) when the prior information is available in…

The inflated beta regression model is widely used for modeling continuous proportions with values at the boundaries. Maximum likelihood estimation for these models is well-known for its sensitivity to outliers, which can severely distort…

A novel approach to price indices, leading to an innovative solution in both a multi-period or a multilateral framework, is presented. The index turns out to be the generalized least squares solution of a regression model linking values and…

Modern algorithms for binary classification rely on an intermediate regression problem for computational tractability. In this paper, we establish a geometric distinction between classification and regression that allows risk in these two…

We address the inference problem concerning regression coefficients in a classical linear regression model using least squares estimates. The analysis is conducted under circumstances where network dependency exists across units in the…

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…

We propose generalized resubstitution error estimators for regression, a broad family of estimators, each corresponding to a choice of empirical probability measures and loss function. The usual sum of squares criterion is a special case…

Reference based multiple imputation methods have become popular for handling missing data in randomised clinical trials. Rubin's variance estimator is well known to be biased compared to the reference based imputation estimator's true…

Data integration has become increasingly popular owing to the availability of multiple data sources. This study considered quantile regression estimation when a key covariate had multiple proxies across several datasets. In a unified…