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For a high-dimensional linear model with a finite number of covariates measured with error, we study statistical inference on the parameters associated with the error-prone covariates, and propose a new corrected decorrelated score test and…
The function-on-function linear regression model in which the response and predictors consist of random curves has become a general framework to investigate the relationship between the functional response and functional predictors.…
In this paper we propose a convolution estimator for estimating the density of a response variable that employs an underlying multiple regression framework to enhance the accuracy of density estimates through the incorporation of auxiliary…
Scalar-on-function logistic regression, where the response is a binary outcome and the predictor consists of random curves, has become a general framework to explore a linear relationship between the binary outcome and functional predictor.…
We develop a new permutation test for inference on a subvector of coefficients in linear models. The test is exact when the regressors and the error terms are independent. Then, we show that the test is asymptotically of correct level,…
We consider a quadratic functional regression model in which a scalar response depends on a functional predictor; the common functional linear model is a special case. We wish to test the significance of the nonlinear term in the model. We…
This paper motivates and develops a novel and focused approach to variable selection in linear regression models. For estimating the regression mean $\mu=\E\,(Y\midd x_0)$, for the covariate vector of a given individual, there is a list of…
When a linear model is adjusted to control for additional explanatory variables the sign of a fitted coefficient may reverse. Here these reversals are studied using coefficients of determination. The resulting theory can be used to…
Understanding statistical inference under possibly non-sparse high-dimensional models has gained much interest recently. For a given component of the regression coefficient, we show that the difficulty of the problem depends on the sparsity…
Testing procedures for assessing a parametric regression model with circular response and $\mathbb{R}^d$-valued covariate are proposed and analyzed in this work both for independent and for spatially correlated data. The test statistics are…
This paper studies inference for quadratic forms of linear regression coefficients with clustered data and many covariates. Our framework covers three important special cases: instrumental variables regression with many instruments and…
We propose a procedure to decide between the null hypothesis of (strict) stationarity and the alternative of non-stationarity, in the context of a Random Coefficient AutoRegression (RCAR). The procedure is based on randomising a diagnostic…
We consider nonparametric estimation of a regression curve when the data are observed with multiplicative distortion which depends on an observed confounding variable. We suggest several estimators, ranging from a relatively simple one that…
The random coefficients model is an extension of the linear regression model that allows for unobserved heterogeneity in the population by modeling the regression coefficients as random variables. Given data from this model, the statistical…
Consider a linear regression model and suppose that our aim is to find a confidence interval for a specified linear combination of the regression parameters. In practice, it is common to perform a Durbin-Watson pretest of the null…
This work gives a simultaneous analysis of both the ordinary least squares estimator and the ridge regression estimator in the random design setting under mild assumptions on the covariate/response distributions. In particular, the analysis…
We study least squares linear regression over $N$ uncorrelated Gaussian features that are selected in order of decreasing variance. When the number of selected features $p$ is at most the sample size $n$, the estimator under consideration…
In this paper we explore partial coherence as a tool for evaluating causal influence of one signal sequence on another. In some cases the signal sequence is sampled from a time- or space-series. The key idea is to establish a connection…
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 presents a selective survey of recent developments in statistical inference and multiple testing for high-dimensional regression models, including linear and logistic regression. We examine the construction of confidence…