Related papers: Least Squares Inference for Data with Network Depe…
This book is meant to provide an introduction to linear models and the theories behind them. Our goal is to give a rigorous introduction to the readers with prior exposure to ordinary least squares. In machine learning, the output is…
In this paper, we consider a class of nonlinear regression problems without the assumption of being independent and identically distributed. We propose a correspondent mini-max problem for nonlinear regression and give a numerical…
We consider a multivariate functional measurement error model $AX\approx B$. The errors in $[A,B]$ are uncorrelated, row-wise independent, and have equal (unknown) variances. We study the total least squares estimator of $X$, which, in the…
Weak consistency and asymptotic normality of the ordinary least-squares estimator in a linear regression with adaptive learning is derived when the crucial, so-called, `gain' parameter is estimated in a first step by nonlinear least squares…
We discuss techniques of estimation and inference for nonstationary nonlinear cohort panels with learning from experience, showing, inter alia, the consistency and asymptotic normality of the nonlinear least squares estimator used in…
Convergence properties of empirical risk minimizers can be conveniently expressed in terms of the associated population risk. To derive bounds for the performance of the estimator under covariate shift, however, pointwise convergence rates…
This paper focuses on the problem of recursive nonlinear least squares parameter estimation in multi-agent networks, in which the individual agents observe sequentially over time an independent and identically distributed (i.i.d.)…
A general method of minimization using correlation coefficients and order statistics is evaluated relative to least squares procedures in the estimation of parameters for normal data in simple linear regression.
In this note a new high performance least squares parameter estimator is proposed. The main features of the estimator are: (i) global exponential convergence is guaranteed for all identifiable linear regression equations; (ii) it…
We provide an improved analysis of standard differentially private gradient descent for linear regression under the squared error loss. Under modest assumptions on the input, we characterize the distribution of the iterate at each time…
Concerning bivariate least squares linear regression, the classical results obtained for extreme structural models in earlier attempts are reviewed using a new formalism in terms of deviation (matrix) traces which, for homoscedastic data,…
Expectile regression is a useful tool for exploring the relation between the response and the explanatory variables beyond the conditional mean. This article develops a continuous threshold expectile regression for modeling data in which…
We consider inference on a scalar regression coefficient under a constraint on the magnitude of the control coefficients. A class of estimators based on a regularized propensity score regression is shown to exactly solve a tradeoff between…
We investigate the problem of statistical inference for logistic regression with high-dimensional covariates in settings where dependence among individuals is induced by an underlying Markov random field. Going beyond the pairwise…
This paper deals with improvement of linear quantile regression, when there are a few distinct values of the covariates but many replicates. On can improve asymptotic efficiency of the estimated regression coefficients by using suitable…
In a regression setting with a response vector and given regressor vectors, a typical question is to what extent the response is related to these regressors, specifically, how well it can be approximated by a linear combination of the…
The standard linear and logistic regression models assume that the response variables are independent, but share the same linear relationship to their corresponding vectors of covariates. The assumption that the response variables are…
Causal inference with observational studies often relies on the assumptions of unconfoundedness and overlap of covariate distributions in different treatment groups. The overlap assumption is violated when some units have propensity scores…
We study the semiparametric efficient estimation of a class of linear functionals in settings where a complete multivariate dataset is supplemented by additional datasets recording subsets of the variables of interest. These datasets are…
Simplicial-simplicial regression refers to the regression setting where both the responses and predictor variables lie within the simplex space, i.e. they are compositional. For this setting, constrained least squares, where the regression…