Related papers: Least Squares with Error in Variables

This paper proposes the capped least squares regression with an adaptive resistance parameter, hence the name, adaptive capped least squares regression. The key observation is, by taking the resistant parameter to be data dependent, the…

The estimation of regression parameters in spatially referenced data plays a crucial role across various scientific domains. A common approach involves employing an additive regression model to capture the relationship between observations…

Hierarchical statistical models are widely employed in information science and data engineering. The models consist of two types of variables: observable variables that represent the given data and latent variables for the unobservable…

A multivariate errors-in-variables (EIV) model with an intercept term, and a polynomial EIV model are considered. Focus is made on a structural homoskedastic case, where vectors of covariates are i.i.d. and measurement errors are i.i.d. as…

We study the least squares estimator in the residual variance estimation context. We show that the mean squared differences of paired observations are asymptotically normally distributed. We further establish that, by regressing the mean…

A linear multiple regression model in function spaces is formulated, under temporal correlated errors. This formulation involves kernel regressors. A generalized least-squared regression parameter estimator is derived. Its asymptotic…

Covariate-adaptive randomization is widely used in clinical trials to balance prognostic factors, and regression adjustments are often adopted to further enhance the estimation and inference efficiency. In practice, the covariates may…

We study the statistical properties of the least squares estimator in unimodal sequence estimation. Although closely related to isotonic regression, unimodal regression has not been as extensively studied. We show that the unimodal least…

This paper is concerned with the least squares estimator for a basic class of nonlinear autoregressive models, whose outputs are not necessarily to be ergodic. Several asymptotic properties of the least squares estimator have been…

In this paper, we propose deep partial least squares for the estimation of high-dimensional nonlinear instrumental variable regression. As a precursor to a flexible deep neural network architecture, our methodology uses partial least…

Linear regression is arguably the most widely used statistical method. With fixed regressors and correlated errors, the conventional wisdom is to modify the variance-covariance estimator to accommodate the known correlation structure of the…

In modern experimental science, there is a common problem of estimating the coefficients of a linear regression in a context where the variables of interest cannot be observed simultaneously. When there is a categorical variable that is…

This study considers various semiparametric difference-in-differences models under different assumptions on the relation between the treatment group identifier, time and covariates for cross-sectional and panel data. The variance lower…

We study the least square estimator, in the framework of simple linear regression, when the deviance term $\varepsilon$ with respect to the linear model is modeled by a uniform distribution. In particular, we give the law of this estimator,…

Many regularization schemes for high-dimensional regression have been put forward. Most require the choice of a tuning parameter, using model selection criteria or cross-validation schemes. We show that a simple non-negative or…

Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required.…

Monte Carlo integration with variance reduction by means of control variates can be implemented by the ordinary least squares estimator for the intercept in a multiple linear regression model with the integrand as response and the control…

Regression analysis is an important instrument to determine the effect of the explanatory variables on response variables. When outliers and bias errors are present, the standard weighted least squares estimator may perform poorly. For this…

Randomized experiments have become important tools in empirical research. In a completely randomized treatment-control experiment, the simple difference in means of the outcome is unbiased for the average treatment effect, and covariate…

As longitudinal data becomes more available in many settings, policy makers are increasingly interested in the effect of time-varying treatments (e.g. sustained treatment strategies). In settings such as this, the preferred analysis…