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We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…

A least product relative error criterion is proposed for multiplicative regression models. It is invariant under scale transformation of the outcome and covariates. In addition, the objective function is smooth and convex, resulting in a…

In regression models involving economic variables such as income, log transformation is typically taken to achieve approximate normality and stabilize the variance. However, often the interest is predicting individual values or means of the…

This paper provides an alternative to penalized estimators for estimation and vari- able selection in high dimensional linear regression models with measurement error or missing covariates. We propose estimation via bias corrected least…

This paper studies the properties of linear regression on centrality measures when network data is sparse and observed with error. We make three contributions in this setting. First, we show that OLS estimators can become inconsistent under…

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.…

The bias of an estimator is defined as the difference of its expected value from the parameter to be estimated, where the expectation is with respect to the model. Loosely speaking, small bias reflects the desire that if an experiment is…

Finite sample properties of multiple imputation estimators under the linear regression model are studied. The exact bias of the multiple imputation variance estimator is presented. A method of reducing the bias is presented and simulation…

Consider the problem of estimating the mean of a Gaussian random vector when the mean vector is assumed to be in a given convex set. The most natural solution is to take the Euclidean projection of the data vector on to this convex set; in…

Penalized spline estimation with discrete difference penalties (P-splines) is a popular estimation method for semiparametric models, but the classical least-squares estimator is highly sensitive to deviations from its ideal model…

A bias-reduced estimator is proposed for the mean absolute deviation parameter of a median regression model. A workaround is devised for the lack of smoothness in the sense conventionally required in general bias-reduced estimation. A local…

In small area estimation different data sources are integrated in order to produce reliable estimates of target parameters (e.g., a mean or a proportion) for a collection of small subsets (areas) of a finite population. Regression models…

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…

It is well known that individual parameters of strongly correlated predictor variables in a linear model cannot be accurately estimated by the least squares regression due to multicollinearity generated by such variables. Surprisingly, an…

In the value-added literature, it is often claimed that regressing on empirical Bayes shrinkage estimates corrects for the measurement error problem in linear regression. We clarify the conditions needed; we argue that these conditions are…

Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work,…

In this paper, a Mixed Data Sampling (MIDAS) model is studied when both low and high frequency variables are contaminated with measurement error. It is shown that the profile likelihood estimator becomes inconsistent in the presence of…

Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of…

The main object of investigation in this paper is a very general regression model in optional setting - when an observed process is an optional semimartingale depending on an unknown parameter. It is well-known that statistical data may…

For the nonparametric regression models with covariates contaminated with normal measurement errors, this paper proposes an extrapolation algorithm to estimate the nonparametric regression functions. By applying the conditional expectation…