msreg: A command for consistent estimation of linear regression models using matched data

Economists often use matched samples, especially when dealing with earning data where some observations are missing in one sample and need to be imputed from another sample. Hirukawa and Prokhorov (2018, Journal of Econometrics 203: 344–358) show that the ordinary least-squares estimator using matched samples is inconsistent and propose two consistent estimators. We describe a new command, msreg, that implements these two consistent estimators based on two samples. The estimators attain the parametric convergence rate if the number of continuous matching variables is no greater than four.

Comparison of Two Estimators of the Regression Coefficient Vector Under Pitman’s Closeness Criterion

Schaffrin and Toutenburg [1] proposed a weighted mixed estimation based on the sample information and the stochastic prior information, and they also show that the weighted mixed estimator is superior to the ordinary least squares estimator under the mean squared error criterion. However, there has no paper to discuss the performance of the two estimators under the Pitman’s closeness criterion. This paper presents the comparison of the weighted mixed estimator and the ordinary least squares estimator using the Pitman’s closeness criterion. A simulation study is performed to illustrate the performance of the weighted mixed estimator and the ordinary least squares estimator under the Pitman’s closeness criterion.

A New Biased Estimator to Combat the Multicollinearity of the Gaussian Linear Regression Model

In a multiple linear regression model, the ordinary least squares estimator is inefficient when the multicollinearity problem exists. Many authors have proposed different estimators to overcome the multicollinearity problem for linear regression models. This paper introduces a new regression estimator, called the Dawoud–Kibria estimator, as an alternative to the ordinary least squares estimator. Theory and simulation results show that this estimator performs better than other regression estimators under some conditions, according to the mean squares error criterion. The real-life datasets are used to illustrate the findings of the paper.

Time–Frequency Regression

Wavelet analysis is widely used to trace macroeconomic and financial phenomena in time–frequency domains. However, existing wavelet measures diverge from conventional regression estimators. Furthermore, a direct comparison between wavelet and traditional regression analyses is difficult. In this study, we modify the partial wavelet gain to provide an estimator that corresponds to the ordinary least squares estimator at each point of the time–frequency space. We argue that from the viewpoint of practical applications, the modified partial wavelet gain is suitable for contemporary regressions across time and frequencies, whereas the original partial wavelet gain is suitable for evaluating an aggregate relationship of contemporaneous and lead-lag relationships.

Two-Parameter Modified Ridge-Type M-Estimator for Linear Regression Model

The general linear regression model has been one of the most frequently used models over the years, with the ordinary least squares estimator (OLS) used to estimate its parameter. The problems of the OLS estimator for linear regression analysis include that of multicollinearity and outliers, which lead to unfavourable results. This study proposed a two-parameter ridge-type modified M-estimator (RTMME) based on the M-estimator to deal with the combined problem resulting from multicollinearity and outliers. Through theoretical proofs, Monte Carlo simulation, and a numerical example, the proposed estimator outperforms the modified ridge-type estimator and some other considered existing estimators.

Performance of Ridge Estimators Based on Weighted Geometric Mean and Harmonic Mean

Ordinary least squares estimator (OLS) becomes unstable if there is a linear dependence between any two predictors. When such situation arises ridge estimator will yield more stable estimates to the regression coefficients than OLS estimator. Here we suggest two modified ridge estimators based on weights, where weights being the first two largest eigen values. We compare their MSE with some of the existing ridge estimators which are defined in the literature. Performance of the suggested estimators is evaluated empirically for a wide range of degree of multicollinearity. Simulation study indicates that the performance of the suggested estimators is slightly better and more stable with respect to degree of multicollinearity, sample size, and error variance.

Inference robust to outliers with ℓ1-norm penalization

This paper considers inference in a linear regression model with outliers in which the number of outliers can grow with sample size while their proportion goes to 0. We propose a square-root lasso ℓ1-norm penalized estimator. We derive rates of convergence and establish asymptotic normality. Our estimator has the same asymptotic variance as the OLS estimator in the standard linear model. This enables us to build tests and confidence sets in the usual and simple manner. The proposed procedure is also computationally advantageous, it amounts to solving a convex optimization program. Overall, the suggested approach offers a practical robust alternative to the ordinary least squares estimator.

Estimation of Survival Function for Rayleigh Distribution by Ranking function:-

In this article, performing and deriving te probability density function for Rayleigh distribution is done by using ordinary least squares estimator method and Rank set estimator method. Then creating interval for scale parameter of Rayleigh distribution. Anew method using is used for fuzzy scale parameter. After that creating the survival and hazard functions for two ranking functions are conducted to show which one is beast.

A Modified New Two-Parameter Estimator in a Linear Regression Model

The literature has shown that ordinary least squares estimator (OLSE) is not best when the explanatory variables are related, that is, when multicollinearity is present. This estimator becomes unstable and gives a misleading conclusion. In this study, a modified new two-parameter estimator based on prior information for the vector of parameters is proposed to circumvent the problem of multicollinearity. This new estimator includes the special cases of the ordinary least squares estimator (OLSE), the ridge estimator (RRE), the Liu estimator (LE), the modified ridge estimator (MRE), and the modified Liu estimator (MLE). Furthermore, the superiority of the new estimator over OLSE, RRE, LE, MRE, MLE, and the two-parameter estimator proposed by Ozkale and Kaciranlar (2007) was obtained by using the mean squared error matrix criterion. In conclusion, a numerical example and a simulation study were conducted to illustrate the theoretical results.