Variance-Covariance Matrix on Mixed Estimator of Spline Truncated, Kernel, and Fourier Series

Regression analysis is an analysis in statistics that is used to investigate the pattern of relationships between response variables and predictor variables. There are three approaches in regression analysis, including parametric, nonparametric, and semiparametric regression. Semiparametric regression which is a combination of parametric and nonparametric regression, meaning that the approach used to establish the link between variables' model has a known data pattern and an unknown data pattern. The most popular nonparametric elements are spline truncated, kernel, and fourier series. Regression analysis is characterized by the amount of responses utilized in addition to the three different methodologies; for example, biresponse regression is employed when the regression model contains two response variables and the responses are correlated. The variance-covariance matrix, which serves as weights in the parameter estimator in the regression model, theoretically expresses the representation of the connection between the answers. There haven't been many research on the variance-covariance matrix used in mixed estimators for biresponse semiparametric regression up to now to account for the correlation between response variables. The goal of this study is to improve the estimation of the variance-covariance matrix in three mixed estimators, including spline truncated, kernel, and fourier series in biresponse semiparametric regression using the Maximum Likelihood Estimate (MLE) method, wherein estimation of three mixed estimators using the Weighted Least Square (WLS) method. The weights in the mixed estimators model of biresponse semiparametric regression are derived from the estimate of the variance-covariance matrix. Wherein, the estimator of variance-covariance matrix is obtained.