Estimation of covariance matrix using multi-response local polynomial estimator for designing children growth charts: A theoretically discussion

In statistical analysis for instance regression analysis we always be faced a estimation problem of regression function which draws relationship between variables in the regression model. In the real cases we frequently meet the relationship between one or more response variables and one or more predictor variables where there are correlations between responses that is called a multi-response regression model. There are two approaches to estimate the multi-response regression model, i.e., parametric and nonparametric. One of estimators in nonparametric regression model is local polynomial estimator for estimating the regression function. Since there are correlations between responses then in the estimating of regression function we need a weight matrix that is to be inverse of covariance matrix of error. Therefore, the main objective of this research is to estimate of covariance matrix of error by using multi-response local polinomial estimator. The result of this research is a covariance matrix estimator that is in the future can be used to design children growth charts.