Estimation Problem Of Estimable Functions For One Type Of Two Seemingly Unrelated Growth Curve Models

Linear model has a wide application in real life, so it is so important to research it. Growth curve model in the study of Economics, biology, and epidemiology of such a short time period growth problems is particularly useful. Two seemingly unrelated growth curve model of this article is a special model of growth curve models.This article mainly discusses estimable function estimation of seemingly unrelated growth curve model which is made up of two growth curve equations. Because of parameter in this model is matrix form, so we first transfer it into a vector. Since the vector is not estimable, so we consider its estimable function and use the covariance-adjusted method to get improved estimator sequence of estimable function. Under certain conditions, the improved estimator sequence can eventually be simplified to unique simpler form. Next, combining with the theory of two-stage estimation, we consider the sample covariance as the estimate of the population variance. Then we can get the two-stage covariance-adjusted estimation and verify that it is unbiased estimate, and under certain conditions it is better than the ordinary least square estimation of one equation.Finally we prove that two-stage covariance-adjusted estimation has higher precision when the sample size and the relevant coefficient are larger based on numerical simulation.