The Balanced LS Estimation Of The Regressive Coefficient In Linear Model And Its Prediction

Inspired by the idea of Zeller's balanced loss function, a new standard is presented for estimating the regression coefficient of linear model and the estimation named Balanced LS Estimation is gained under the new standard.In Chapter 3, the existed theories and methods of linear model are discussed. In Chapter 2, the Balanced LS Estimation is defined for the linear model when its error covariance is positive definite or singular. The new estimation as well as the necessary and sufficient conditions is gained for its unbiasedness, efficiency and admissibility. Because the estimation contains parameters t and L, what the value of t and L brings to the Balanced LS Estimation is discussed. A necessary and sufficient condition for the unbiasedness of Balanced LS Estimation is gained, and for the given L, t can be chosen to make the MSEM of the Balanced LS Estimation less than that of OLS Estimation. For the given t when the Balanced LS Estimation is unbiased, L can be chosen to make the MSEM of the Balanced LS Estimation less than that of OLS Estimation. When X is satisfied with some conditions, the sufficient conditions are gained for the Balanced LS Estimation to be efficient than OLS Estimation.In Chapter 3, the estimations of the regression coefficients are studied when they are restricted by linear equations and when they are bounded.In Chapter 4, a new concept--balanced LS prediction is presented in the field of prediction of the linear model, and the optimal unbiased balanced LS prediction is gained.In Chapter 5, a linear regression model for the trade datas is set up. When the multilinearity exist in the design matrix X, the ridge estimation and the Balanced LS Estimation is respectively used to improve OLS estimation. Under this circumstances the error squares of Balanced LS Estimation is less than that of the ridge estimation.