Admissibility Of Linear Predictions In Linear Models With Constraints

In this paper, admissibility of linear prediction in linear models with constraints under quadratic loss function (d - Qy)'(d - Qy) and matrix loss function (d -Qy)(d -Qy)' are investigated respectively. This thesis is composed of five chapters.In the first chapter, we state some results about linear predictions in the linear models, and the origin of the problems we discussed. And the main works of this paper are also simply introduced.In the second chapter and the third chapter, we study the linear model with linear equality constraint: y = Xβ + e, E(e) = 0, Var(e) = V, V≥0, M'β = 0. Under the above stated loss functions, we give the definitions of conditional admissible prediction and obtain some necessary and sufficient conditions for linear predictions Ly_s (Ly_s +a) of conditional linear predictable variable Qy to be admissible.In chapter 4, we study the linear model with inequality constraint: y = Xβ + e, E(e) = 0, Var(e) = V, V≥ 0, l'β ≥ 0. Under quadratic loss function, the definition of conditional admissible prediction is given and some necessary and sufficient conditions for linear predictions Ly_s (Ly_s + a) of conditional linear predictable variable Qy to be admissible are obtained.Finally, in chapter 5, we also study the linear model with inequality constraint: y = Xβ + e, E(e)=0, Var(e) = σ~2V, V≥0, σ>0, l'β≥0. Under the matrix loss function, we obtained a series of necessary and sufficient conditions for inhomogeneous linear prediction Ly_s + a of conditional linear predictable variable Qy to be admissible.