This article considers the admissibility of the linear estimators for the regression coefficients in the growth curve model subject to an incomplete ellipsoidal restriction. The necessary and sufficient conditions for...This article considers the admissibility of the linear estimators for the regression coefficients in the growth curve model subject to an incomplete ellipsoidal restriction. The necessary and sufficient conditions for linear estimators to be admissible in classes of the homogeneous and non-homogeneous linear estimators, respectively, are obtained under the quadratic loss function. They are generalizations of some existing results in literature.展开更多
In this paper, we study the issue of admissibility in the growth curve model with respect to restricted parameter sets under matrix loss function. We obtain some neces- sary and sufficient conditions that the linear e...In this paper, we study the issue of admissibility in the growth curve model with respect to restricted parameter sets under matrix loss function. We obtain some neces- sary and sufficient conditions that the linear estimators of KBL are admissible in the class of homogeneous linear estimators and in the class of non-homogeneous linear estimators under the growth curve model with respect to restricted parameter sets, respectively.展开更多
For the growth curve model with respect to inequality restriction： Y = XBZ ＋ε,ε（0, σ2V I）, trNB ≥0, this paper gives some necessary and sufficient conditions for the linear estimator of KBL to be admissible in...For the growth curve model with respect to inequality restriction： Y = XBZ ＋ε,ε（0, σ2V I）, trNB ≥0, this paper gives some necessary and sufficient conditions for the linear estimator of KBL to be admissible in the class of homogeneous linear estimators LH and nonhomogeneous linear estimators LI, respectively, under the quadratic loss function tr（d（Y） - KBL）＇（d（Y） - KBL）.展开更多
In this paper, we first study the linear regression model and obtain a norm-minimized estimator of the parameter vector by using the g-inverse and the singular value decomposition of matrix X. We then investigate the ...In this paper, we first study the linear regression model and obtain a norm-minimized estimator of the parameter vector by using the g-inverse and the singular value decomposition of matrix X. We then investigate the growth curve model (GCM) and extend the GCM to a generalized GCM (GGCM) by using high order tensors. The parameter estimations in GGCMs are also achieved in this way.展开更多
By using the vector-method of matrix, we study Growth Curve Model with respect to linear constraint. Under matrix loss function and vector loss function, we obtain necessary and sufficient conditions for admissibility...By using the vector-method of matrix, we study Growth Curve Model with respect to linear constraint. Under matrix loss function and vector loss function, we obtain necessary and sufficient conditions for admissibility of linear estimators of parameters in the inhomogeneous linear class.展开更多
This paper considers the simultaneous estimation of linear function tr(D’B)+tr(C∑) of the regression coefficients matrix B and the covariance matrix ∑,and gives(i) the MINQLE(U,I) tr(D’B)+tr(C∑) of an estimable f...This paper considers the simultaneous estimation of linear function tr(D’B)+tr(C∑) of the regression coefficients matrix B and the covariance matrix ∑,and gives(i) the MINQLE(U,I) tr(D’B)+tr(C∑) of an estimable function tr(O’B)+tr(C∑); (ii) the n.s.conditions for tr(D’B)+tr(C∑) to be the UMVIQLUE of tr(D’B)+tr(C∑);(iii) the n.s.conditions for tr(D’B)+tr(C∑)’s UMVIQLUE to be existent,and shows that tr(D’B) +tr(C∑) is just the UMVIQLUE of tr(D’B)+tr(C∑) (provided a UMVIQLUE exists);(iv) the n.s.conditions for any invariant quadratic plus linear estimation y’MAMy + a’y to be the UMVIQLUE of tr(D’B)+tr(C∑).展开更多
Abstract： In this paper, we discuss the influence analysis of BLUE in growth curve model with covariate matrix disturbance, and establish the relationships of BLUEs among different models, give the measurement and co...Abstract： In this paper, we discuss the influence analysis of BLUE in growth curve model with covariate matrix disturbance, and establish the relationships of BLUEs among different models, give the measurement and computational formula which can assess the disturbing influence.展开更多
基金Supported by Pre-Study Program of NBRP (2003CCA02400)NSFC (10671007)NSFC (60772036),China
文摘This article considers the admissibility of the linear estimators for the regression coefficients in the growth curve model subject to an incomplete ellipsoidal restriction. The necessary and sufficient conditions for linear estimators to be admissible in classes of the homogeneous and non-homogeneous linear estimators, respectively, are obtained under the quadratic loss function. They are generalizations of some existing results in literature.
基金supported by the NNSF of China(60736047,10671080)NCET(06-672)
文摘In this paper, we study the issue of admissibility in the growth curve model with respect to restricted parameter sets under matrix loss function. We obtain some neces- sary and sufficient conditions that the linear estimators of KBL are admissible in the class of homogeneous linear estimators and in the class of non-homogeneous linear estimators under the growth curve model with respect to restricted parameter sets, respectively.
文摘For the growth curve model with respect to inequality restriction： Y = XBZ ＋ε,ε（0, σ2V I）, trNB ≥0, this paper gives some necessary and sufficient conditions for the linear estimator of KBL to be admissible in the class of homogeneous linear estimators LH and nonhomogeneous linear estimators LI, respectively, under the quadratic loss function tr（d（Y） - KBL）＇（d（Y） - KBL）.
文摘In this paper, we first study the linear regression model and obtain a norm-minimized estimator of the parameter vector by using the g-inverse and the singular value decomposition of matrix X. We then investigate the growth curve model (GCM) and extend the GCM to a generalized GCM (GGCM) by using high order tensors. The parameter estimations in GGCMs are also achieved in this way.
文摘By using the vector-method of matrix, we study Growth Curve Model with respect to linear constraint. Under matrix loss function and vector loss function, we obtain necessary and sufficient conditions for admissibility of linear estimators of parameters in the inhomogeneous linear class.
基金Project supported by the National Natural Science Foundation of China
文摘This paper considers the simultaneous estimation of linear function tr(D’B)+tr(C∑) of the regression coefficients matrix B and the covariance matrix ∑,and gives(i) the MINQLE(U,I) tr(D’B)+tr(C∑) of an estimable function tr(O’B)+tr(C∑); (ii) the n.s.conditions for tr(D’B)+tr(C∑) to be the UMVIQLUE of tr(D’B)+tr(C∑);(iii) the n.s.conditions for tr(D’B)+tr(C∑)’s UMVIQLUE to be existent,and shows that tr(D’B) +tr(C∑) is just the UMVIQLUE of tr(D’B)+tr(C∑) (provided a UMVIQLUE exists);(iv) the n.s.conditions for any invariant quadratic plus linear estimation y’MAMy + a’y to be the UMVIQLUE of tr(D’B)+tr(C∑).
文摘Abstract： In this paper, we discuss the influence analysis of BLUE in growth curve model with covariate matrix disturbance, and establish the relationships of BLUEs among different models, give the measurement and computational formula which can assess the disturbing influence.
