Robustness of Minimum Norm Quadratic Unbiased Estimator of Variance Under the General Linear Model

Necessary and sufficient conditions for equalities between a 2 y′(I-P Xx)y and minimum norm quadratic unbiased estimator of variance under the general linear model, where a 2 is a known positive number, are derived. Further, when the Gauss? Markov estimators and the ordinary least squares estimator are identical, a relative simply equivalent condition is obtained. At last, this condition is applied to an interesting example.

QUADRATIC ADMISSIBLE ESTIMATE OF COVARIANCE IN PSEUDO-ELLIPTICAL CONTOURED DISTRIBUTION

This article mainly discusses the admissibility of quadratic estimate of covariance in pseudoelliptical distribution. Under the quadratic loss function, the necessary and sufficient conditions that a quadratic estimator is an admissible estimator of covariance in the class of quadratic estimators are obtained. A complete class of the quadratic estimator class is also given.

Parameter Method Data Processing for CPⅢ Precise Trigonometric Leveling Network

In view of the limitation of the difference method,the adjustment model of CPⅢprecise trigonometric leveling control network based on the parameter method was proposed in the present paper.The experiment results show that this model has a simple algorithm and high data utilization,avoids the negative influences caused by the correlation among the data acquired from the difference method and its accuracy is improved compared with the difference method.In addition,the strict weight of CPⅢprecise trigonometric leveling control network was also discussed in this paper.The results demonstrate that the ranging error of trigonometric leveling can be neglected when the vertical angle is less than 3 degrees.The accuracy of CPⅢprecise trigonometric leveling control network has not changed significantly before and after strict weight.

Robustness of Minimum Norm Quadratic Unbiased Estimator of Variance for the General Linear Model

In this paper, necessary and sufficient conditions for equalities betweenα~2y^1(I-P_X)y and under the general linear model, whereand α~2 is a known positive number, are derived. Furthermore, when the Gauss-Markovestimators and the ordinary least squares estimators are identical, we obtain a simpleequivalent condition.

ADMISSIBILITY OF LINEAR ESTIMATORS OF REGRESSION COEFFICIENTS UNDER QUADRATIC LOSS

For the general fixed effects linear model: Y = X_T+ε, ε～N(0, V), V≥0, weobtain the necessary and sufficient conditions for LY +a to be admissible for a linear estimablefunction S_r in the class of all estimators under the loss function (d -- Sr)'D(d --Sr), whereD≥0 is known. For the general random effects linear model: Y = Xβ+ε,(βε)～N((Aα 0), (V_(11)V_(12)V_(21)V_(22))), ∧= XV_(11)X'+XV_(12)+ V_(21)X+V_(22)≥0, we also get the necessaryand sufficient conditions for LY+a to be admissible for a linear estimable function Sα+Qβin the class of all estimators under the loss function (d-Sα-Qβ)'D(d-Sα-Qβ).whereD≥0 is known.

Trabecular spacing estimation based on quadratic transformation algorithm

The quadratic transformation method is proposed to estimate the trabecular spac- ing （Tb.Sp）, an important index for osteoporosis diagnosis. The performance of this algorithm was investigated by scatter model, two-dimension finite difference time domain （2D-FDTD） simulation and in vitro experiments of bovine cancellous bone specimens. Comparing with the other four methods autoregressive cepstrum （AR）, adaptive filter- autoregressive cepstral （AFAR）, inverse filter-autoregressive eepstrum （InvAR）, and simplified inverse filter tracking （SIFT）, quadratic transformation is much more stable and accurate. The results demonstrated that quadratic transformation is a great algorithm for Tb.SD estimation.