The authors consider the uniformly most powerful invariant test of the testing problems (Ⅰ) H 0: μ′Σ -1 μ≥CH 1: μ′Σ -1 μ<C and (Ⅱ) H 00 : β′X′Xβσ 2≥CH 11 : β′X′Xβσ 2<C u...The authors consider the uniformly most powerful invariant test of the testing problems (Ⅰ) H 0: μ′Σ -1 μ≥CH 1: μ′Σ -1 μ<C and (Ⅱ) H 00 : β′X′Xβσ 2≥CH 11 : β′X′Xβσ 2<C under m dimensional normal population N m(μ, Σ) and normal linear model (Y, Xβ, σ 2) respectively. Furthermore, an application of the uniformly most powerful invariant test is given.展开更多
Abstract Comparison is made between the MINQUE and simple estimate of the error variance in the normal linear model under the mean square errors criterion, where the model matrix need not have full rank and the disper...Abstract Comparison is made between the MINQUE and simple estimate of the error variance in the normal linear model under the mean square errors criterion, where the model matrix need not have full rank and the dispersion matrix can be singular. Our results show that any one of both estimates cannot be always superior to the other. Some sufficient criteria for any one of them to be better than the other are established. Some interesting relations between these two estimates are also given.展开更多
We obtain an ahnost sure central limit theorem(ASCLT)for heavily trimmed sums.We also prove a function-typed ASCLT under the same conditions that assure measurable functions to satisfy the ASCLT for the partial sums o...We obtain an ahnost sure central limit theorem(ASCLT)for heavily trimmed sums.We also prove a function-typed ASCLT under the same conditions that assure measurable functions to satisfy the ASCLT for the partial sums of i.i.d,random variables with EX_1=0,EX_1~2=1.展开更多
Consider the partly linear model K = X1& + go(Ti) + ei, where {(Ti, Xi)}T is a strictlystationary Sequence of random variable8, the ei’8 are i.i.d. random errorsl the K’s are realvalued responsest fo is a &v...Consider the partly linear model K = X1& + go(Ti) + ei, where {(Ti, Xi)}T is a strictlystationary Sequence of random variable8, the ei’8 are i.i.d. random errorsl the K’s are realvalued responsest fo is a &vector of parameters, X is a &vector of explanatory variables,Ti is another explanatory variable ranging over a nondegenerate compact interval. Bnd ona segmnt of observations (T1, Xi 1 Y1 ),’’’ f (Tn, X;, Yn), this article investigates the rates ofconvrgence of the M-estimators for Po and go obtained from the minimisation problemwhere H is a space of B-spline functions of order m + 1 and p(-) is a function chosen suitablyUnder some regularity conditions, it is shown that the estimator of go achieves the optimalglobal rate of convergence of estimators for nonparametric regression, and the estdriator offo is asymptotically normal. The M-estimators here include regression quantile estimators,Li-estimators, Lp-norm estimators, Huber’s type M-estimators and usual least squares estimators. Applications of the asymptotic theory to testing the hypothesis H0: A’β0 =β are alsodiscussed, where β is a given vector and A is a known d × do matrix with rank d0.展开更多
文摘The authors consider the uniformly most powerful invariant test of the testing problems (Ⅰ) H 0: μ′Σ -1 μ≥CH 1: μ′Σ -1 μ<C and (Ⅱ) H 00 : β′X′Xβσ 2≥CH 11 : β′X′Xβσ 2<C under m dimensional normal population N m(μ, Σ) and normal linear model (Y, Xβ, σ 2) respectively. Furthermore, an application of the uniformly most powerful invariant test is given.
基金Partially supported by the National Natural Science Foundation of China (No.10271010)the Natural Science Foundation of Beijing and a Project of Science and Technology of Beijing Education Committee.
文摘Abstract Comparison is made between the MINQUE and simple estimate of the error variance in the normal linear model under the mean square errors criterion, where the model matrix need not have full rank and the dispersion matrix can be singular. Our results show that any one of both estimates cannot be always superior to the other. Some sufficient criteria for any one of them to be better than the other are established. Some interesting relations between these two estimates are also given.
基金Supported by the National Natural Science Foundation of China(No.10071003)Beijing Municipal Education Commission(KM200310028107)
文摘We obtain an ahnost sure central limit theorem(ASCLT)for heavily trimmed sums.We also prove a function-typed ASCLT under the same conditions that assure measurable functions to satisfy the ASCLT for the partial sums of i.i.d,random variables with EX_1=0,EX_1~2=1.
文摘Consider the partly linear model K = X1& + go(Ti) + ei, where {(Ti, Xi)}T is a strictlystationary Sequence of random variable8, the ei’8 are i.i.d. random errorsl the K’s are realvalued responsest fo is a &vector of parameters, X is a &vector of explanatory variables,Ti is another explanatory variable ranging over a nondegenerate compact interval. Bnd ona segmnt of observations (T1, Xi 1 Y1 ),’’’ f (Tn, X;, Yn), this article investigates the rates ofconvrgence of the M-estimators for Po and go obtained from the minimisation problemwhere H is a space of B-spline functions of order m + 1 and p(-) is a function chosen suitablyUnder some regularity conditions, it is shown that the estimator of go achieves the optimalglobal rate of convergence of estimators for nonparametric regression, and the estdriator offo is asymptotically normal. The M-estimators here include regression quantile estimators,Li-estimators, Lp-norm estimators, Huber’s type M-estimators and usual least squares estimators. Applications of the asymptotic theory to testing the hypothesis H0: A’β0 =β are alsodiscussed, where β is a given vector and A is a known d × do matrix with rank d0.
