In this paper we extend the concept of Sλ^L（I）- asymptotically statistical equivalence which is a natural combination of λ - statistical convergence and asymptotically I -equivalence. We use the sequence P = （Pk...In this paper we extend the concept of Sλ^L（I）- asymptotically statistical equivalence which is a natural combination of λ - statistical convergence and asymptotically I -equivalence. We use the sequence P = （Pk） which is the sequence of positive real numbers.展开更多
ωB-splines have many optimal properties and can reproduce plentiful commonly-used analytical curves.In this paper,we further propose a non-stationary subdivision method of hierarchically and efficiently generatingωB...ωB-splines have many optimal properties and can reproduce plentiful commonly-used analytical curves.In this paper,we further propose a non-stationary subdivision method of hierarchically and efficiently generatingωB-spline curves of arbitrary order ofωB-spline curves and prove its C^k?2-continuity by two kinds of methods.The first method directly prove that the sequence of control polygons of subdivision of order k converges to a C^k?2-continuousωB-spline curve of order k.The second one is based on the theories upon subdivision masks and asymptotic equivalence etc.,which is more convenient to be further extended to the case of surface subdivision.And the problem of approximation order of this non-stationary subdivision scheme is also discussed.Then a uniform ωB-spline curve has both perfect mathematical representation and efficient generation method,which will benefit the application ofωB-splines.展开更多
A generalized non-stationary curve subdivision （GNS for short） scheme of arbitrary order k≥3 with a parameter has been proposed by Fang et al. in the paper （Fang Mei-e et al., CAGD, 2010（27）： 720-733）. It has ...A generalized non-stationary curve subdivision （GNS for short） scheme of arbitrary order k≥3 with a parameter has been proposed by Fang et al. in the paper （Fang Mei-e et al., CAGD, 2010（27）： 720-733）. It has been proved that the proposed scheme of order k generates C^k-2 continuous curves for k≥4. But the proof of the smoothness in this paper is uncompleted. Moreover, the Cl-continuity of the third order scheme has not been discussed. For this reason, in this paper, we provide a full corrected proof of the smoothness of the GNS scheme of order k for k≥3.展开更多
Linear mixed-effects models are a powerful tool for the analysis of longitudinal data. The aim of this paper is to study model averaging for linear mixed-effects models. The asymptotic distribution of the frequentist ...Linear mixed-effects models are a powerful tool for the analysis of longitudinal data. The aim of this paper is to study model averaging for linear mixed-effects models. The asymptotic distribution of the frequentist model average estimator is derived, and a confidence interval procedure with an actual coverage probability that tends to the nominal level in large samples is developed. The two confidence intervals based on the model averaging and based on the full model are shown to be asymptotically equivalent. A simulation study shows good finite sample performance of the model average estimators.展开更多
文摘In this paper we extend the concept of Sλ^L（I）- asymptotically statistical equivalence which is a natural combination of λ - statistical convergence and asymptotically I -equivalence. We use the sequence P = （Pk） which is the sequence of positive real numbers.
基金the National Natural Science Foundation of China(61772164,61761136010)the Natural Science Foundation of Zhejiang Province(LY17F020025).
文摘ωB-splines have many optimal properties and can reproduce plentiful commonly-used analytical curves.In this paper,we further propose a non-stationary subdivision method of hierarchically and efficiently generatingωB-spline curves of arbitrary order ofωB-spline curves and prove its C^k?2-continuity by two kinds of methods.The first method directly prove that the sequence of control polygons of subdivision of order k converges to a C^k?2-continuousωB-spline curve of order k.The second one is based on the theories upon subdivision masks and asymptotic equivalence etc.,which is more convenient to be further extended to the case of surface subdivision.And the problem of approximation order of this non-stationary subdivision scheme is also discussed.Then a uniform ωB-spline curve has both perfect mathematical representation and efficient generation method,which will benefit the application ofωB-splines.
基金Supported by National Natural Science Foundation of China(Nos.61272032,60904070)
文摘A generalized non-stationary curve subdivision （GNS for short） scheme of arbitrary order k≥3 with a parameter has been proposed by Fang et al. in the paper （Fang Mei-e et al., CAGD, 2010（27）： 720-733）. It has been proved that the proposed scheme of order k generates C^k-2 continuous curves for k≥4. But the proof of the smoothness in this paper is uncompleted. Moreover, the Cl-continuity of the third order scheme has not been discussed. For this reason, in this paper, we provide a full corrected proof of the smoothness of the GNS scheme of order k for k≥3.
文摘Linear mixed-effects models are a powerful tool for the analysis of longitudinal data. The aim of this paper is to study model averaging for linear mixed-effects models. The asymptotic distribution of the frequentist model average estimator is derived, and a confidence interval procedure with an actual coverage probability that tends to the nominal level in large samples is developed. The two confidence intervals based on the model averaging and based on the full model are shown to be asymptotically equivalent. A simulation study shows good finite sample performance of the model average estimators.
