Moment estimation for multivariate extreme value distribution is describedin this paper. Asymptotic covariance matrix of the estimators is given. The relativeefficiencies of moment estimators as compared with the maxi...Moment estimation for multivariate extreme value distribution is describedin this paper. Asymptotic covariance matrix of the estimators is given. The relativeefficiencies of moment estimators as compared with the maximum likelihood and thestepwise estimators are computed. We show that when there is strong dependencebetween the variates, the generalized variance of moment estimators is much lower thanthe stepwise estimators. It becomes more obvious when the dimension increases.展开更多
In this paper, we consider the change-point estimation in the censored regression model assuming that there exists one change point. A nonparametric estimate of the change-point is proposed and is shown to be strongly...In this paper, we consider the change-point estimation in the censored regression model assuming that there exists one change point. A nonparametric estimate of the change-point is proposed and is shown to be strongly consistent. Furthermore, its convergence rate is also obtained.展开更多
For partial linear model Y = X τ β 0 + g 0(T) + ∈ with unknown β 0 ∈ ? d and an unknown smooth function g 0, this paper considers the Huber-Dutter estimators of β 0, scale σ for the errors and the function g 0 ...For partial linear model Y = X τ β 0 + g 0(T) + ∈ with unknown β 0 ∈ ? d and an unknown smooth function g 0, this paper considers the Huber-Dutter estimators of β 0, scale σ for the errors and the function g 0 approximated by the smoothing B-spline functions, respectively. Under some regularity conditions, the Huber-Dutter estimators of β 0 and σ are shown to be asymptotically normal with the rate of convergence n ?1/2 and the B-spline Huber-Dutter estimator of g 0 achieves the optimal rate of convergence in nonparametric regression. A simulation study and two examples demonstrate that the Huber-Dutter estimator of β 0 is competitive with its M-estimator without scale parameter and the ordinary least square estimator.展开更多
The generalized Friedman’s urn model is a popular urn model which is widely used in many disciplines.In particular,it is extensively used in treatment allocation schemes in clinical trials.In this paper,we show that ...The generalized Friedman’s urn model is a popular urn model which is widely used in many disciplines.In particular,it is extensively used in treatment allocation schemes in clinical trials.In this paper,we show that both the urn composition process and the allocation proportion process can be approximated by a multi-dimensional Gaussian process almost surely for a multi-color generalized Friedman’s urn model with both homogeneous and non-homogeneous generating matrices.The Gaussian process is a solution of a stochastic differential equation.This Gaussian approximation is important for the understanding of the behavior of the urn process and is also useful for statistical inferences.As an application,we obtain the asymptotic properties including the asymptotic normality and the law of the iterated logarithm for a multi-color generalized Friedman's urn model as well as the randomized-play-the-winner rule as a special case.展开更多
Assume that the characteristic index α of stable distribution satisfies 1 < α < 2, and that the distribution is symmetrical about its mean. We consider the change point estimators for stable distribution with ...Assume that the characteristic index α of stable distribution satisfies 1 < α < 2, and that the distribution is symmetrical about its mean. We consider the change point estimators for stable distribution with α or scale parameter β shift. For the one case that mean is a known constant, if α or β changes, then density function will change too. To this end, we suppose the kernel estimation for a change point. For the other case that mean is an unknown constant, we suppose to apply empirical characteristic function to estimate the change-point location. In the two cases, we consider the consistency and strong convergence rate of estimators. Furthermore, we consider the mean shift case. If mean changes, then corresponding characteristic function will change too. To this end, we also apply empirical characteristic function to estimate change point. We obtain the similar convergence rate. Finally, we consider its application on the detection of mean shift in financial market.展开更多
This paper discusses inference for ordered parameters of multinomial distributions. We first show that the asymptotic distributions of their maximum likelihood estimators (MLEs) are not always normal and the bootstrap...This paper discusses inference for ordered parameters of multinomial distributions. We first show that the asymptotic distributions of their maximum likelihood estimators (MLEs) are not always normal and the bootstrap distribution estimators of the MLEs can be inconsistent. Then a class of weighted sum estimators (WSEs) of the ordered parameters is proposed. Properties of the WSEs are studied, including their asymptotic normality. Based on those results, large sample inferences for smooth functions of the ordered parameters can be made. Especially, the confidence intervals of the maximum cell probabilities are constructed. Simulation results indicate that this interval estimation performs much better than the bootstrap approaches in the literature. Finally, the above results for ordered parameters of multinomial distributions are extended to more general distribution models.展开更多
文摘Moment estimation for multivariate extreme value distribution is describedin this paper. Asymptotic covariance matrix of the estimators is given. The relativeefficiencies of moment estimators as compared with the maximum likelihood and thestepwise estimators are computed. We show that when there is strong dependencebetween the variates, the generalized variance of moment estimators is much lower thanthe stepwise estimators. It becomes more obvious when the dimension increases.
基金This work was partially supported by the National Natural Science Foundation of China (Grant No. 10471136) Ph.D. Program Foundation of the Ministry of Education of ChinaSpecial Foundations of the Chinese Academy of Science and USTC.
文摘In this paper, we consider the change-point estimation in the censored regression model assuming that there exists one change point. A nonparametric estimate of the change-point is proposed and is shown to be strongly consistent. Furthermore, its convergence rate is also obtained.
基金the National Natural Science Foundation of China (Grant Nos. 10671106, 10771017)
文摘For partial linear model Y = X τ β 0 + g 0(T) + ∈ with unknown β 0 ∈ ? d and an unknown smooth function g 0, this paper considers the Huber-Dutter estimators of β 0, scale σ for the errors and the function g 0 approximated by the smoothing B-spline functions, respectively. Under some regularity conditions, the Huber-Dutter estimators of β 0 and σ are shown to be asymptotically normal with the rate of convergence n ?1/2 and the B-spline Huber-Dutter estimator of g 0 achieves the optimal rate of convergence in nonparametric regression. A simulation study and two examples demonstrate that the Huber-Dutter estimator of β 0 is competitive with its M-estimator without scale parameter and the ordinary least square estimator.
基金supported by National Natural Science Foundation of China (Grant No. 10771192)National Science Foundation of USA (Grant No. DMS-0349048)
文摘The generalized Friedman’s urn model is a popular urn model which is widely used in many disciplines.In particular,it is extensively used in treatment allocation schemes in clinical trials.In this paper,we show that both the urn composition process and the allocation proportion process can be approximated by a multi-dimensional Gaussian process almost surely for a multi-color generalized Friedman’s urn model with both homogeneous and non-homogeneous generating matrices.The Gaussian process is a solution of a stochastic differential equation.This Gaussian approximation is important for the understanding of the behavior of the urn process and is also useful for statistical inferences.As an application,we obtain the asymptotic properties including the asymptotic normality and the law of the iterated logarithm for a multi-color generalized Friedman's urn model as well as the randomized-play-the-winner rule as a special case.
基金the National Natural Science Foundation of China (Grant No.10471135) Graduate Innovation Fund of the University of Science and Technology of China (Grant No.KD2006063)
文摘Assume that the characteristic index α of stable distribution satisfies 1 < α < 2, and that the distribution is symmetrical about its mean. We consider the change point estimators for stable distribution with α or scale parameter β shift. For the one case that mean is a known constant, if α or β changes, then density function will change too. To this end, we suppose the kernel estimation for a change point. For the other case that mean is an unknown constant, we suppose to apply empirical characteristic function to estimate the change-point location. In the two cases, we consider the consistency and strong convergence rate of estimators. Furthermore, we consider the mean shift case. If mean changes, then corresponding characteristic function will change too. To this end, we also apply empirical characteristic function to estimate change point. We obtain the similar convergence rate. Finally, we consider its application on the detection of mean shift in financial market.
基金supported by National Natural Science Foundation of China (Grant No. 10371126)
文摘This paper discusses inference for ordered parameters of multinomial distributions. We first show that the asymptotic distributions of their maximum likelihood estimators (MLEs) are not always normal and the bootstrap distribution estimators of the MLEs can be inconsistent. Then a class of weighted sum estimators (WSEs) of the ordered parameters is proposed. Properties of the WSEs are studied, including their asymptotic normality. Based on those results, large sample inferences for smooth functions of the ordered parameters can be made. Especially, the confidence intervals of the maximum cell probabilities are constructed. Simulation results indicate that this interval estimation performs much better than the bootstrap approaches in the literature. Finally, the above results for ordered parameters of multinomial distributions are extended to more general distribution models.
