This paper discusses a randomized Logistic equation $\dot N(t) = (r + \alpha \dot B(t))N(t)[1 - \frac{{N(t)}}{K}]$ with an initial value N(0) = N 0, and N 0 is a random variable satisfying 0 < N 0 < K. The exist...This paper discusses a randomized Logistic equation $\dot N(t) = (r + \alpha \dot B(t))N(t)[1 - \frac{{N(t)}}{K}]$ with an initial value N(0) = N 0, and N 0 is a random variable satisfying 0 < N 0 < K. The existence, uniqueness and global attractivity of positive solutions and maximum likelihood estimate (MLE) of the parameters of the equation are studied.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
Recently generalized exponential distribution has received considerable attentions. In this paper, we deal with the Bayesian inference of the unknown parameters of the progressively censored generalized exponential di...Recently generalized exponential distribution has received considerable attentions. In this paper, we deal with the Bayesian inference of the unknown parameters of the progressively censored generalized exponential distribution. It is assumed that the scale and the shape parameters have independent gamma priors. The Bayes estimates of the unknown parameters cannot be obtained in the closed form. Lindley’s approximation and importance sampling technique have been suggested to compute the approximate Bayes estimates. Markov Chain Monte Carlo method has been used to compute the approximate Bayes estimates and also to construct the highest posterior density credible intervals. We also provide different criteria to compare two different sampling schemes and hence to find the optimal sampling schemes. It is observed that finding the optimum censoring procedure is a computationally expensive process. And we have recommended to use the sub-optimal censoring procedure, which can be obtained very easily. Monte Carlo simulations are performed to compare the performances of the different methods and one data analysis has been performed for illustrative purposes.展开更多
This paper presents an estimator of location vector based on one dimensional projection of high dimensional data.The properties of the new estimator including consistency,asymptotic normality and robustness are discus...This paper presents an estimator of location vector based on one dimensional projection of high dimensional data.The properties of the new estimator including consistency,asymptotic normality and robustness are discussed.It is proved that the estimator is not only strongly consistent and asymptotically normal but also with a breakdown point 1/2 and a bounded influence function.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
基金This work was partially supported by the National Natural Science Foundation of China(Grant Nos.10431010 and 10571021)the Key Laboratory for Applied Statistics of Ministry of Education of China(KLAS)
文摘This paper discusses a randomized Logistic equation $\dot N(t) = (r + \alpha \dot B(t))N(t)[1 - \frac{{N(t)}}{K}]$ with an initial value N(0) = N 0, and N 0 is a random variable satisfying 0 < N 0 < K. The existence, uniqueness and global attractivity of positive solutions and maximum likelihood estimate (MLE) of the parameters of the equation are studied.
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supported by a grant from the Department of Science and Technology, Government of India
文摘Recently generalized exponential distribution has received considerable attentions. In this paper, we deal with the Bayesian inference of the unknown parameters of the progressively censored generalized exponential distribution. It is assumed that the scale and the shape parameters have independent gamma priors. The Bayes estimates of the unknown parameters cannot be obtained in the closed form. Lindley’s approximation and importance sampling technique have been suggested to compute the approximate Bayes estimates. Markov Chain Monte Carlo method has been used to compute the approximate Bayes estimates and also to construct the highest posterior density credible intervals. We also provide different criteria to compare two different sampling schemes and hence to find the optimal sampling schemes. It is observed that finding the optimum censoring procedure is a computationally expensive process. And we have recommended to use the sub-optimal censoring procedure, which can be obtained very easily. Monte Carlo simulations are performed to compare the performances of the different methods and one data analysis has been performed for illustrative purposes.
文摘This paper presents an estimator of location vector based on one dimensional projection of high dimensional data.The properties of the new estimator including consistency,asymptotic normality and robustness are discussed.It is proved that the estimator is not only strongly consistent and asymptotically normal but also with a breakdown point 1/2 and a bounded influence function.
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.
