In this paper, the author studies the asymptotic accuracies of the one-term Edgeworth expansions and the bootstrap approximation for the studentized MLE from randomly censored exponential population. It is shown that ...In this paper, the author studies the asymptotic accuracies of the one-term Edgeworth expansions and the bootstrap approximation for the studentized MLE from randomly censored exponential population. It is shown that the Edgeworth expansions and the bootstrap approaimation are asymptotically close to the exact distribution of the studentized MLE with a rate.展开更多
The paper discusses the Edgeworth expansion for the mean direction =μ(Fn) of directional data and its 'Studentization'. As an application of the results,we give the corresponding result of von Mises population.
In this paper,Edgeworth expansion for the nearest neighbor\|kernel estimate and random weighting approximation of conditional density are given and the consistency and convergence rate are proved.
We present necessary and sufficient conditions of Edgeworth expansion for distributions of extreme values. As a corollary, rates of the uniform convergence for distributions of extreme values are obtained.
In Part Ⅰ the concept of the general regular variation of n-th order is proposed and its construction is discussed. The uniqueness of the standard expression and the higher order regularity of the auxiliary functions...In Part Ⅰ the concept of the general regular variation of n-th order is proposed and its construction is discussed. The uniqueness of the standard expression and the higher order regularity of the auxiliary functions are proved.展开更多
In this paper, under some fairly general conditions, a first-order Edgeworth expansion for the standardized statistic of βin partial linear models is given, then a non-residual type of consistent estimation for the e...In this paper, under some fairly general conditions, a first-order Edgeworth expansion for the standardized statistic of βin partial linear models is given, then a non-residual type of consistent estimation for the error variance is constructed, and finally an Edgeworth expansion for the corresponding studentized version is presented.展开更多
We give an Edgeworth expansion for densities of order statistics with fixed rank k. The Edgeworth expansion for densities of extreme values is then obtained as a special case k = 1.
In this part II the fundamental inequality of the third order general regular variation is proved and the second order Edgeworth expansion of the distribution of the extreme values is discussed.
This paper is concerned with the distributional properties of a median unbiased estimator of ARCH（0,1） coefficient. The exact distribution of the estimator can be easily derived, however its practical calculations a...This paper is concerned with the distributional properties of a median unbiased estimator of ARCH（0,1） coefficient. The exact distribution of the estimator can be easily derived, however its practical calculations are too heavy to implement, even though the middle range of sample sizes. Since the estimator is shown to have asymptotic normality, asymptotic expansions for the distribution and the percentiles of the estimator are derived as the refinements. Accuracies of expansion formulas are evaluated numerically, and the results of which show that we can effectively use the expansion as a fine approximation of the distribution with rapid calculations. Derived expansion are applied to testing hypothesis of stationarity, and an implementation for a real data set is illustrated.展开更多
Suppose that Z1 , Z2,’’’ Zn are independent normal random variables with common meanμ and variance σ2. Then S2 and have distribution andtn-1 distribution respectively. If the normal assumption fails, there will b...Suppose that Z1 , Z2,’’’ Zn are independent normal random variables with common meanμ and variance σ2. Then S2 and have distribution andtn-1 distribution respectively. If the normal assumption fails, there will be the remaindersof the distribution functions and density functions. This paper gives the direct expansions ofdistribution functions and density functions of S2 alld T up to o(n-1). They are more intuitiveand convenient than usual Edgeworth expansions.展开更多
In this paper, we give an one-term Edgeworth expansion for the standardized least square estimator (LSE) in a linear regression model and its random weighting approximation. So we have not only improved the expansion ...In this paper, we give an one-term Edgeworth expansion for the standardized least square estimator (LSE) in a linear regression model and its random weighting approximation. So we have not only improved the expansion result but also given a practical approximating method.展开更多
A saddlepoint approximation for a two-sample permutation test was obtained by Robinson[7].Although the approximation is very accurate, the formula is very complicated and difficult toapply. In this papert we shall rev...A saddlepoint approximation for a two-sample permutation test was obtained by Robinson[7].Although the approximation is very accurate, the formula is very complicated and difficult toapply. In this papert we shall revisit the same problem from a different angle. We shall first turnthe problem into a conditional probability and then apply a Lugannani-Rice type formula to it,which was developed by Skovagard[8] for the mean of i.i.d. samples and by Jing and Robinson[5]for smooth function of vector means. Both the Lugannani-Rice type formula and Robinson'sformula achieve the same relative error of order O(n-3/2), but the former is very compact andmuch easier to use in practice. Some numerical results will be presented to compare the twoformulas.展开更多
文摘In this paper, the author studies the asymptotic accuracies of the one-term Edgeworth expansions and the bootstrap approximation for the studentized MLE from randomly censored exponential population. It is shown that the Edgeworth expansions and the bootstrap approaimation are asymptotically close to the exact distribution of the studentized MLE with a rate.
文摘The paper discusses the Edgeworth expansion for the mean direction =μ(Fn) of directional data and its 'Studentization'. As an application of the results,we give the corresponding result of von Mises population.
文摘In this paper,Edgeworth expansion for the nearest neighbor\|kernel estimate and random weighting approximation of conditional density are given and the consistency and convergence rate are proved.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19771004) Education Foundation of Yunnan Province .
文摘We present necessary and sufficient conditions of Edgeworth expansion for distributions of extreme values. As a corollary, rates of the uniform convergence for distributions of extreme values are obtained.
文摘In Part Ⅰ the concept of the general regular variation of n-th order is proposed and its construction is discussed. The uniqueness of the standard expression and the higher order regularity of the auxiliary functions are proved.
文摘In this paper, under some fairly general conditions, a first-order Edgeworth expansion for the standardized statistic of βin partial linear models is given, then a non-residual type of consistent estimation for the error variance is constructed, and finally an Edgeworth expansion for the corresponding studentized version is presented.
文摘We give an Edgeworth expansion for densities of order statistics with fixed rank k. The Edgeworth expansion for densities of extreme values is then obtained as a special case k = 1.
基金This work supported by the National Natural Science Foundation of China （Grand No. 10071003）
文摘In this part II the fundamental inequality of the third order general regular variation is proved and the second order Edgeworth expansion of the distribution of the extreme values is discussed.
文摘This paper is concerned with the distributional properties of a median unbiased estimator of ARCH（0,1） coefficient. The exact distribution of the estimator can be easily derived, however its practical calculations are too heavy to implement, even though the middle range of sample sizes. Since the estimator is shown to have asymptotic normality, asymptotic expansions for the distribution and the percentiles of the estimator are derived as the refinements. Accuracies of expansion formulas are evaluated numerically, and the results of which show that we can effectively use the expansion as a fine approximation of the distribution with rapid calculations. Derived expansion are applied to testing hypothesis of stationarity, and an implementation for a real data set is illustrated.
文摘Suppose that Z1 , Z2,’’’ Zn are independent normal random variables with common meanμ and variance σ2. Then S2 and have distribution andtn-1 distribution respectively. If the normal assumption fails, there will be the remaindersof the distribution functions and density functions. This paper gives the direct expansions ofdistribution functions and density functions of S2 alld T up to o(n-1). They are more intuitiveand convenient than usual Edgeworth expansions.
文摘In this paper, we give an one-term Edgeworth expansion for the standardized least square estimator (LSE) in a linear regression model and its random weighting approximation. So we have not only improved the expansion result but also given a practical approximating method.
文摘A saddlepoint approximation for a two-sample permutation test was obtained by Robinson[7].Although the approximation is very accurate, the formula is very complicated and difficult toapply. In this papert we shall revisit the same problem from a different angle. We shall first turnthe problem into a conditional probability and then apply a Lugannani-Rice type formula to it,which was developed by Skovagard[8] for the mean of i.i.d. samples and by Jing and Robinson[5]for smooth function of vector means. Both the Lugannani-Rice type formula and Robinson'sformula achieve the same relative error of order O(n-3/2), but the former is very compact andmuch easier to use in practice. Some numerical results will be presented to compare the twoformulas.
