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
We present a family of formal expansions for the density function of a general one-dimensional asymptotic normal sequence Xn. Members of the family are indexed by a parameter τ with an interval domain which we refer ...We present a family of formal expansions for the density function of a general one-dimensional asymptotic normal sequence Xn. Members of the family are indexed by a parameter τ with an interval domain which we refer to as the spectrum of the family. The spectrum provides a unified view of known expansions for the density of Xn. It also provides a means to explore for new expansions. We discuss such applications of the spectrum through that of a sample mean and a standardized mean. We also discuss a related expansion for the cumulative distribution function of Xn.展开更多
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
In this paper, we consider the finite sample property of the ordinary least squares (OLS) estimator for an AR(1) model with measurement error. We present the Edgeworth approximation for a finite distribution of OLS up...In this paper, we consider the finite sample property of the ordinary least squares (OLS) estimator for an AR(1) model with measurement error. We present the Edgeworth approximation for a finite distribution of OLS up to O(T1/2). We introduce an instrumental variable estimator that is consistent in the presence of measurement error. Finally, a simulation study is conducted to assess the theoretical results and to compare the finite sample performances of these estimators.展开更多
In this paper we propose a method to approximate a class of statistics which admit Edgeworth expansions. The accuracy of the approximation is proved to be at the same optimal rate as the well known bootstrap and rando...In this paper we propose a method to approximate a class of statistics which admit Edgeworth expansions. The accuracy of the approximation is proved to be at the same optimal rate as the well known bootstrap and random weighting. In practice conditional distributions of uni-dimensional statistics constructed by our method can exactly be derived. Meanwhile, our method has a nice model robustness.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
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We present a family of formal expansions for the density function of a general one-dimensional asymptotic normal sequence Xn. Members of the family are indexed by a parameter τ with an interval domain which we refer to as the spectrum of the family. The spectrum provides a unified view of known expansions for the density of Xn. It also provides a means to explore for new expansions. We discuss such applications of the spectrum through that of a sample mean and a standardized mean. We also discuss a related expansion for the cumulative distribution function of Xn.
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In this paper, we consider the finite sample property of the ordinary least squares (OLS) estimator for an AR(1) model with measurement error. We present the Edgeworth approximation for a finite distribution of OLS up to O(T1/2). We introduce an instrumental variable estimator that is consistent in the presence of measurement error. Finally, a simulation study is conducted to assess the theoretical results and to compare the finite sample performances of these estimators.
文摘In this paper we propose a method to approximate a class of statistics which admit Edgeworth expansions. The accuracy of the approximation is proved to be at the same optimal rate as the well known bootstrap and random weighting. In practice conditional distributions of uni-dimensional statistics constructed by our method can exactly be derived. Meanwhile, our method has a nice model robustness.
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.
