Let {Xn, n≥1} be a strictly stationary sequence of random variables, which are either associated or negatively associated, f(.) be their common density. In this paper, the author shows a central limit theorem for a k...Let {Xn, n≥1} be a strictly stationary sequence of random variables, which are either associated or negatively associated, f(.) be their common density. In this paper, the author shows a central limit theorem for a kernel estimate of f(.) under certain regular conditions.展开更多
The authors derive laws of the iterated logarithm for kernel estimator of regression function based on directional data. The results are distribution free in the sense that they are true for all distributions of desig...The authors derive laws of the iterated logarithm for kernel estimator of regression function based on directional data. The results are distribution free in the sense that they are true for all distributions of design variable.展开更多
The nearest neighbor (n.n.) and its related methods are widely used in density and hazard function estimations. Even though the asymptotic normality of the n.n. density estimate is well known (see [1]), similar result...The nearest neighbor (n.n.) and its related methods are widely used in density and hazard function estimations. Even though the asymptotic normality of the n.n. density estimate is well known (see [1]), similar results for the n.n. hazard estimate have not been shown in the literature. In this paper, we develop a different approach to deal with the n.n. type estimator. For a mixed censorship-truneation model, we show that, under mild conditions, the n. n. estimate can be approximated by an estimate formed with a proper fixed bandwidth sequence and derive the asymptotic normality as a consequence.展开更多
文摘Let {Xn, n≥1} be a strictly stationary sequence of random variables, which are either associated or negatively associated, f(.) be their common density. In this paper, the author shows a central limit theorem for a kernel estimate of f(.) under certain regular conditions.
基金Project supported by the National Natural Science Foundation of China (Nos. 19631040 19971085), the Doctoral Program Foundatio
文摘The authors derive laws of the iterated logarithm for kernel estimator of regression function based on directional data. The results are distribution free in the sense that they are true for all distributions of design variable.
文摘The nearest neighbor (n.n.) and its related methods are widely used in density and hazard function estimations. Even though the asymptotic normality of the n.n. density estimate is well known (see [1]), similar results for the n.n. hazard estimate have not been shown in the literature. In this paper, we develop a different approach to deal with the n.n. type estimator. For a mixed censorship-truneation model, we show that, under mild conditions, the n. n. estimate can be approximated by an estimate formed with a proper fixed bandwidth sequence and derive the asymptotic normality as a consequence.
