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31.
Michael Lavine 《统计学通讯:模拟与计算》2013,42(1):269-283
Cook (1986) presented the idea of local influence to study the sensitivity of inferences to model assumptions:introduce a vector δ of perturbations to the model; choose a discrepancy function D to measure differences between the original inference and the inference under the perturbed model; study the behavior of D near δ = 0, the original model, usually by taking derivatives. Johnson and Geisser (1983) measure influence in Bayesian inference by the Kullback-Leibler divergence between predictive distributions. I~IcCulloch (1989) is a synthesis of Cook and Johnson and Geisser, using Kullback-Leibler divergence between posterior or predictive distributions as the discrepancy function in Bayesian local influence analyses. We analyze a special case for which McCulloch gives the general theory; namely, the linear model with conjugate prior. We present specific formulae for local influence measures for 1) changes in the parameters of the gamma prior for the precision, 2) changes in the mean of the normal prior for the regression coefficients, 3) changes in the covariance matrix of the normal prior for the regression coefficients and 4) changes in the case weights. Our method is an easy way to find locally influential subsets of points without knowing in advance the sizes of the subsets. The techniques are illustrated with a regression example. 相似文献
32.
Lijian Yang 《统计学通讯:理论与方法》2013,42(5-6):1347-1365
GARCH model has been commonly used to describe the volatility of foreign exchange returns, which typically depends on returns many lags before, While the GARCH model provides a simple geometric decaying structure for persistence in time, it restricts tiie impact of variables to Quadratic functions. A finite nonparametric GARCH model is proposed that allows the variables' impact to be a smooth function of any form. A direct local polynomial estimation method for this finite GARCH model is proposed based on results on proportional additive model, and is applied to the German Mark (DEM)/US Dollar (USD) daily returns data. Estimators uf both the decaying rate and the impact function are obtained. Diagnostics show satisfactory out-of-sampie prediction based on the proposed model, which helps to better understand the dynamics of foreign exchange volatility. 相似文献
33.
Mohammad Fraiwan Al-Saleh 《统计学通讯:理论与方法》2013,42(7):1433-1439
In this article, we address the similarity structure between pairs of order statistics of an identically distributed independent random variables X1,…, Xn. The overlapping coefficient (Δ) of Weitzman (1970), is used to assess the degree of similarity or closeness between pairs of order statistics. It appears that the degree of the similarity between any of such pairs is independent of the parent distribution. Using this notion, it is shown that for i < j, the degree of similarity between distributions of the ith and the jth order statistics decreases as i and j sunder. Some possible biometric applicability of the value of Δ are explored. In particular, the use of this measure in estimation of the number of possible strata, subgroups or natural subdivisions in a population are suggested. 相似文献
34.
D. Szatmari-Voicu 《统计学通讯:理论与方法》2013,42(11):2037-2048
The median absolute deviation (MAD) is known to be the M-estimator of scale with minimum gross errors sensitivity (GES) when the error distribution is known to be symmetric and strongly unimodal. The problem considered here is to find the Fisher consistent M-estimator with minimum GES when the error distribution is symmetric but not necessarily unimodal. Under some general conditions, the score function χ corresponding to the minimizing M-estimator has the form χ(x) = ?1 when |x| < a; χ(x) = c when a < |x| < b; χ(x) = 1 when |x| > b. An example is given in which the M-estimator with minimum GES does not correspond to the MAD. 相似文献
35.
This paper finds the mathematical forms of the distribution of the product where x and x follow a bivariate normal distribution In this paper the distribution when PT0 is expressed as an integral, a new, fundamental result. From this general form, six different cases can be distinguished depending on what is known about the parameters and p. The special cases are Aroian $year:1959 and (6) Additionally, we prove that if and as the distribution of the product approaches the Type III distribution. When p=0# Aroian $year:1959 and Aroian and Meeker $year:1977, give tables for various values of 6., 6 . The results in this paper will be used to provide brief tables for p^O in a separate paper 相似文献
36.
M. Safiul Haq 《统计学通讯:理论与方法》2013,42(9):857-866
The location-scale model with equi-correlated responses is discussed. The structure of the location-scale model is utilised to genera-te the prediction distribution of a future response and that of a set of future responses. The method avoids the integration procedures usually involved in derivation of prediction distributions and yields results same as those obtained by the Bayes method with the vague prior distribution* Finally the re-suits have been specialised to cover the case of the normal intra-class model. 相似文献
37.
In this paper we consider the problem of obtaining best linear unbiased estimators of individual response coefficients in a Random Coefficient Linear Regression (RCR} Model, comparing alternative estimators for these response vectors through a simulation study. We also provide an empirical example that illustrates the estimation procedure proposed here. 相似文献
38.
39.
Nader Ebrahimi 《统计学通讯:理论与方法》2013,42(5):651-659
Let x be a random variable having the normal distribution with mean μ and variance c2μ2, where c is a known constant. The maximum likelihood estimation of μ when the lowest r1 and the highest r2 sample values censored have been given the asymptotic variance of the maximum likelihood estimator is obtained. 相似文献
40.