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111.
Mohamed M. Bugaighis 《统计学通讯:模拟与计算》2013,42(2):601-611
The Maximum Likelihood (ML) and Best Linear Unbiased (BLU) estimators of the location and scale parameters of an extreme value distribution (Lawless [1982]) are compared under conditions of small sample sizes and Type I censorship. The comparisons were made in terms of the mean square error criterion. According to this criterion, the ML estimator of σ in the case of very small sample sizes (n < 10) and heavy censorship (low censoring time) proved to be more efficient than the corresponding BLU estimator. However, the BLU estimator for σ attains parity with the corresponding ML estimator when the censoring time increases even for sample sizes as low as 10. The BLU estimator of σ attains equivalence with the ML estimator when the sample size increases above 10, particularly when the censoring time is also increased. The situation is reversed when it came to estimating the location parameter μ, as the BLU estimator was found to be consistently more efficient than the ML estimator despite the improved performance of the ML estimator when the sample size increases. However, computational ease and convenience favor the ML estimators. 相似文献
112.
In this article, a state-space model based on an underlying hidden Markov chain model (HMM) with factor analysis observation process is introduced. The HMM generates a piece-wise constant state evolution process and the observations are produced from the state vectors by a conditionally heteroscedastic factor analysis observation process. More specifically, we concentrate on situations where the factor variances are modeled by univariate Generalized Quadratic Autoregressive Conditionally Heteroscedastic processes (GQARCH). An expectation maximization (EM) algorithm combined with a mixed-state version of the Viterbi algorithm is derived for maximum likelihood estimation. The various regimes, common factors, and their volatilities are supposed unobservable and the inference must be carried out from the observable process. Extensive Monte Carlo simulations show promising results of the algorithms, especially for segmentation and tracking tasks. 相似文献
113.
This article considers the estimation of R = P(Y < X) when X and Y are distributed as two independent three-parameter generalized exponential (GE) random variables with different shape parameters but having the same location and scale parameters. A modified maximum likelihood method and a Bayesian technique are used to estimate R on the basis of independent complete samples. The Bayes estimator cannot be obtained in explicit form, and therefore it has been determined using an importance sampling procedure. An analysis of a real life data set is presented for illustrative purposes. 相似文献
114.
We consider the competing risks problem with two risks and develop empirical likelihood ratio type tests for testing the null hypothesis that the cumulative incidence functions corresponding to these two risks are equal against the alternatives: (a) they are not equal and (b) they are linearly ordered. The asymptotic null distributions of the proposed test statistics are shown to have simple distribution-free representations in terms of a standard Brownian motion process. The results of a simulation study indicate that the proposed test for testing for the presence of the linear order is more powerful than a test designed for the same situation in Aly et al. (1994). To illustrate the theoretical results, we discuss an example involving survival times of mice exposed to radiation. 相似文献
115.
AbstractWe consider an SIR stochastic epidemic model in which new infections occur at rate f(x, y), where x and y are, respectively, the number of susceptibles and infectives at the time of infection and f is a positive sequence of real functions. A simple explicit formula for the final size distribution is obtained. Some efficient recursive methods are proved for the exact calculation of this distribution. In addition, we give a Gaussian approximation for the final distribution using a diffusion process approximation. 相似文献
116.
Ahmed El Ghini 《统计学通讯:理论与方法》2013,42(21):4651-4661
For the class of autoregressive-moving average (ARMA) processes, we examine the relationship between the dual and the inverse processes. It is demonstrated that the inverse process generated by a causal and invertible ARMA (p, q) process is a causal and invertible ARMA (q, p) model. Moreover, it is established that this representation is strong if and only if the generating process is Gaussian. More precisely, it is derived that the linear innovation process of the inverse process is an all-pass model. Some examples and applications to time reversibility are given to illustrate the obtained results. 相似文献
117.
(一) 2005年7月7日和7月21日,伦敦相继发生恐怖主义爆炸事件;2005年7月23日埃及沙姆沙伊赫也发生了恐怖主义袭击事件,这些事件引发了许多亟待解决的问题. 相似文献
118.
In the competing risks problem an important role is played by the cumulative incidence function (CIF), whose value at time
t is the probability of failure by time t from a particular type of risk in the presence of other risks. Assume that the lifetime distributions of two populations
are uniformly stochastically ordered. Since this ordering may not hold for the empiricals due to sampling variability, it
is natural to estimate these distributions under this constraint. This will in turn affect the estimation of the CIFs. This
article considers this estimation problem. We do not assume that the risk sets in the two populations are related, give consistent
estimators of all the CIFs and study the weak convergence of the resulting processes. We also report the results of a simulation
study that show that our restricted estimators outperform the unrestricted ones in terms of mean square error. A real life
example is used to illustrate our theoretical results. 相似文献
119.
Control charts for residuals, based on the regression model, require a robust fitting technique for minimizing the error resulting from the fitted model. However, in the multivariate case, when the number of variables is high and data become complex, traditional fitting techniques, such as ordinary least squares (OLS), lose efficiency. In this paper, support vector regression (SVR) is used to construct robust control charts for residuals, called SVR-chart. This choice is based on the fact that the SVR is designed to minimize the structural error whereas other techniques minimize the empirical error. An application shows that SVR methods gives competitive results in comparison with the OLS and the partial least squares method, in terms of standard deviation of the error prediction and the standard error of performance. A sensitivity study is conducted to evaluate the SVR-chart performance based on the average run length (ARL) and showed that the SVR-chart has the best ARL behaviour in comparison with the other residuals control charts. 相似文献
120.
Mohamed Boutahar 《Statistical Methods and Applications》2010,19(2):193-215
We establish the limiting distributions for empirical estimators of the coefficient of skewness, kurtosis, and the Jarque–Bera normality test statistic for long memory linear processes. We show that these estimators, contrary to the case of short memory, are neither ${\sqrt{n}}We establish the limiting distributions for empirical estimators of the coefficient of skewness, kurtosis, and the Jarque–Bera
normality test statistic for long memory linear processes. We show that these estimators, contrary to the case of short memory,
are neither ?n{\sqrt{n}}-consistent nor asymptotically normal. The normalizations needed to obtain the limiting distributions depend on the long memory
parameter d. A direct consequence is that if data are long memory then testing normality with the Jarque–Bera test by using the chi-squared
critical values is not valid. Therefore, statistical inference based on skewness, kurtosis, and the Jarque–Bera normality
test, needs a rescaling of the corresponding statistics and computing new critical values of their nonstandard limiting distributions. 相似文献