基尼系数的区间估计及其应用

 本文给出了收入为离散分布的三种计算基尼系数的新方法。利用收入份额法导出了基尼系数协方差算法的离散形式,并因此产生了计算基尼系数的回归系数法。文章重点讨论了基尼系数进行区间估计的两种方法,这些方法也适用于集中度指数,因而它们在测度社会经济领域的不平等中具有着十分广泛的用途。实际应用表明,新算法有效地简化了对基尼系数区间估计的标准差估算。     

Parameter Estimation Through Weighted Least-Squares Rank Regression with Specific Reference to the Weibull and Gumbel Distributions

Probability plots are often used to estimate the parameters of distributions. Using large sample properties of the empirical distribution function and order statistics, weights to stabilize the variance in order to perform weighted least squares regression are derived. Weighted least squares regression is then applied to the estimation of the parameters of the Weibull, and the Gumbel distribution. The weights are independent of the parameters of the distributions considered. Monte Carlo simulation shows that the weighted least-squares estimators outperform the usual least-squares estimators totally, especially in small samples.     

Zone control charts with estimated parameters for detecting prespecified changes in linear profiles

ABSTRACT

In profile monitoring, control charts are proposed to detect unanticipated changes, and it is usually assumed that the in-control parameters are known. However, due to the characteristics of a system or process, the prespecified changes would appear in the process. Moreover, in most applications, the in-control parameters are usually unknown. To overcome these issues, we develop the zone control charts with estimated parameters to detect small shifts of these prespecified changes. The effects of estimation error have been investigated on the performance of the proposed charts. To account for the practitioner-to-practitioner variability, the expected average run length (ARL) and the standard deviation of the average run length (SDARL) is used as the performance metrics. Our results show that the estimation error results in the significant variation in the ARL distribution. Furthermore, in order to adequately reduce the variability, more phase I samples are required in terms of the SDARL metric than that in terms of the expected ARL metric. In addition, more observations on each sampled profile are suggested to improve the charts' performance, especially for small phase I sample sizes. Finally, an illustrative example is given to show the performance of the proposed zone control charts.     

Maximum likelihood estimation in a Weibull regression model with type-1 censoring: a Monte Carlo study

Results of the Monte Carlo study of the performance of a maximum likelihood estimation in a Weibull parametric regression model with two explanatory variables are presented. One simulation run contained 1000 samples censored on the average by the amount of 0-30%. Each simulatedsample was generated in a form of two-factor two-level balanced experiment. The confidence intervals were computed using the large-sample normal approximation via the matrix of observed information. For small sample sizes the estimates of the scale parameter b of the loglifetime were significantly negatively biased, which resulted in a poor quality of confidence intervals for b and the low-level quantiles. All estimators improved their quality when the nominal value of b decreased. A moderate amount of censoring improved the quality of point and confidence estimation. The reparametrization b 7 produced rather accurate confidence intervals. Exact confidence intervals for b in case of non-censoring were obtained using the pivotal quantity b/b.     

Asymptotic Results for Spatial ARMA Models

Causal quadrantal-type spatial ARMA(p, q) models with independent and identically distributed innovations are considered. In order to select the orders (p, q) of these models and estimate their autoregressive parameters, estimators of the autoregressive coefficients, derived from the extended Yule–Walker equations are defined. Consistency and asymptotic normality are obtained for these estimators. Then, spatial ARMA model identification is considered and simulation study is given.     

Time series analysis for repeated surveys

Estimation of a characteristic based on surveys repeated at regular intervals is considered. A state space formulation is given for the problem and the Kalman Filter is used to obtain an estimate and its variance. Some examples are also given to illustrate the methodology.     

Convergence of non-linear functionals of smoothed empirical processes and kernel density estimates

We consider regularizations by convolution of the empirical process and study the asymptotic behaviour of non-linear functionals of this process. Using a result for the same type of non-linear functionals of the Brownian bridge, shown in a previous paper [4], and a strong approximation theorem, we prove several results for the p-deviation in estimation of the derivatives of the density. We also study the asymptotic behaviour of the number of crossings of the smoothed empirical process defined by Yukich [17] and of a modified version of the Kullback deviation.     

Analysis of nonlinear state space model with dependent measurement noises

This paper presents a nonlinear state space model with considering a first-order autoregressive model for measurement noises. A recursive method using Taylor series based approximations for filtering, prediction and smoothing problem of hidden states from the noisy observations is designed. Also, an expectation-maximization algorithm for calculating the maximum likelihood estimators of parameters is presented. The closed form solutions are obtained for estimating of the hidden states and the unknown parameters. Finally, the performance of the designed methods are verified in a simulation study.