Characterizations of Bivariate Models Using Some Dynamic Conditional Information Divergence Measures

In this article, we study some relevant information divergence measures viz. Renyi divergence and Kerridge’s inaccuracy measures. These measures are extended to conditionally specified models and they are used to characterize some bivariate distributions using the concepts of weighted and proportional hazard rate models. Moreover, some bounds are obtained for these measures using the likelihood ratio order.     

基于自适应组LASSO估计的高维门限因子模型一致选择

门限因子模型设定载荷具有阈值型区制转换结构,可以同时刻画高维时间序列的共变性和区制转换特征。针对高维门限因子模型,本文基于自适应组LASSO技术给出了一种一致模型选择过程。这一模型选择过程将因子个数设定、门限效应推断纳入统一的分析框架,不仅解决了模型选择的一致性问题,还同时实现了模型选择误差的统一控制,这对于高维门限因子模型而言是非常重要的。理论研究和随机模拟结论表明本文给出的一致模型选择过程具有良好的大样本性质和有限样本表现。最后,本文将门限因子模型应用于我国金融市场分析,实证结果进一步验证了本文理论的有效性。     

The effect of undercount on the accuracy of small-area population estimates: Implications for the use of administrative data for improving population enumeration

The effects of underenumeration on the accuracy of alternative methods of population estimation have not been sufficiently analyzed. Although the US Bureau of the Census has decided not to adjust either the counts or its estimates for underenumeration in 1990, the extent to which local population estimates may account for underenumeration is of importance both for those who may wish to adjust existing estimates and in anticipation of future census adjustments. This paper examines the accuracy of small-area population estimation methods with and without adjustment. Mean Percent Errors, Mean Absolute Percent Errors, and Mean Percent Absolute Differences between local estimates for 1990 and 1990 adjusted and unadjusted census counts are computed. Population estimates for 1990 made using housing unit, ratio correlation, and component methods are compared for 451 counties and 2,633 places in the states of California, Florida, Texas, and Wisconsin. An analysis of the data for counties shows little indication that local estimates more accurately estimate the adjusted than the unadjusted population counts. The results for places show clear improvements in accuracy for places in Florida and Texas. Implications of the findings for issues related to undercount adjustment and local population estimates are discussed.     

Dynamics of contraceptive use and breastfeeding during the post-partum period in Peru and Indonesia

This paper examines the interaction between contraceptive use and breastfeeding in relation to resumption of intercourse and duration of amenorrhea post-partum. We used data from the month-by-month calendar of reproductive events from Demographic and Health Surveys (DHS) in Peru and Indonesia. The analyses show that breastfeeding women were less likely than non-breastfeeding women to have resumed sexual intercourse in the early months post-partum in both countries. In Peru, but not in Indonesia, breastfeeding women had a significantly lower odds than non-breastfeeding women of adopting contraception. Although the likelihood of contraceptive adoption was highest in the month women resumed menstruation in both countries, about ten per cent of subsequent pregnancies occurred to women before they resumed menses. These results emphasize the importance of integrating breastfeeding counselling and family planning services in programmes serving post-partum women, as a means of enabling those who wish to space their next birth to avoid exposure to the risk of a pregnancy that may precede the return of menses.     

Asymptotics for an Adaptive Trimmed Likelihood Location Estimator

An asymptotic normality result is given for an adaptive trimmed likelihood estimator of location, which parallels the asymptotic normality result for the adaptive trimmed mean. The new result comes out of studying the adaptive trimmed likelihood estimator modelled parametrically by a normal family but then examining the behavior when the underlying distribution is in fact some F different from normal. The asymptotic variance of the adaptive estimator is equal to the asymptotic variance of the trimmed likelihood estimator at the optimal trimming proportion for the distribution F, subject to that trimming proportion being positive and F being suitably smooth.     

Multi-Sample Likelihood Ratio Tests Based on Bipolar Watson Distributions Defined on the Hypersphere

We derive likelihood ratio tests for the equality of the directional parameters of k bipolar Watson distributions defined on the hypersphere with common concentration parameter. We analyze the power of these tests in the case of two distributions supposing in the alternative hypothesis two directional parameters forming an angle, which varies from 18° to 90°. We also compare the likelihood ratio tests with a high-concentration F-test.     

Asymptotic Tail Properties of Student's t-Distribution

We investigate the asymptotic behavior of the probability density function (pdf) and the cumulative distribution function (cdf) of Student's t-distribution with ν > 0 degrees of freedom (t _ν for short) for ν tending to infinity when the argument x = x _ν of the pdf (cdf) depends on ν and tends to ± ∞ (?∞). To this end, we consider the ratio of the pdf's (cdf's) of the t _ν- and the standard normal distribution. Depending on the choice of the argument x _ν, the pdf-ratio (cdf-ratio) tends to 1, a fixed value greater than 1, or to ∞. As a byproduct, we obtain a result for Mill' ratio when x _ν → ?∞.     

Discriminating Between the Log-Normal and Log-Logistic Distributions

Log-normal and log-logistic distributions are often used to analyze lifetime data. For certain ranges of the parameters, the shape of the probability density functions or the hazard functions can be very similar in nature. It might be very difficult to discriminate between the two distribution functions. In this article, we consider the discrimination procedure between the two distribution functions. We use the ratio of maximized likelihood for discrimination purposes. The asymptotic properties of the proposed criterion are investigated. It is observed that the asymptotic distributions are independent of the unknown parameters. The asymptotic distributions are used to determine the minimum sample size needed to discriminate between these two distribution functions for a user specified probability of correct selection. We perform some simulation experiments to see how the asymptotic results work for small sizes. For illustrative purpose, two data sets are analyzed.     

A Robust Score Test for Testing Several Coefficients of Variation with Unknown Underlying Distributions

A parametric robust test is proposed for comparing several coefficients of variation. This test is derived by properly correcting the normal likelihood function according to the technique suggested by Royall and Tsou. The proposed test statistic is asymptotically valid for general random variables, as long as their underlying distributions have finite fourth moments.

Simulation studies and real data analyses are provided to demonstrate the effectiveness of the novel robust procedure.     

Bayes Estimation of Weibull Distribution Parameters Using Ranked Set Sampling

Estimation of the parameters of Weibull distribution is considered using different methods of estimation based on different sampling schemes namely, Simple Random Sample (SRS), Ranked Set Sample (RSS), and Modified Ranked Set Sample (MRSS). Methods of estimation used are Maximum Likelihood (ML), Method of moments (Mom), and Bayes. Comparison between estimators is made through simulation via their Biases, Relative Efficiency (RE), and Pitman Nearness Probability (PN). Estimators based on RSS and MRSS have many advantages over those that are based on SRS.