Influence Diagnostics on Testing Linear Hypothesis in Linear Models with Correlated Errors

To assess the influence of observations on the parameter estimates, case deletion diagnostics are commonly used in linear regression models. For linear models with correlated errors we study the influence of observations on testing a linear hypothesis using single and multiple case deletions. The change in likelihood ratio test and F test theoretically is derived and it is shown these tests to be completely determined by two proposed generalized externally studentized residuals. An illustrative example of a real data set is also reported.     

Confidence intervals for the mean of a normal distribution with restricted parameter space

For a normal distribution with known variance, the standard confidence interval of the location parameter is derived from the classical Neyman procedure. When the parameter space is known to be restricted, the standard confidence interval is arguably unsatisfactory. Recent articles have addressed this problem and proposed confidence intervals for the mean of a normal distribution where the parameter space is not less than zero. In this article, we propose a new confidence interval, rp interval, and derive the Bayesian credible interval and likelihood ratio interval for general restricted parameter space. We compare these intervals with the standard interval and the minimax interval. Simulation studies are undertaken to assess the performances of these confidence intervals.     

On a system of nonhomogeneous components sharing a common frailty

The components of a reliability system subjected to a common random environment usually have dependent lifetimes. This paper studies the stochastic properties of such a system with lifetimes of the components following multivariate frailty models and multivariate mixed proportional reversed hazard rate (PRHR) models, respectively. Through doing stochastic comparison, we devote to throwing a new light on how the random environment affects the number of working components of a reliability system and on assessing the performance of a k-out-of-n system.     

Conditional and marginal estimates in case-control family data – extensions and sensitivity analyses

This work considers two specific estimation techniques for the family-specific proportional hazards model and for the population-averaged proportional hazards model. So far, these two estimation procedures were presented and studied under the gamma frailty distribution mainly because of its simple interpretation and mathematical tractability. Modifications of both procedures for other frailty distributions, such as the inverse Gaussian, positive stable and a specific case of discrete distribution, are presented. By extensive simulations, it is shown that under the family-specific proportional hazards model, the gamma frailty model appears to be robust to frailty distribution mis-specification in both bias and efficiency loss in the marginal parameters. The population-averaged proportional hazards model, is found to be robust under the gamma frailty model mis-specification only under moderate or weak dependency within cluster members.     

Hazard Analysis and Safety Requirements for Small Drone Operations: To What Extent Do Popular Drones Embed Safety?

Currently, published risk analyses for drones refer mainly to commercial systems, use data from civil aviation, and are based on probabilistic approaches without suggesting an inclusive list of hazards and respective requirements. Within this context, this article presents: (1) a set of safety requirements generated from the application of the systems theoretic process analysis (STPA) technique on a generic small drone system; (2) a gap analysis between the set of safety requirements and the ones met by 19 popular drone models; (3) the extent of the differences between those models, their manufacturers, and the countries of origin; and (4) the association of drone prices with the extent they meet the requirements derived by STPA. The application of STPA resulted in 70 safety requirements distributed across the authority, manufacturer, end user, or drone automation levels. A gap analysis showed high dissimilarities regarding the extent to which the 19 drones meet the same safety requirements. Statistical results suggested a positive correlation between drone prices and the extent that the 19 drones studied herein met the safety requirements generated by STPA, and significant differences were identified among the manufacturers. This work complements the existing risk assessment frameworks for small drones, and contributes to the establishment of a commonly endorsed international risk analysis framework. Such a framework will support the development of a holistic and methodologically justified standardization scheme for small drone flights.     

On an asymptotic relative efficiency concept based on expected volumes of confidence regions

ABSTRACT

The paper deals with an asymptotic relative efficiency concept for confidence regions of multidimensional parameters that is based on the expected volumes of the confidence regions. Under standard conditions the asymptotic relative efficiencies of confidence regions are seen to be certain powers of the ratio of the limits of the expected volumes. These limits are explicitly derived for confidence regions associated with certain plugin estimators, likelihood ratio tests and Wald tests. Under regularity conditions, the asymptotic relative efficiency of each of these procedures with respect to each one of its competitors is equal to 1. The results are applied to multivariate normal distributions and multinomial distributions in a fairly general setting.     

Modified likelihood ratio tests in heteroskedastic multivariate regression models with measurement error

In this paper, we develop modified versions of the likelihood ratio test for multivariate heteroskedastic errors-in-variables regression models. The error terms are allowed to follow a multivariate distribution in the elliptical class of distributions, which has the normal distribution as a special case. We derive the Skovgaard-adjusted likelihood ratio statistics, which follow a chi-squared distribution with a high degree of accuracy. We conduct a simulation study and show that the proposed tests display superior finite sample behaviour as compared to the standard likelihood ratio test. We illustrate the usefulness of our results in applied settings using a data set from the WHO MONICA Project on cardiovascular disease.     

男女性别比失衡问题的思考

目前,我国男女性别比例严重失衡,由此带来性犯罪现象增加、婚姻挤压、拜金主义思想等各种社会问题,究其原因,除了传统的重男轻女观念的影响和妇女地位的不平等外,还有科技手段的滥用。应该树立先进的社会性别意识,禁止非法的胎儿性别鉴定,提高女性的社会地位,这样,才能切实解决出生人口性别比例失调问题。     

Testing dominance of biometric functions

The hazard rate (HR) and mean residual lifetime are two of the most practical and best-known functions in biometry, reliability, statistics and life testing. Recently, the reversed HR function is found to have interesting properties useful in additional areas such as censored data and forensic science. For these three biometric functions, we propose testing methods that they take on a known functional form against that they dominate or are dominated by this known form. This goodness-of-fit-type testing is wider in applications and more interesting than the long-standing testing procedures for exponentiality against the monotonicity of these functions or even the change point problems. This is so since we can test against any choice of the survival distribution and not just exponentiality. For this general testing, we present easy to implement tests and generalize them into classes of statistics that could lead to more powerful and efficient testing.     

Comparing diagnostic tests: test of hypothesis for likelihood ratios

Likelihood ratios (LRs) are used to characterize the efficiency of diagnostic tests. In this paper, we use the classical weighted least squares (CWLS) test procedure, which was originally used for testing the homogeneity of relative risks, for comparing the LRs of two or more binary diagnostic tests. We compare the performance of this method with the relative diagnostic likelihood ratio (rDLR) method and the diagnostic likelihood ratio regression (DLRReg) approach in terms of size and power, and we observe that the performances of CWLS and rDLR are the same when used to compare two diagnostic tests, while DLRReg method has higher type I error rates and powers. We also examine the performances of the CWLS and DLRReg methods for comparing three diagnostic tests in various sample size and prevalence combinations. On the basis of Monte Carlo simulations, we conclude that all of the tests are generally conservative and have low power, especially in settings of small sample size and low prevalence.