Modified inference about the mean of the exponential distribution using moving extreme ranked set sampling

The maximum likelihood estimator (MLE) and the likelihood ratio test (LRT) will be considered for making inference about the scale parameter of the exponential distribution in case of moving extreme ranked set sampling (MERSS). The MLE and LRT can not be written in closed form. Therefore, a modification of the MLE using the technique suggested by Maharota and Nanda (Biometrika 61:601–606, 1974) will be considered and this modified estimator will be used to modify the LRT to get a test in closed form for testing a simple hypothesis against one sided alternatives. The same idea will be used to modify the most powerful test (MPT) for testing a simple hypothesis versus a simple hypothesis to get a test in closed form for testing a simple hypothesis against one sided alternatives. Then it appears that the modified estimator is a good competitor of the MLE and the modified tests are good competitors of the LRT using MERSS and simple random sampling (SRS).     

Consistency of minimizing a penalized density power divergence estimator for mixing distribution

In this paper, we study the MDPDE (minimizing a density power divergence estimator), proposed by Basu et al. (Biometrika 85:549–559, 1998), for mixing distributions whose component densities are members of some known parametric family. As with the ordinary MDPDE, we also consider a penalized version of the estimator, and show that they are consistent in the sense of weak convergence. A simulation result is provided to illustrate the robustness. Finally, we apply the penalized method to analyzing the red blood cell SLC data presented in Roeder (J Am Stat Assoc 89:487–495, 1994). This research was supported (in part) by KOSEF through Statistical Research Center for Complex Systems at Seoul National University.     

A note on the equality of the OLSE and the BLUE of the parametric function in the general Gauss–Markov model

In this note we consider the equality of the ordinary least squares estimator (OLSE) and the best linear unbiased estimator (BLUE) of the estimable parametric function in the general Gauss–Markov model. Especially we consider the structures of the covariance matrix V for which the OLSE equals the BLUE. Our results are based on the properties of a particular reparametrized version of the original Gauss–Markov model.      

Estimating a sensitive proportion through randomized response procedures based on auxiliary information

Randomized response techniques are widely employed in surveys dealing with sensitive questions to ensure interviewee anonymity and reduce nonrespondents rates and biased responses. Since Warner’s (J Am Stat Assoc 60:63–69, 1965) pioneering work, many ingenious devices have been suggested to increase respondent’s privacy protection and to better estimate the proportion of people, π _A , bearing a sensitive attribute. In spite of the massive use of auxiliary information in the estimation of non-sensitive parameters, very few attempts have been made to improve randomization strategy performance when auxiliary variables are available. Moving from Zaizai’s (Model Assist Stat Appl 1:125–130, 2006) recent work, in this paper we provide a class of estimators for π _A , for a generic randomization scheme, when the mean of a supplementary non-sensitive variable is known. The minimum attainable variance bound of the class is obtained and the best estimator is also identified. We prove that the best estimator acts as a regression-type estimator which is at least as efficient as the corresponding estimator evaluated without allowing for the auxiliary variable. The general results are then applied to Warner and Simmons’ model.     

Estimation of a relative potency of two preparations with correlated responses

Estimation of a relative potency of two preparations in so-called parallel-line assays is presented. A special type of incomplete Latin square designs where doses of preparations are administered is considered. Testing hypotheses about similarity of preparations and their relative potency in the case of correlated observations are regarded. Confidence interval for the relative potency of preparations is also given. Theoretical considerations are applied to point and interval estimation of potencies of new tuberculins with respect to some international standards tested in experiments on guinea-pigs.     

Using relative utility curves to evaluate risk prediction

Summary.  Because many medical decisions are based on risk prediction models that are constructed from medical history and results of tests, the evaluation of these prediction models is important. This paper makes five contributions to this evaluation: the relative utility curve which gauges the potential for better prediction in terms of utilities, without the need for a reference level for one utility, while providing a sensitivity analysis for misspecification of utilities, the relevant region, which is the set of values of prediction performance that are consistent with the recommended treatment status in the absence of prediction, the test threshold, which is the minimum number of tests that would be traded for a true positive prediction in order for the expected utility to be non-negative, the evaluation of two-stage predictions that reduce test costs and connections between various measures of performance of prediction. An application involving the risk of cardiovascular disease is discussed.     

Bullying and Victimization Among Young Elementary School Children: The Role of Child Ethnicity and Ethnic School Composition

School-aged children with an ethnic minority background are relatively often involved in bullying and victimization, but the role of ethnic composition of schools in this context remains unclear. This study examined the relation between ethnic minority background, ethnic school composition, and bullying behaviour around primary school entry in the Netherlands. The study was based on a 2008/2009 school survey in Rotterdam, a Dutch city where about 50 % of children have a non-Dutch background. For 8523 children, teacher reports of bullying behaviour at age 5–6 years were available. Children with a non-Dutch background had higher odds of being a victim (adjusted OR 1.41, 95 % CI 1.11, 1.80), bully (OR 1.38, 95 % CI 1.20, 1.58) or bully-victim (OR 1.38, 95 % CI 1.19, 1.62) than children of Dutch national origin. Ethnic diversity in schools increased children’s risk of bullying behaviour (e.g. OR_victim per 0.1 increase in 0–1 diversity range = 1.06, 95 % CI 1.00, 1.13), with children of both Dutch and non-Dutch national origin relatively more often involved in bullying in ethnically diverse schools. The proportion of same-ethnic peers in school reduced the risk of bullying among children of Dutch national origin (e.g. OR_victim per 10 % more same-ethnic children = 0.90, 95 % CI 0.83, 0.98), but not among non-Dutch children. In conclusion, ethnic minority background and ethnic diversity within schools are risk factors for bullying among 5–6 year olds. Plausibly, reductions in absolute numbers of bullying events may be obtained with tailor-made interventions in ethnically diverse schools. Such interventions should preferably be offered early in the school curriculum.     

Wealth Inequality in Black and White: Cultural and Structural Sources of the Racial Wealth Gap

Using data from the 2013 Survey of Consumer Finances, this research examines competing and complementary cultural and structural explanations of the sources of racial differences in wealth. We use OLS regression and quantile regression to identify the major individual-level sources of wealth differences between African Americans and whites. Whites have more favorable wealth characteristics than do African Americans on all of the variables in the analysis: gender of household head, bankruptcies, spending patterns, stock ownership, business ownership, home ownership, inheritance, educational attainment, income, occupation, age, and number of children. Cultural factors, having a female-headed family, spending patterns, and inheritance account for little of the racial wealth gap. Racial differences in income, stock ownership, and business ownership account for much of the explained racial wealth gap. Moreover, compared with whites, African Americans receive significantly lower wealth returns to education, age, income, stock ownership, and business ownership. We discuss the implications of our findings.