On using percentiles to fit data by a johnson distribution

The well-known Johnson system of distributions was developed by N. L. Johnson (1949). Slifker and Shapiro (1980) presented a criterion for choosing a member from the three distributional classes (S_B,S_L, and S_v) in the Johnson system to fit a set of data. The criterion is based on the value of a quantile ratio which depends on a specified positive z value and the parameters of the distribution. In this paper, we present some properties of the quantile ratio for various distributions and for some selected z values. Some comments are made on using the criterion for selecting a Johnson distribution to fit empirical data.     

The Bivariate Normal Copula

We collect well-known and less-known facts about the bivariate normal distribution and translate them into copula language. In addition, we provide various (equivalent) expressions for the bivariate normal copula, we compute its Gini's gamma, and we derive improved bounds and approximations on its diagonal.     

Constrained penalized splines

The penalized spline is a popular method for function estimation when the assumption of “smoothness” is valid. In this paper, methods for estimation and inference are proposed using penalized splines under additional constraints of shape, such as monotonicity or convexity. The constrained penalized spline estimator is shown to have the same convergence rates as the corresponding unconstrained penalized spline, although in practice the squared error loss is typically smaller for the constrained versions. The penalty parameter may be chosen with generalized cross‐validation, which also provides a method for determining if the shape restrictions hold. The method is not a formal hypothesis test, but is shown to have nice large‐sample properties, and simulations show that it compares well with existing tests for monotonicity. Extensions to the partial linear model, the generalized regression model, and the varying coefficient model are given, and examples demonstrate the utility of the methods. The Canadian Journal of Statistics 40: 190–206; 2012 © 2012 Statistical Society of Canada     

Individual- and Contextual-Level Factors Affecting the Use of Social Support Services among Older Adults

ABSTRACT

By 2060, the number of Americans aged 65 and older is expected to more than double, while the number of Americans aged 85 and older is expected to nearly triple. As the nation's aging population grows, older adults will need to rely on social support services, such as transportation and housing services, in order to remain active and lead independent lives. In this study we use data collected from the elderly supplement of the Southeastern Pennsylvania Household Health Survey (SPHHS) (n = 3,042) to explore the relationship between the availability of elderly specific social service providers and utilization of social support services among older adults. We find that while the number of elderly specific social service providers can increase use of social support services among older adults, its impact is relatively minimal. We find that individual factors, instead, are stronger predictors of service use. This is a finding that should be particularly encouraging for elder care providers who may not have the resources needed to undertake large structural changes (like building new facilities). Still, future research should explore how the availability of a broader range of elderly specific social services (than explored in this study) impacts use.     

Estimation of Conditional Ranks and Tests of Exogeneity in Nonparametric Nonseparable Models

Consider a nonparametric nonseparable regression model Y = ?(Z, U), where ?(Z, U) is strictly increasing in U and U ～ U[0, 1]. We suppose that there exists an instrument W that is independent of U. The observable random variables are Y, Z, and W, all one-dimensional. We construct test statistics for the hypothesis that Z is exogenous, that is, that U is independent of Z. The test statistics are based on the observation that Z is exogenous if and only if V = F_Y|Z(Y|Z) is independent of W, and hence they do not require the estimation of the function ?. The asymptotic properties of the proposed tests are proved, and a bootstrap approximation of the critical values of the tests is shown to be consistent and to work for finite samples via simulations. An empirical example using the U.K. Family Expenditure Survey is also given. As a byproduct of our results we obtain the asymptotic properties of a kernel estimator of the distribution of V, which equals U when Z is exogenous. We show that this estimator converges to the uniform distribution at faster rate than the parametric n^{? 1/2}-rate.     

A brief telephone interview to identify lesbian and bisexual women in random digit dialing sampling

Lesbian health research has most often relied on nonprobability samples that are biased and restrict generalizability. Random sampling could reduce bias, but requires development of a method for fast and reliable screening of a large number of women. We tested the feasibility of using a brief telephone interview to assess sexual attraction, behavior, and identity. Using Random Digit Dialing in a neighborhood of Boston with a high density of lesbian residents, we interviewed 202 women aged 18 to 59. Of the respondents, 33% reported some sexual attraction to other women, 20% reported sex with women since age 18, and 14% identified as a lesbian. The high level of cooperation with the study among eligible women (94%) and the high proportion of women who disclosed homosexual attraction, behavior, or identity show that it is feasible to use a brief screening questionnaire about sexuality of women over the telephone even without building special rapport with the respondents.     

Factors affecting household-level environmental decision making: A three-country comparison of the determinants of household recycling

As urban scales and income-driven levels of consumption rise with development, waste generation expands, and urban ecosystems become ever more sensitive to local patterns of waste disposal. Local incineration and landfilling generate more urban ecosystem stresses than does recycling activity. Arguably, household-level decisions about materials demand and recycling effort levels are central to any society's private environmental decision making.Whatever public influences may be brought to bear on households, their decisions and behaviors are likely to be attributable to factors that may not be subject to modification by public action. These influences include the decision makers' locus of control, sense of responsibility, knowledge of choices, and attitude toward the decision problem, all factors inclined to vary with political and cultural contexts.We use data from the 1993 International Social Survey Program: Environment collected from Great Britain, Italy, and the Netherlands to permit comparative analysis of the household recycling decision process and how it varies within the European Union. The survey data collected demonstrate extreme variation in the factors described above and indicate that replicability of successful projects—or the development of model recycling plans—is likely to be extremely difficult, possibly resulting in reliance on suboptimal approaches to stimulating household recycling efforts. The efforts presented, however, may be applied to existing programs to enhance their current undertakings.     

Infant mortality decline in Malaysia, 1946–1975: The roles of changes in variables and changes in the structure of relationships

This analysis has identified several factors contributing to the dramatic decline in infant mortality since World War II in Malaysia, as well as one factor that prevented the infant mortality rate from declining even more rapidly. Our main findings are the following: On average, mothers' education more than doubled over the study period, contributing to the decline in their infants' mortality. In addition, the beneficial effect of mothers' education on infant survival appears to have become stronger over the study period. Hence, further advances in education should lead to further improvements in infants' survival prospects. Another analysis of these data (Peterson et al. 1985) found that education is somewhat more influential in affecting child mortality in low-mortality, high-income areas than in the opposite type of areas. Therefore, socioeconomic development may have complemented, instead of substituted for, the the beneficial effect of mothers' education in promoting infant and child survival in Malaysia. Improvements in water and sanitation also contributed to the infant mortality decline, especially for babies who did not breastfeed. However, unlike education, these influences have become less important over time, especially for babies who are not breastfed. Hence, further improvements in water and sanitation, a goal of Malaysia's Rural Environmental Sanitation Programme, may have smaller relative effects on infant mortality than did previous improvements. Targeting such improvements on areas where women breastfeed little or not at all, however, will increase their effectiveness in promoting infant survival. The substantial reductions in breastfeeding that have taken place since World War II have kept the infant mortality rate in Malaysia from declining as rapidly as it would have otherwise. We estimate that, in our sample, the detrimental effects on infant survival of the decline in breastfeeding have more than offset the beneficial effects of improvements in water and sanitation. Unlike some other researchers (e.g., Palloni 1981), we find that changes in fertility levels and in the timing and spacing of births have had negligible effect in explaining the decline in infant mortality within the samples we have considered. We have excluded births to older women from our analysis, however; this exclusion may have led to an understatement of the influence of changes in the age pattern of childbearing.(ABSTRACT TRUNCATED AT 400 WORDS)