Convergence on the two-child family norm in Australia

This paper examines childbearing patterns of ever-married women in Australia and establishes that during the process of fertility transition from high to low levels which largely began after 1971, significant changes occurred in the timing of the first birth after marriage, the length of the first and inter-birth intervals and the proportion of women progressing to have a first birth or births beyond the second. The analysis also confirms the predominance of the twochild family norm and shows the emergence of a converging trend on that family norm. The study applies the life tables technique to the marriage and birth history data collected in the Family Formation Survey conducted by the ABS in September 1986.     

The abs population projections: Overview and evaluation

The paper provides a brief history of the ABS projection services in the context of its role as the central statistical agency in Australia. It also presents an overview of the methodology used for generating the projections and details the procedures used for compiling the various components of change incorporated in the projections. The accuracy of the ABS past projections is assessed by comparing their results, both at the national and state/territory levels, with corresponding estimated resident population figures. The paper also describes the range of projection services currently provided by the ABS, lists present unmet needs and indicates some of the developments likely to occur in the future in satisfying unmet demand, consolidation of existing services and dissemination of output.     

Risk-adjusted martingales and the design of “indifference” gambles

In the probability literature, a martingale is often referred to as a “fair game.” A martingale investment is a stochastic sequence of wealth levels, whose expected value at any future stage is equal to the investor’s current wealth. In decision theory, a risk neutral investor would therefore be indifferent between holding on to a martingale investment, and receiving its payoff at any future stage, or giving it up and maintaining his current wealth. But a risk-averse decision maker would not be indifferent between a martingale investment and his current wealth level, since he values uncertain deals less than their mean. A risk seeking decision maker, on the other hand, would readily accept a martingale investment in exchange for his current wealth, and would repeat this investment any number of times. These ideas lead us to introduce the notion of a “risk-adjusted martingale”; a stochastic sequence of wealth levels that a rational decision maker with any attitude toward risk would value constantly with time, and would be indifferent between receiving its pay-off at any future stage, or giving it up and maintaining his current wealth level. We show how to construct such risk-adjusted investments for any decision maker with a continuous monotonic utility function. The fundamental result we derive is that a pay-off structure of an investment (i) is a risk-adjusted martingale and (ii) can be represented by a lattice if and only if the pay-off functions are invariant transformations of the given utility function.     

Invariant multiattribute utility functions

We present a method to characterize the preferences of a decision maker in decisions with multiple attributes. The approach modifies the outcomes of a multivariate lottery with a multivariate transformation and observes the change in the decision maker’s certain equivalent. If the certain equivalent follows this multivariate transformation, we refer to this situation as multiattribute transformation invariance, and we derive the functional form of the utility function. We then show that any additive or multiplicative utility function that is formed of continuous and strictly monotonic utility functions of the individual attributes must satisfy transformation invariance with a multivariate transformation. This result provides a new interpretation for multiattribute utility functions with mutual utility independence as well as a necessary and sufficient condition that must be satisfied when assuming these widely used functional forms. We work through several examples to illustrate the approach.     

New estimation and feature selection methods in mixture‐of‐experts models

We study estimation and feature selection problems in mixture‐of‐experts models. An $l_2$ ‐penalized maximum likelihood estimator is proposed as an alternative to the ordinary maximum likelihood estimator. The estimator is particularly advantageous when fitting a mixture‐of‐experts model to data with many correlated features. It is shown that the proposed estimator is root‐$n$ consistent, and simulations show its superior finite sample behaviour compared to that of the maximum likelihood estimator. For feature selection, two extra penalty functions are applied to the $l_2$ ‐penalized log‐likelihood function. The proposed feature selection method is computationally much more efficient than the popular all‐subset selection methods. Theoretically it is shown that the method is consistent in feature selection, and simulations support our theoretical results. A real‐data example is presented to demonstrate the method. The Canadian Journal of Statistics 38: 519–539; 2010 © 2010 Statistical Society of Canada     

Analysis of Frechet Distribution Using Reference Priors

This article develops the Bayesian estimators in the context of reference priors for the two-parameter Frechet distribution. The general forms of the second-order matching priors are also derived in case of any parameter of interest and concluded that the reference prior is also a second order matching prior. Since the Bayesian estimators cannot be obtained in closed form, they are obtained using Monte Carlo simulation and Laplace approximation. The Bayesian and maximum likelihood estimates are compared via simulation study. Two real-life data sets are analyzed for illustration and comparison purpose.     

Optimal design of the variable sampling size and sampling interval variable dimension T2 control chart for monitoring the mean vector of a multivariate normal process

This paper develops the algorithm for the optimization designs of the adaptive T² Control Chart for Monitoring the Mean Vector of a Multivariate Normal Process. It includes the variable sample size, variable sampling interval and variable dimensional chart. The VDT² control chart performs well for moderate and large shifts in the mean vector. However, its performance for small shifts is poor. To improve the chart's performance in detecting such shifts, we propose the application of the variable sample size and sampling interval technique to the VDT² control chart, resulting in the VSSIVDT² control chart.     

A Father's Education as a Determinant of Socioeconomic and Cultural Characteristics of Families in a Sample of Iranian Adolescents*

In order to find out the degree to which a father's education can be used as a predictor of the socioeconomic status (SES) of the family, 1,047 high school students in and around Shiraz, Iran were given a questionnaire covering a wide variety of issues. A considerable variation was found in the physical, cultural, and financial milieus of subjects with different FEs (father's education). Results indicate a close association between a father's education and his occupational status and income. Subjects with better-educated fathers have reported a higher rate of literacy among their mothers and a more culturally enriched home environment than those with less-educated fathers. The parental homes of the high FE group also appear to be mostly located in the more fashionable, modern residential areas of the city and to contain a larger number of rooms. The findings are taken as further justification for the use of FE as an index of parental SES. The significance of education as a means of social mobility in the Iranian culture is briefly discussed and the implication of this for the educational system of the country is commented upon.     

Extending the Bradley–Terry model for paired comparisons to accommodate weights

In the method of paired comparisons (PCs), treatments are compared on the basis of qualitative characteristics they possess, in the light of their sensory evaluations made by judges. However, there may emerge the situations where in addition to qualitative merits/worths, judges may assign quantitative weights to reflect/specify the relative importance of the treatments. In this study, an attempt is made to reconcile the qualitative and the quantitative PCs through assigning quantitative weights to treatments having qualitative merits using/extending the Bradley–Terry (BT) model. Behaviors of the existing BT model and the proposed weighted BT model are studied through the test of goodness-of-fit. Experimental and simulated data sets are used for illustration.     

Adolescent experiences with online racial discrimination: Implications for prevention and coping

Online aggression represents a wide range of negative experiences, including online discrimination targeting individuals based on race, but adolescent perspectives are not well-represented. We interviewed 15 adolescents regarding their experiences with online racial discrimination. After a phenomenological analysis, four main themes emerged: types of online racial aggression, processes supporting online racism, personal coping, and strategies to prevent online racial aggression. These themes provided insights into adolescent experiences, including feelings about targeted online racial discrimination, intersectionality with sexual harassment, and comfort through processing with friends. This study highlights adolescents' thoughts regarding advocacy, education, and social media reform to prevent online racial aggression. Future research should ensure that youth voices from minoritized racial backgrounds are integrated into efforts to address these critical social issues.