On Optimality of Bayesian Wavelet Estimators

Abstract.  We investigate the asymptotic optimality of several Bayesian wavelet estimators, namely, posterior mean, posterior median and Bayes Factor, where the prior imposed on wavelet coefficients is a mixture of a mass function at zero and a Gaussian density. We show that in terms of the mean squared error, for the properly chosen hyperparameters of the prior, all the three resulting Bayesian wavelet estimators achieve optimal minimax rates within any prescribed Besov space     for p  ≥ 2. For 1 ≤  p  < 2, the Bayes Factor is still optimal for (2 s +2)/(2 s +1) ≤  p  < 2 and always outperforms the posterior mean and the posterior median that can achieve only the best possible rates for linear estimators in this case.     

RURAL POVERTY, URBAN POVERTY, AND PSYCHOLOGICAL WELL-BEING

Data from the National Survey of Families and Households are used to compare the psychological well-being of the rural and urban poor. Overall, the urban poor are higher in perceived health than the rural poor, although no differences are apparent in happiness or depression. Significant interactions are present between rural/urban poverty and sex, race, and family status. The psychological well-being of poor African Americans is higher in rural than urban areas, whereas the well-being of poor whites is higher in urban than rural areas. This trend is especially pronounced for depression among males. In addition, single men without children have especially high depression scores in rural areas, whereas married women without children have especially low depression scores in urban areas. The results are interpreted in terms of the environmental quality of inner-city neighborhoods and attitudes toward poverty in urban and rural communities.     

Parent‐Adolescent Involvement: The Relative Influence of Parent Gender and Residence

The 1995 wave of the Add Health study is used to investigate the relative influence of parent gender and residence on patterns of parental involvement with adolescents. Adolescent reports (N =17,330) of shared activities, shared communication, and relationship quality with both biological parents are utilized. A multidimensional scaling analysis reveals that parent gender explains most of the variance in parent‐adolescent involvement, with residential status playing a secondary yet a fundamental role in accounting for these patterns. Resident mothers who do not live with adolescents’ biological fathers engage in the broadest range of activities with their children. Unpartnered resident fathers display patterns of parenting that are as similar to mothers as they are to other fathers.     

Economic hardship in the family of origin and children's psychological well‐Being in adulthood

Past research consistently indicates that poverty and economic hardship have negative consequences for children. Few studies, however, have examined whether these consequences persist into adulthood. This study addresses this gap by assessing whether economic resources in the family of origin have long‐term effects on psychological well‐being in adulthood. Specifically, we test two processes—one involving interpersonal processes in the family of origin, and the other involving children's socioeconomic attainment—that may help to explain the link between early economic factors and later well‐being. Using 17‐year longitudinal data from two generations (N= 589), we find evidence that economic hardship in the family of origin predicts later adult well‐being through the parents’ marital relationship, the parent‐teen relationship, children's educational attainment, and children's earned income. Supplementary analyses suggest that economic hardship is particularly problematic when it is of long duration or when it occurs during adolescence.     

Research on Divorce: Continuing Trends and New Developments

Research on divorce during the past decade has focused on a range of topics, including the predictors of divorce, associations between divorce and the well‐being of children and former spouses, and interventions for divorcing couples. Methodological advances during the past decade include a greater reliance on nationally representative longitudinal samples, genetically informed designs, and statistical models that control for time‐invariant sources of unobserved heterogeneity. Emerging perspectives, such as a focus on the number of family transitions rather than on divorce as a single event, are promising. Nevertheless, gaps remain in the research literature, and the review concludes with suggestions for new studies.     

Patterns of nonresident father contact

We used the National Longitudinal Survey of Youth 1979 cohort (NLSY79) from 1979 to 2002 and the Children of the National Longitudinal Survey of Youth (CNLSY) from 1986 to 2002 to describe the number, shape, and population frequencies of U.S. nonresident father contact trajectories over a 14-year period using growth mixture models. The resulting four-category classification indicated that nonresident father involvement is not adequately characterized by a single population with a monotonic pattern of declining contact over time. Contrary to expectations, about two-thirds of fathers were consistently either highly involved or rarely involved in their children’s lives. Only one group, constituting approximately 23% of fathers, exhibited a clear pattern of declining contact. In addition, a small group of fathers (8%) displayed a pattern of increasing contact. A variety ofvariables differentiated between these groups, including the child’s age at father-child separation, whether the child was born within marriage, the mother’s education, the mother’s age at birth, whether the father pays child support regularly, and the geographical distance between fathers and children.     

Wavelet kernel penalized estimation for non-equispaced design regression

The paper considers regression problems with univariate design points. The design points are irregular and no assumptions on their distribution are imposed. The regression function is retrieved by a wavelet based reproducing kernel Hilbert space (RKHS) technique with the penalty equal to the sum of blockwise RKHS norms. In order to simplify numerical optimization, the problem is replaced by an equivalent quadratic minimization problem with an additional penalty term. The computational algorithm is described in detail and is implemented with both the sets of simulated and real data. Comparison with existing methods showed that the technique suggested in the paper does not oversmooth the function and is superior in terms of the mean squared error. It is also demonstrated that under additional assumptions on design points the method achieves asymptotic optimality in a wide range of Besov spaces.     

Precursors of Young Women's Family Formation Pathways

We used latent class analysis to create family formation pathways for women between the ages of 18 and 23. Input variables included cohabitation, marriage, parenthood, full-time employment, and attending school. Data (n = 2,290) came from Waves I and III of the National Longitudinal Study of Adolescent Health (Add Health). The analysis revealed seven latent pathways: college-no family formation (29%), high school-no family formation (19%), cohabitation without children (15%), married mothers (14%), single mothers (10%), cohabiting mothers (8%), and inactive (6%). Three sets of variables distinguished between the groups: personal and social resources in adolescence, family socioeconomic resources and adolescent academic achievement, and conservative values and behavior in adolescence.