Equivariance of ridge estimators through standardization,a note

We show that standardization of data recommended for Ridge Regression (RR) by Hoerl and Kennard (1970 a8b), Marquardt and Snee (1975), and others is worthwhile despite the criticisms by Swamy, Mehta and Rappoport (SMR) (1978).     

Estimation of the limit variance for sums under a new weak dependence condition

We prove a self-normalized central limit theorem for a mixing class of processes introduced in Kacem M, Loisel S, Maume-Deschamps V. [Some mixing properties of conditionally independent processes. Commun Statist Theory Methods. 2016;45:1241–1259]. This class is larger than more classical strongly mixing processes and thus our result is more general than [Peligrad M, Shao QM. Estimation of the variance of partial sums for ρ-mixing random variables. J Multivar Anal. 1995;52:140–157; Shi S. Estimation of the variance for strongly mixing sequences. Appl Math J Chinese Univ. 2000;15(1):45–54] ones. The fact that some conditionally independent processes satisfy this kind of mixing properties motivated our study. We investigate the weak consistency as well as the asymptotic normality of the estimator of the variance that we propose.     

What is the best model of grit among junior high students: Model selection,measurement invariance,and group difference

Grit is a non-cognitive construct based on personality theory that fosters individuals to perform better and achieve their goals. Previous researchers validated the psychometric properties of grit for adults and older adolescents but ignored that for early adolescents. An inappropriate measurement model may mislead researchers and teachers to misapprehend grit measures. This study aimed to identify the most appropriate grit model for early adolescents. Three factorial models (i.e., two-factor, one-factor, and bi-factor models) were evaluated and compared. Subsequently, we tested the measurement invariance (MI) and mean differences of grit across grade and gender groups. Participants were 672 junior high students (51% boys, aged 12–15) in Taiwan. The results showed that the two-factor model was the best grit model. This finding revealed that adolescents tend to comprehend grit with two distinct concepts, consistency in interest (CI) and perseverance of effort (PE), instead of a single compound. In addition, the results showed that the two-factor model retained strong invariance for grade and gender, justifying the comparison of grit scores over grade and gender groups for junior high students. Moreover, we did not find any group difference in the facets of grit by gender and grades. This result showed that grit is a stable personality for junior high students. The relationships between grit constructs and criteria, such as conscientiousness and academic achievements, were tested and discussed.     

Racial/Ethnic Composition and Violence: Size‐of‐Place Variations in Percent Black and Percent Latino Effects on Violence Rates

According to racial invariance positions and mainstream sociological perspectives on race and crime, race differences in structural conditions should account for most if not all of the racial composition (or percent black) effect on aggregate‐level violence rates. However, prior research (mostly conducted prior to 1990) generally provides mixed or contrary evidence for this position, showing instead that greater concentrations of blacks are linked to increased violence even after accounting for racial differences in socioeconomic conditions. The current study uses recent data and a novel unit of analysis to go beyond extant research in two ways. First, we include percent Latino in our examination of the extent to which both racial and ethnic composition effects on violent crime rates are mediated by racial/ethnic disparities in socioeconomic disadvantage. Second, we test whether racial/ethnic composition effects are conditioned by size of place, through the use of census places as a uniquely varying unit of analysis. We find that both black and Latino composition effects are partly explained by controlling for structural conditions (especially structural disadvantage), but this characterizes smaller places much more than the largest, most urbanized places.     

Wrestling Proteus: Assessing the Varying Nature of Father Involvement Across Contexts

This study investigated the common assumption that measures of father involvement are invariant across child age, gender, and reporter. Measurement invariance was tested with 320 families who were interviewed at child ages 10, 12, and 14. Criterion validity was also examined, using observational, survey, and physiologic measures with factor rotation type considered. It was found that invariance did not hold across gender for child report but did hold for mother and father reports. Differing factors were found across time and reporter. Child report and orthogonally rotated solutions demonstrated the greatest criterion validity. The findings suggest that typical father involvement assumptions may not hold and, when this is the case, involvement should be conceptualized in light of varying involvement domains. Implications for conceptualizing and analytically examining father involvement are considered.     

Relationships Between Parents’ And Children’s Salient Values For Future And Children’s Overall Life Satisfaction. A Comparison Across Countries

In this paper, a model is set forth relating (a) overall life satisfaction of children to children’s values and (b) children’s values to parents’ values. Using confirmatory factor analysis models three dimensions of values (materialistic values, capacities and knowledge values and interpersonal relationship values) consistently emerged in 5 countries (Brazil, South Africa, Norway, Spain and India) for both parents and children. There was a considerable amount of missing data, mainly because the parent’s questionnaire was often not returned. Full information maximum likelihood estimators with missing data were thus used.Multiple-group analyses were next performed to assess factor invariance of the three value dimensions across the five countries for both parents and children. This implies testing the equality of factor loadings and intercepts across groups. This equality is required to ensure that factors have the same interpretation in all groups, which is necessary when comparing any aspect of the factor distribution across groups.The only two countries for which the interpretation of value dimensions was invariant for both parents and children were Brazil and Spain. The results of other countries could thus not be compared. Multiple-group structural equation models revealed that both parents and children scored higher on most values in Brazil than in Spain. In both countries, each child value dimension was only significantly predicted by the same value dimension of the parents. R-squares were in the 4–12% range and slightly higher in Brazil. The only value dimension that had some effect on overall life satisfaction was capacities and knowledge, which was so in both countries.Acknowledgements are due to the country project directors and their associates Per Egil Mjaavatn (Norwegian University of Science and Technology, Trondheim, Norway), Usha Nayar (Tata Institute of Social Sciences, India), Irene Rizzini (Pontifícia Universidade Católica do Rio de Janeiro, Brazil), Rose September (Western Cape University, South Africa) and Ferran Casas (Catalan Network of Child Researchers – XCIII – in co-operation with the University of Girona, Spain) for permitting us to use part of their project and to Childwatch International, Oslo, for sponsorship.     

D‐optimal minimax fractional factorial designs

The D‐optimal minimax criterion is proposed to construct fractional factorial designs. The resulting designs are very efficient, and robust against misspecification of the effects in the linear model. The criterion was first proposed by Wilmut & Zhou (2011); their work is limited to two‐level factorial designs, however. In this paper we extend this criterion to designs with factors having any levels (including mixed levels) and explore several important properties of this criterion. Theoretical results are obtained for construction of fractional factorial designs in general. This minimax criterion is not only scale invariant, but also invariant under level permutations. Moreover, it can be applied to any run size. This is an advantage over some other existing criteria. The Canadian Journal of Statistics 41: 325–340; 2013 © 2013 Statistical Society of Canada     

Priority Rules and Other Asymmetric Rationing Methods

In a rationing problem, each agent demands a quantity of a certain commodity and the available resources fall short of total demand. A rationing method solves this problem at every level of resources and individual demands. We impose three axioms: Consistency—with respect to variations of the set of agents—Upper Composition and Lower Composition—with respect to variations of the available resources. In the model where the commodity comes in indivisible units, the three axioms characterize the family of priority rules, where individual demands are met lexicographically according to an exogeneous ordering of the agents. In the (more familiar) model where the commodity is divisible, these three axioms plus Scale Invariance—independence of the measurement unit—characterize a rich family of methods. It contains exactly three symmetric methods, giving equal shares to equal demands: these are the familiar proportional, uniform gains, and uniform losses methods. The asymmetric methods in the family partition the agents into priority classes; within each class, they use either the proportional method or a weighted version of the uniform gains or uniform losses methods.     

Asymptotic Distribution Theory for Nonparametric Entropy Measures of Serial Dependence

Entropy is a classical statistical concept with appealing properties. Establishing asymptotic distribution theory for smoothed nonparametric entropy measures of dependence has so far proved challenging. In this paper, we develop an asymptotic theory for a class of kernel‐based smoothed nonparametric entropy measures of serial dependence in a time‐series context. We use this theory to derive the limiting distribution of Granger and Lin's (1994) normalized entropy measure of serial dependence, which was previously not available in the literature. We also apply our theory to construct a new entropy‐based test for serial dependence, providing an alternative to Robinson's (1991) approach. To obtain accurate inferences, we propose and justify a consistent smoothed bootstrap procedure. The naive bootstrap is not consistent for our test. Our test is useful in, for example, testing the random walk hypothesis, evaluating density forecasts, and identifying important lags of a time series. It is asymptotically locally more powerful than Robinson's (1991) test, as is confirmed in our simulation. An application to the daily S&P 500 stock price index illustrates our approach.