On the Bias of the Maximum Likelihood Estimator for the Two-Parameter Lomax Distribution

The Lomax (Pareto II) distribution has found wide application in a variety of fields. We analyze the second-order bias of the maximum likelihood estimators of its parameters for finite sample sizes, and show that this bias is positive. We derive an analytic bias correction which reduces the percentage bias of these estimators by one or two orders of magnitude, while simultaneously reducing relative mean squared error. Our simulations show that this performance is very similar to that of a parametric bootstrap correction based on a linear bias function. Three examples with actual data illustrate the application of our bias correction.     

Asymptotically Optimal Nonparametric Empirical Bayes Via Predictive Recursion

An empirical Bayes problem has an unknown prior to be estimated from data. The predictive recursion (PR) algorithm provides fast nonparametric estimation of mixing distributions and is ideally suited for empirical Bayes applications. This article presents a general notion of empirical Bayes asymptotic optimality, and it is shown that PR-based procedures satisfy this property under certain conditions. As an application, the problem of in-season prediction of baseball batting averages is considered. There the PR-based empirical Bayes rule performs well in terms of prediction error and ability to capture the distribution of the latent features.     

Bias reduction for the maximum likelihood estimator of the doubly-truncated Poisson distribution

ABSTRACT

We derive an analytic expression for the bias of the maximum likelihood estimator of the parameter in a doubly-truncated Poisson distribution, which proves highly effective as a means of bias correction. For smaller sample sizes, our method outperforms the alternative of bias correction via the parametric bootstrap. Bias is of little concern in the positive Poisson distribution, the most common form of truncation in the applied literature. Bias appears to be the most severe in the doubly-truncated Poisson distribution, when the mean of the distribution is close to the right (upper) truncation.     

An Approximate Bayesian Marginal Likelihood Approach for Estimating Finite Mixtures

Estimation of finite mixture models when the mixing distribution support is unknown is an important problem. This article gives a new approach based on a marginal likelihood for the unknown support. Motivated by a Bayesian Dirichlet prior model, a computationally efficient stochastic approximation version of the marginal likelihood is proposed and large-sample theory is presented. By restricting the support to a finite grid, a simulated annealing method is employed to maximize the marginal likelihood and estimate the support. Real and simulated data examples show that this novel stochastic approximation and simulated annealing procedure compares favorably with existing methods.     

A Starting Point for Navigating the World of Daily Fantasy Basketball

Fantasy sports, particularly the daily variety in which new lineups are selected each day, are a rapidly growing industry. The two largest companies in the daily fantasy business, DraftKings and Fanduel, have been valued as high as $2 billion. This research focuses on the development of a complete system for daily fantasy basketball, including both the prediction of player performance and the construction of a team. First, a Bayesian random effects model is used to predict an aggregate measure of daily NBA player performance. The predictions are then used to construct teams under the constraints of the game, typically related to a fictional salary cap and player positions. Permutation based and K-nearest neighbors approaches are compared in terms of the identification of “successful” teams—those who would be competitive more often than not based on historical data. We demonstrate the efficacy of our system by comparing our predictions to those from a well-known analytics website, and by simulating daily competitions over the course of the 2015–2016 season. Our results show an expected profit of approximately $9,000 on an initial $500 investment using the K-nearest neighbors approach, a 36% increase relative to using the permutation-based approach alone. Supplementary materials for this article are available online.     

Parents’ and children’s power effectiveness during polyadic family conflict: Process and outcome

Parent–child power effectiveness was investigated during naturally occurring polyadic family conflict with young children involving three or more family members. In 35/39 families, 210 conflict sequences were identified and coded for type of power, power effectiveness, and conflict outcome. Effective use of power overall and by each partner was assessed using two methods: microscopic (target’s response to an actor’s power move during the process of conflict) and macroscopic (power moves related to conflict outcome). Actor findings revealed that parents were more effective using certain types of power microscopically (i.e., simple, legitimate, reward) and macroscopically (i.e., simple, legitimate, questioning), whereas children were more effective using reward power macroscopically. Our findings support the unique qualities of the parent–child relationship and the complex context of polyadic family conflict. The study contributes to the literature on the socialization of young children in the family context.     

Compassion Satisfaction,Compassion Fatigue,and Burnout: A Replication Study with Victim Advocates

Abstract

Past research has investigated the rates of compassion satisfaction (CS), compassion fatigue (CF), and burnout within health-care providers. Findings indicate higher levels of CS and lower levels of CF predict lower rates of burnout. The current study extended prior research by replicating past research findings, but with victim advocates. This study enrolled a national sample of 142 victim advocates. A hierarchal linear regression was run to test the research questions. In level 1, years of experience was not significant and only accounted for 1.1% of the variance in burnout. When adding CS, the model became significant (p?<?.001) and CS accounted for an additional 51.8% of the variance. When CF was added to the final model, it was significant (p?<?.001), and accounted for an additional 19.3% of the variance. When comparing the findings to past studies, our findings were similar; however, our study did find that CS and CF accounted for significantly more variance than past studies with health-care providers. Therefore, CS and CF might be greater predictors of burnout in victim advocates than in health-care providers. Future studies should aim to create interventions to increase CS and decrease CF, to reduce burnout.     

“We're gonna get you through it”: The role of bonding social capital in the development of bridging social capital

Many programs that place low-income students of color in high-achieving college preparatory high schools seek to nurture bridging social capital, connections across class lines that provide leverage in the process of “getting ahead.” Bonding social capital, which focuses more on emotional support and “getting by,” is frequently characterized as less useful for social mobility. Drawing upon in-depth interviews with alumni from one such program, we challenge the notion of bridging and bonding social capital as discrete, countervailing forms of social capital, and demonstrate how the two may complement each other. Specifically, we find that bonding social capital served as a critical resource that students drew upon as they navigated their elite high schools in the face of racism and classism. In doing so, this bonding social capital ultimately facilitated the development of bridging social capital by encouraging student persistence at these institutions. Our findings support critiques of traditional accounts of social capital that devalue the capital possessed by marginalized communities and fuel deficit ideologies. Furthermore, they highlight the personal costs that youth may face in the pursuit of bridging capital, complicating the narrative of social mobility as an unmitigated good.     

生活在上海

我喜欢教学,也喜欢教学给我带来的感受。当看到学生们渐渐取得进步,就会心生成就感,我想这就是我对工作的满意度吧。所有这些,给我带来的,是让我觉得在上海生活的每一天都很有意思。