The choice of bandwidth is crucial to the kernel density estimation (KDE) and kernel based regression. Various bandwidth selection methods for KDE and local least square regression have been developed in the past decade. It has been known that scale and location parameters are proportional to density functionals∫γ(x)f2(x)dxwith appropriate choice ofγ(x)and furthermore equality of scale and location tests can be transformed to comparisons of the density functionals among populations.∫γ(x)f2(x)dxcan be estimated nonparametrically via kernel density functionals estimation (KDFE). However, the optimal bandwidth selection for KDFE of∫γ(x)f2(x)dxhas not been examined. We propose a method to select the optimal bandwidth for the KDFE. The idea underlying this method is to search for the optimal bandwidth by minimizing the mean square error (MSE) of the KDFE. Two main practical bandwidth selection techniques for the KDFE of∫γ(x)f2(x)dxare provided: Normal scale bandwidth selection (namely, “Rule of Thumb”) and direct plug-in bandwidth selection. Simulation studies display that our proposed bandwidth selection methods are superior to existing density estimation bandwidth selection methods in estimating density functionals.

Pre-bronchodilator lung function including forced vital capacity (FVC), forced expiratory flow in 1 second (FEV1), their ratio (FEV1/FVC), and forced expiratory flow 25–75% (FEF25–75) measured at age 10, 18, and 26 years in the Isle of Wight birth cohort was analyzed for developmental patterns (trajectories). Early life risk factors before the age of 10 years were assessed for the trajectories. Members of the birth cohort (1989/90) were followed at age 1, 2, 4, 10, 18, and 26 years. Allergic sensitization and questionnaire data were collected. Spirometry tests were performed and evaluated according to the American Thoracic Society (ATS) criteria at 10, 18, and 26 years. To identify developmental trajectories for FVC, FEV1, FEV1/FVC, and FEF25–75 from 10 to 26 years, a finite mixture model was applied to the longitudinal lung function data, separately for males and females. Associations of early life factors with the respective lung function trajectories were assessed using log-linear and logistic regression analyses. Both high and low lung function trajectories were observed in men and women. FVC continued to grow beyond 18 years in men and women, whereas FEV1 peaked at age 18 years in female trajectories and in one male trajectory. For the FEV1/FVC ratios and FEF25–75 most trajectories appeared highest at age 18 and declined thereafter. However, the low FEV1/FVC trajectory in both sexes showed an early decline at 10 years. Lower birth weight was linked with lower lung function trajectories in males and females. Eczema in the first year of life was a risk factor for later lung function deficits in females, whereas the occurrence of asthma at 4 years of age was a risk factor for later lung function deficits in males. A positive skin prick test at age four was a risk for the low FEV1 trajectory in females and for the low FEV1/FVC trajectory in males. Men and women showed distinctive lung function trajectories and associated risk factors. Lower lung function trajectories can be explained by not achieving maximally attainable function at age 18 years and by a function decline from 18 to 26 years.

Epigenetic factors have been suggested as mediators of early-life nutrition to future health. Prior studies focused on breastfeeding effects on DNA methylation (DNAm), ignoring other feeding modes. In this analysis of the Isle of Wight birth cohort, feeding modes were categorized as exclusive breastfeeding (EBF), exclusive formula feeding (EFF), and mixed feeding based on whether the respective feeding mode lasted for at least 3 months. In addition, in the past, infant feeding modes were assessed using DNAm at one time point in childhood, not changes of DNAm. In this paper, methylation differences (delta DNAm) were calculated by subtracting residual methylation values at birth from age 10 years (adjusting for cell types and season of blood collection at both ages). These deltas were estimated for all methylation sites where cytosine was followed by guanine (cytosine guanine dinucleotide (CpG) sites). Then, we performed an epigenome-wide association study contrasting EBF, EFF, and mixed feeding with delta DNAm that represents changes in methylation from birth to 10 years. A total of 87 CpGs (EBF: 27 CpGs, EFF: 48 CpGs, mixed: 12 CpGs) were identified using separate linear regression models adjusting for confounders and multiple testing. The sum of all changes in methylation from birth to age 10 years was significantly lower in the EFF group. Correspondingly, the number of CpGs with a methylation decline was 4.7% higher reflecting 13,683 CpGs. Lower methylation related to exclusive formula feeding and its adverse potential for the child’s development needs future research to reduce adverse health effects.

This paper describes a new automated disengagement tracking system (DTS) that detects learners’ maladaptive behaviors, e.g. mind-wandering and impetuous responding, in an intelligent tutoring system (ITS), called AutoTutor. AutoTutor is a conversation-based intelligent tutoring system designed to help adult literacy learners improve their reading comprehension skills. Learners interact with two computer agents in natural language in 30 lessons focusing on word knowledge, sentence processing, text comprehension, and digital literacy. Each lesson has one to three dozen questions to assess and enhance learning. DTS automatically retrieves and aggregates a learner's response accuracies and time on the first three to five questions in a lesson, as a baseline performance for the lesson when they are presumably engaged, and then detects disengagement by observing if the learner's following performance significantly deviates from the baseline. DTS is computed with an unsupervised learning method and thus does not rely on any self-reports of disengagement. We analyzed the response time and accuracy of 252 adult literacy learners who completed lessons in AutoTutor. Our results show that items that the detector identified as the learner being disengaged had a performance accuracy of 18.5%, in contrast to 71.8% for engaged items. Moreover, the three post-test reading comprehension scores from Woodcock Johnson III, RISE, and RAPID had a significant association with the accuracy of engaged items, but not disengaged items.

The ‘k‐sample problem’ aims to detect statistical differences among multiple populations. A statistical test, capable of detecting any departure from the null hypothesis of ‘statistical equality’ such as the equality in distribution, is typically referred to as an ‘omnibus test.’ A short overview of historic developments and a detailed discussion of the more prominent state‐of‐the‐art techniques are presented with references to numerous sources and studies. Both classical and modern omnibus tests are systematically categorized in terms of seminal probabilistic and statistical concepts into tests that are based upon the empirical distribution, characteristic or kernel density function, etc. To demonstrate the strengths and weaknesses of each particular approach with regard to its statistical performance, applicability, computational complexity, and parameter tuning, eight representatively selected omnibus tests (along with the Kruskal–Wallis test) are numerically implemented and compared under various ‘archetypal’ scenarios. Recommendations are made accordingly along with a discussion of challenges and potential future research directions for this problem. WIREs Comput Stat 2018, 10:e1418. doi: 10.1002/wics.1418This article is categorized under: Statistical Models > Linear Models Statistical and Graphical Methods of Data Analysis > Nonparametric Methods