Statistical inferences for functional data

With modern technology development, functional data are being observed frequently in many scientific fields. A popular method for analyzing such functional data is ``smoothing first, then estimation.'' That is, statistical inference such as estimation and hypothesis testing about functional data is conducted based on the substitution of the underlying individual functions by their reconstructions obtained by one smoothing technique or another. However, little is known about this substitution effect on functional data analysis. In this paper this problem is investigated when the local polynomial kernel (LPK) smoothing technique is used for individual function reconstructions. We find that under some mild conditions, the substitution effect can be ignored asymptotically. Based on this, we construct LPK reconstruction-based estimators for the mean, covariance and noise variance functions of a functional data set and derive their asymptotics. We also propose a GCV rule for selecting good bandwidths for the LPK reconstructions. When the mean function also depends on some time-independent covariates, we consider a functional linear model where the mean function is linearly related to the covariates but the covariate effects are functions of time. The LPK reconstruction-based estimators for the covariate effects and the covariance function are also constructed and their asymptotics are derived. Moreover, we propose a $L^2$-norm-based global test statistic for a general hypothesis testing problem about the covariate effects and derive its asymptotic random expression. The effect of the bandwidths selected by the proposed GCV rule on the accuracy of the LPK reconstructions and the mean function estimator is investigated via a simulation study. The proposed methodologies are illustrated via an application to a real functional data set collected in climatology.Comment: Published at http://dx.doi.org/10.1214/009053606000001505 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Basic Psychological Needs Satisfaction, Autonomy Support, and Mindsets as Predictors of Self-Regulation in University Online Learners

Problem In contrast to more traditional learning environments, it can be difficult to see and hear both the instructor and, more crucially, the students when engaging in online education. This has been one of the most common criticisms leveled against online education for a long time. The COVID-19 disruption and transformation of online learning in higher education underlines the fact that variance among online learners in terms of academic success and psychological well-being are determined by the level and quality of self-regulation. What is the degree of self-regulation among American university students who study online because of the COVID-19 pandemic\u27s impact, and what variables might affect or perhaps predict this level of self-regulation? Purpose of Study The purpose of the present study was to test a theoretical model that explains how autonomy support, satisfaction of basic psychological needs, and mindsets predict self-regulation among university online learners in the United States. Based on the model fit and direct effect results of the first research hypothesis, the second research model was developed to examine the mediating effect of basic psychological needs satisfaction on the relationship between autonomy support and self-regulation, and whether mindsets could moderate the indirect effect of basic psychological needs satisfaction on the relationship between autonomy support and self-regulation. To assess the data, structural equation modeling (SEM) was employed. Method This study used quantitative analysis of non-experimental survey data collected via Alchemer. A model-testing design was used to examine a theoretical model which proposed that basic psychological needs satisfaction (autonomy, competency, relatedness), autonomy support, and mindsets predict online learners\u27 self-regulation. 1257 people in all completed the survey. The number of complete and valid participant responses was a sample of 404. Excel, SPSS version 26, Mplus version 8.3 were used for data analysis. Structural equation modeling (SEM) was adopted as the main statistical technique. Results The first research model of this study hypothesized that autonomy support, basic psychological needs satisfaction, and mindsets predict university online learners’ self-regulation. Analysis of the data indicated that the first hypothesized research model fit the data (X2=464.364, df=200, Normed Chi-Square=2.231, CFI=0.925, TLI=0.913, RMSEA=0.057, SRMR=0.053). The path analysis indices of model one suggested that autonomy support positively affected university online learners’ basic psychological needs satisfaction (b=0.82, p\u3c0.001). Basic psychological needs satisfaction positively affected self-regulation (b=0.44, p\u3c0.001) and mindsets positively affected self-regulation (b=0.23, p\u3c0.001). Overall, research model one explained 44.2% variance of online learners\u27 self-regulation. The model fit indices showed that the second hypothesized research model fit the data (X2=378.398, df=146, Normed Chi-Square=2.259, CFI=0.921, TLI=0.908, RMSEA=0.063, SRMR=0.050). A significant mediator effect of basic psychological needs satisfaction was found between autonomy support and self-regulation. The results indicated that the conditional indirect effect of autonomy support on self-regulation via basic psychological needs satisfaction was significant both when the mindsets score was high (which suggests growth mindset orientation) (β=0.216, 95% CI [0.098, 0.316]) and when the mindsets score was low (which suggests fixed mindset orientation) (β=0.150, 95% CI [0.031, 0.250]). Conclusions Applying SEM technique for data analysis, the model fit indices showed that the first hypothesized research model of this study fit the data and explained 44.2% variance of university online learners\u27 self-regulation. The path analysis indices of model one suggests that basic psychological needs satisfaction and mindsets play a predictive role in self-regulation among university online learners whereas autonomy support could not be used as a predictor of self-regulation among university online learners. In addition, the path analysis indices of research model one indicates that autonomy support and basic psychological needs satisfaction could not be used as a predictor of mindsets among university online learners whereas autonomy support could predict basic psychological needs satisfaction as suggested by the theoretical framework. A significant mediator effect of basic psychological needs satisfaction was found between autonomy support and self-regulation. Furthermore, the results of the second research model indicate that the conditional indirect effect of autonomy support on self-regulation via basic psychological needs satisfaction was both significant when the mindsets score was high (which suggests growth mindset orientation) and when the mindsets score was low (which suggests fixed mindset orientation). The difference (though not significant) between these two slopes suggests that the mediation effect of basic psychological needs satisfaction on the relationship between autonomy support and self-regulation was slightly stronger when the mindsets score was higher indicating a growth mindset

Diffusion Dynamics, Moments, and Distribution of First Passage Time on the Protein-Folding Energy Landscape, with Applications to Single Molecules

We study the dynamics of protein folding via statistical energy-landscape theory. In particular, we concentrate on the local-connectivity case with the folding progress described by the fraction of native conformations. We obtain information for the first passage-time (FPT) distribution and its moments. The results show a dynamic transition temperature below which the FPT distribution develops a power-law tail, a signature of the intermittency phenomena of the folding dynamics. We also discuss the possible application of the results to single-molecule dynamics experiments

Dcr-1 Maintains Drosophila Ovarian Stem Cells

SummaryMicroRNAs (miRNAs) regulate gene expression by controlling the turnover, translation, or both of specific mRNAs. In Drosophila, Dicer-1 (Dcr-1) is essential for generating mature miRNAs from their corresponding precursors. Because miRNAs are known to modulate developmental events, such as cell fate determination and maintenance in many species, we investigated whether a lack of Dcr-1 would affect the maintenance of stem cells (germline stem cells, GSCs; somatic stem cells, SSCs) in the Drosophila ovary by specifically removing its function from the stem cells. Our results show that dcr-1 mutant GSCs cannot be maintained and are lost rapidly from the niche without discernable features of cell death, indicating that Dcr-1 controls GSC self-renewal but not survival. bag of marbles (bam), the gene that encodes an important differentiating factor in the Drosophila germline, however, is not upregulated in dcr-1 mutant GSCs, and its removal does not slow down dcr-1 mutant GSC loss, suggesting that Dcr-1 controls GSC self-renewal by repressing a Bam-independent differentiation pathway. Furthermore, Dcr-1 is also essential for the maintenance of SSCs in the Drosophila ovary. Our data suggest that miRNAs produced by Dcr-1 are required for maintaining two types of stem cells in the Drosophila ovary