scholarly journals Confidence Regions for Multivariate Quantiles

Water ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 996 ◽  
Author(s):  
Maximilian Coblenz ◽  
Rainer Dyckerhoff ◽  
Oliver Grothe
Keyword(s):  
Simulation Study ◽  
Level Sets ◽  
Confidence Regions ◽  
Small Sample ◽  
Sample Sizes ◽  
Coverage Probabilities ◽  
Sample Application ◽  
Small Sample Sizes ◽  
Reliable Methods ◽  
Insight Into

Multivariate quantiles are of increasing importance in applications of hydrology. This calls for reliable methods to evaluate the precision of the estimated quantile sets. Therefore, we focus on two recently developed approaches to estimate confidence regions for level sets and extend them to provide confidence regions for multivariate quantiles based on copulas. In a simulation study, we check coverage probabilities of the employed approaches. In particular, we focus on small sample sizes. One approach shows reasonable coverage probabilities and the second one obtains mixed results. Not only the bounded copula domain but also the additional estimation of the quantile level pose some problems. A small sample application gives further insight into the employed techniques.

Does Spending Money on Others Promote Happiness?: A Registered Replication Report

2020 ◽  
Author(s):  
Lara Beth Aknin ◽  
Elizabeth Warren Dunn ◽  
Jason Douglas Edward Proulx ◽  
Iris Lok ◽  
Michael I. Norton
Keyword(s):  
Prosocial Behavior ◽  
Small Sample ◽  
Task Engagement ◽  
Sample Sizes ◽  
Null Results ◽  
Prosocial Spending ◽  
Low Levels ◽  
Momentary Happiness ◽  
Small Sample Sizes ◽  
Insight Into

Research indicates that spending money on others—prosocial spending—leads to greater happiness than spending money on oneself (e.g., Dunn, Aknin, & Norton, 2008; 2014). These findings have received widespread attention because they offer insight into why people engage in costly prosocial behavior, and what constitutes happier spending more broadly. However, most studies on prosocial spending (like most research on the emotional benefits of generosity) utilized small sample sizes (n<100/cell). In light of new, improved standards for evidentiary value, we conducted high-powered registered replications of the central paradigms used in prosocial spending research. In Experiment 1, 712 students were randomly assigned to make a purchase for themselves or a stranger in need and then reported their happiness. As predicted, participants assigned to engage in prosocial (vs. personal) spending reported greater momentary happiness. In Experiment 2, 1950 adults recalled a time they spent money on themselves or someone else and then reported their current happiness; contrary to predictions, participants in the prosocial spending condition did not report greater happiness than those in the personal spending condition. Because low levels of task engagement may have produced these null results, we conducted a replication with minor changes designed to increase engagement; in this Experiment 3 (N = 5,199), participants who recalled a prosocial (vs. personal) spending memory reported greater happiness but differences were small. Taken together, these studies support the hypothesis that spending money on others does promote happiness, but demonstrate that the magnitude of the effect depends on several methodological features.

scholarly journals Inference for Long-memory Time Series Models Based on Modified Empirical Likelihood

2020 ◽  
Vol 49 (5) ◽  
pp. 68-79
Author(s):  
Ramadha D. Piyadi Gamage ◽  
Wei Ning
Keyword(s):  
Time Series ◽  
Empirical Likelihood ◽  
Long Memory ◽  
Small Sample ◽  
Likelihood Method ◽  
Time Series Models ◽  
Sample Sizes ◽  
Coverage Probabilities ◽  
Memory Time ◽  
Small Sample Sizes

Empirical likelihood method has been applied to short-memory time series models by Monti (1997) through the Whittle's estimation method. Yau (2012) extended this idea to long-memory time series models. Asymptotic distributions of the empirical likelihood ratio statistic for short and long-memory time series have been derived to construct confidence regions for the corresponding model parameters. However, it experiences the undercoverage issue which causes the coverage probabilities of parameters lower than the given nominal levels, especially for small sample sizes. In this paper, we propose a modified empirical likelihood which combines the advantages of the adjusted empirical likelihood and the transformed empirical likelihood to modify the one proposed by Yau (2012) for autoregressive fractionally integrated moving average (ARFIMA) model for the purpose of improving coverage probabilities.Asymptotic null distribution of the test statistic has been established as the standard chi-square distribution with the degree of freedom one. Simulations have been conducted to investigate the performance of the proposed method as well as the comparisons of other existing methods to illustrate that the proposed method can provide better coverage probabilities especially for small sample sizes.

scholarly journals Analysis of power of the classical and robust normality tests against bimodal distribution

2009 ◽  
Vol 57 (6) ◽  
pp. 253-260
Author(s):  
Luboš Střelec
Keyword(s):  
Simulation Study ◽  
Bimodal Distribution ◽  
Small Sample ◽  
The Other ◽  
Sample Sizes ◽  
Test Statistic ◽  
Lilliefors Test ◽  
The Mean ◽  
Anderson Darling ◽  
Small Sample Sizes

The aim of this paper is to compare the power of selected normality tests to detect a bimodal distribution. We use some classical normality tests (the Shapiro-Wilk test, the Lilliefors test, the Anderson-Darling test, the classical Jarque-Bera test and the Jarque-Bera-Urzua test), some robust normality tests (the robust Jarque-Bera test and the Medcouple test) and the modified Jarque-Bera tests, where the median instead of the mean is used in the classical Jarque-Bera test statistic. The results of simulation study show that the Anderson-Darling and the Shapiro-Wilk tests outperform the others, especially in small sample sizes. On the other hand the classical Jarque-Bera, the Jarque-Bera-Urzua and robust Jarque-Bera tests are biased, especially in small sample sizes again. Finally, the modification of the Jarque-Bera test leads to increase of power against bimodal distribution.

No Evidence that Experiencing Physical Warmth Promotes Interpersonal Warmth: Two Failures to Replicate Williams and Bargh (2008)

2018 ◽  
Author(s):  
Christopher Chabris ◽  
Patrick Ryan Heck ◽  
Jaclyn Mandart ◽  
Daniel Jacob Benjamin ◽  
Daniel J. Simons
Keyword(s):  
Null Hypothesis ◽  
Small Sample ◽  
Sample Sizes ◽  
Double Blind ◽  
Bayesian Analyses ◽  
Physical Warmth ◽  
Small Sample Sizes ◽  
Interpersonal Warmth

Williams and Bargh (2008) reported that holding a hot cup of coffee caused participants to judge a person’s personality as warmer, and that holding a therapeutic heat pad caused participants to choose rewards for other people rather than for themselves. These experiments featured large effects (r = .28 and .31), small sample sizes (41 and 53 participants), and barely statistically significant results. We attempted to replicate both experiments in field settings with more than triple the sample sizes (128 and 177) and double-blind procedures, but found near-zero effects (r = –.03 and .02). In both cases, Bayesian analyses suggest there is substantially more evidence for the null hypothesis of no effect than for the original physical warmth priming hypothesis.

scholarly journals G-computation and machine learning for estimating the causal effects of binary exposure statuses on binary outcomes

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Florent Le Borgne ◽  
Arthur Chatton ◽  
Maxime Léger ◽  
Rémi Lenain ◽  
Yohann Foucher
Keyword(s):  
Machine Learning ◽  
Support Vector Machine ◽  
Statistical Power ◽  
Small Sample ◽  
Causal Effects ◽  
Small Samples ◽  
Support Vector ◽  
Sample Sizes ◽  
Super Learner ◽  
Small Sample Sizes

AbstractIn clinical research, there is a growing interest in the use of propensity score-based methods to estimate causal effects. G-computation is an alternative because of its high statistical power. Machine learning is also increasingly used because of its possible robustness to model misspecification. In this paper, we aimed to propose an approach that combines machine learning and G-computation when both the outcome and the exposure status are binary and is able to deal with small samples. We evaluated the performances of several methods, including penalized logistic regressions, a neural network, a support vector machine, boosted classification and regression trees, and a super learner through simulations. We proposed six different scenarios characterised by various sample sizes, numbers of covariates and relationships between covariates, exposure statuses, and outcomes. We have also illustrated the application of these methods, in which they were used to estimate the efficacy of barbiturates prescribed during the first 24 h of an episode of intracranial hypertension. In the context of GC, for estimating the individual outcome probabilities in two counterfactual worlds, we reported that the super learner tended to outperform the other approaches in terms of both bias and variance, especially for small sample sizes. The support vector machine performed well, but its mean bias was slightly higher than that of the super learner. In the investigated scenarios, G-computation associated with the super learner was a performant method for drawing causal inferences, even from small sample sizes.

scholarly journals What can we Learn from Studies Based on Small Sample Sizes? Comment on Regan, Lakhanpal, and Anguiano (2012)

2013 ◽  
Vol 113 (1) ◽  
pp. 221-224 ◽  
Author(s):  
David R. Johnson ◽  
Lauren K. Bachan
Keyword(s):  
Sample Size ◽  
Recent Article ◽  
Small Sample ◽  
Sample Sizes ◽  
Relationship Outcomes ◽  
Small Sample Sizes

In a recent article, Regan, Lakhanpal, and Anguiano (2012) highlighted the lack of evidence for different relationship outcomes between arranged and love-based marriages. Yet the sample size ( n = 58) used in the study is insufficient for making such inferences. This reply discusses and demonstrates how small sample sizes reduce the utility of this research.

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