An Asymptotic Characterization of Finite Degree U-statistics With Sample Size-Dependent Kernels: Applications to Nonparametric Estimators and Test Statistics

2015 ◽  
Vol 44 (15) ◽  
pp. 3251-3265 ◽  
Author(s):  
Feng Yao ◽  
Carlos Martins-Filho
2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Estibaliz Gómez-de-Mariscal ◽  
Vanesa Guerrero ◽  
Alexandra Sneider ◽  
Hasini Jayatilaka ◽  
Jude M. Phillip ◽  
...  

AbstractBiomedical research has come to rely on p-values as a deterministic measure for data-driven decision-making. In the largely extended null hypothesis significance testing for identifying statistically significant differences among groups of observations, a single p-value is computed from sample data. Then, it is routinely compared with a threshold, commonly set to 0.05, to assess the evidence against the hypothesis of having non-significant differences among groups, or the null hypothesis. Because the estimated p-value tends to decrease when the sample size is increased, applying this methodology to datasets with large sample sizes results in the rejection of the null hypothesis, making it not meaningful in this specific situation. We propose a new approach to detect differences based on the dependence of the p-value on the sample size. We introduce new descriptive parameters that overcome the effect of the size in the p-value interpretation in the framework of datasets with large sample sizes, reducing the uncertainty in the decision about the existence of biological differences between the compared experiments. The methodology enables the graphical and quantitative characterization of the differences between the compared experiments guiding the researchers in the decision process. An in-depth study of the methodology is carried out on simulated and experimental data. Code availability at https://github.com/BIIG-UC3M/pMoSS.


2020 ◽  
Vol 2 (6) ◽  
pp. 2234-2254 ◽  
Author(s):  
Troels Lindahl Christiansen ◽  
Susan R. Cooper ◽  
Kirsten M. Ø. Jensen

We review the use of pair distribution function analysis for characterization of atomic structure in nanomaterials.


RSC Advances ◽  
2016 ◽  
Vol 6 (45) ◽  
pp. 39469-39479 ◽  
Author(s):  
R. Pazik ◽  
A. Zięcina ◽  
B. Poźniak ◽  
M. Malecka ◽  
L. Marciniak ◽  
...  

Blue emitting, up-converting NP's of SrTiO3:Tm3+/Yb3+ synthesized using the citric route are biocompatible towards J774.E whereas the cytotoxic effect to U2OS cells is not particle size dependent but most probably is related to Sr2+ ion release.


2016 ◽  
Vol 11 (4) ◽  
pp. 551-554 ◽  
Author(s):  
Martin Buchheit

The first sport-science-oriented and comprehensive paper on magnitude-based inferences (MBI) was published 10 y ago in the first issue of this journal. While debate continues, MBI is today well established in sport science and in other fields, particularly clinical medicine, where practical/clinical significance often takes priority over statistical significance. In this commentary, some reasons why both academics and sport scientists should abandon null-hypothesis significance testing and embrace MBI are reviewed. Apparent limitations and future areas of research are also discussed. The following arguments are presented: P values and, in turn, study conclusions are sample-size dependent, irrespective of the size of the effect; significance does not inform on magnitude of effects, yet magnitude is what matters the most; MBI allows authors to be honest with their sample size and better acknowledge trivial effects; the examination of magnitudes per se helps provide better research questions; MBI can be applied to assess changes in individuals; MBI improves data visualization; and MBI is supported by spreadsheets freely available on the Internet. Finally, recommendations to define the smallest important effect and improve the presentation of standardized effects are presented.


1987 ◽  
Vol 24 (04) ◽  
pp. 838-851 ◽  
Author(s):  
W. J. Voorn

Maximum stability of a distribution with respect to a positive integer random variable N is defined by the property that the type of distribution is not changed when considering the maximum value of N independent observations. The logistic distribution is proved to be the only symmetric distribution which is maximum stable with respect to each member of a sequence of positive integer random variables assuming value 1 with probability tending to 1. If a distribution is maximum stable with respect to such a sequence and minimum stable with respect to another, then it must be logistic, loglogistic or ‘backward' loglogistic. The only possible sample size distributions in these cases are geometric.


2018 ◽  
Author(s):  
Arghavan Bahadorinejad ◽  
Ivan Ivanov ◽  
Johanna W Lampe ◽  
Meredith AJ Hullar ◽  
Robert S Chapkin ◽  
...  

AbstractWe propose a Bayesian method for the classification of 16S rRNA metagenomic profiles of bacterial abundance, by introducing a Poisson-Dirichlet-Multinomial hierarchical model for the sequencing data, constructing a prior distribution from sample data, calculating the posterior distribution in closed form; and deriving an Optimal Bayesian Classifier (OBC). The proposed algorithm is compared to state-of-the-art classification methods for 16S rRNA metagenomic data, including Random Forests and the phylogeny-based Metaphyl algorithm, for varying sample size, classification difficulty, and dimensionality (number of OTUs), using both synthetic and real metagenomic data sets. The results demonstrate that the proposed OBC method, with either noninformative or constructed priors, is competitive or superior to the other methods. In particular, in the case where the ratio of sample size to dimensionality is small, it was observed that the proposed method can vastly outperform the others.Author summaryRecent studies have highlighted the interplay between host genetics, gut microbes, and colorectal tumor initiation/progression. The characterization of microbial communities using metagenomic profiling has therefore received renewed interest. In this paper, we propose a method for classification, i.e., prediction of different outcomes, based on 16S rRNA metagenomic data. The proposed method employs a Bayesian approach, which is suitable for data sets with small ration of number of available instances to the dimensionality. Results using both synthetic and real metagenomic data show that the proposed method can outperform other state-of-the-art metagenomic classification algorithms.


2017 ◽  
Author(s):  
Malte Elson ◽  
Andrew K Przybylski

Editorial of the Journal of Media Psychology special issue on "Technology & Human Behavior", and meta-analysis of the empirical research published in JMP since 2008.DATA AVAILABILITYWe were not able to identify a single publication reporting a link to research data in a public repository or the journal’s supplementary materials.STATISTICAL REPORTING ERRORSWe extracted a total of 1036 NHSTs reported in 98 articles. 129 tests were flagged as inconsistent (i.e., reported test statistics and degrees of freedom do not match reported p-values), of which 23 were grossly inconsistent (the reported p-value is <.05 while the recomputed p-value is >.05, or vice-versa). 41 publications reported at least one inconsistent NHST, and 16 publications reported at least one grossly inconsistent NHST. Thus, a substantial proportion of publications in JMP seem to contain inaccurately reported statistical analyses, of which some might affect the conclusions drawn from them.STATISTICAL POWERAs in other fields, surveys tend to have healthy sample sizes apt to reliably detect medium to large relationships between variables. The median sample size for survey studies is 327, allowing researchers to detect small bivariate correlations of r=.1 at 44% power (rs=.3/.5 both > 99%).For (quasi-)experiments, the outlook is a bit different, with a median sample size of 107. Across all types of designs, the median condition size is 30.67. Thus, the average power of experiments published in JMP to detect small differences between conditions (d=.20) is 12% (d=.50 at 49%, d=.80 at 87%).


Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 993
Author(s):  
Jeong-Gon Lee ◽  
Mohammad Fozouni ◽  
Kul Hur ◽  
Young Bae Jun

In 2020, Kang, Song and Jun introduced the notion of multipolar intuitionistic fuzzy set with finite degree, which is a generalization of intuitionistic fuzzy set, and they applied it to BCK/BCI-algebras. In this paper, we used this notion to study p-ideals of BCI-algebras. The notion of k-polar intuitionistic fuzzy p-ideals in BCI-algebras is introduced, and several properties were investigated. An example to illustrate the k-polar intuitionistic fuzzy p-ideal is given. The relationship between k-polar intuitionistic fuzzy ideal and k-polar intuitionistic fuzzy p-ideal is displayed. A k-polar intuitionistic fuzzy p-ideal is found to be k-polar intuitionistic fuzzy ideal, and an example to show that the converse is not true is provided. The notions of p-ideals and k-polar ( ∈ , ∈ ) -fuzzy p-ideal in BCI-algebras are used to study the characterization of k-polar intuitionistic p-ideal. The concept of normal k-polar intuitionistic fuzzy p-ideal is introduced, and its characterization is discussed. The process of eliciting normal k-polar intuitionistic fuzzy p-ideal using k-polar intuitionistic fuzzy p-ideal is provided.


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