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Analysis of Variance (ANOVA) is a popular method to infer, based on the sampled data, whether the true means of a set of subpopulations differ from each other. The variance of conditional expectation (VOCE) is the variance of these effects in sub-populations, and this is estimated by sampling a sub-population of size n k , for each sub-population labeled k, and by sampling K such sub-populations in the experiment. For the general case of varying n k , it is unknown what the variance of the VOCE estimator is, though it is known for the special case n k = n , n ≥ 2 for all k ∈ 1 , 2 , ... , K as derived in the literature. The following derivation settles the former question and is of value in situations where sampling has constraints or only a skewed sampling budget is available. Our first application is with regard to the decision of whether samples from pilot simulation can be included in the regular simulation to estimate VOCE. The second application is an estimation technique where the estimate of optimal inner-loop size n * can be updated throughout the duration of simulation. We demonstrate with these 2 applications where we observe a 20% reduction in the variance of the VOCE estimate, when the proposed method is applied. [ABSTRACT FROM AUTHOR]

The paper treats the modeling of stationary multivariate stochastic processes via frequency domain, and extends the notion of generalized autocovariance function, given by Proietti and Luati (2015) for univariate time series, to the multivariate setting. The generalized autocovariance matrices are defined for stationary multivariate stochastic processes as the Fourier transform of the power transformation of the spectral density matrix. Then we prove the consistency and derive the asymptotic distribution of frequency domain non-parametric estimators of the generalized autocovariance matrices, based on the power transformation of the periodogram matrix. Generalized autocovariance matrices are used to construct white noise hypothesis testing, to discriminate stochastic processes, and to introduce a generalized Yule–Walker estimator for the spectrum. A so-called λ–squared distance between two multivariate stochastic processes is also defined by using their generalized autocovariance matrices, and it serves for clustering time series and estimation by feature matching. Another use is in discriminant analysis. [ABSTRACT FROM AUTHOR]

Information theory explains how systems encode and transmit information. This article examines the neuronal system, which processes information via neurons that react to stimuli and transmit electrical signals. Specifically, we focus on transfer entropy to measure the flow of information between sequences and explore its use in determining effective neuronal connectivity. We analyze the causal relationships between two discrete time series, X : = X t : t ∈ Z and Y : = Y t : t ∈ Z , which take values in binary alphabets. When the bivariate process (X , Y) is a jointly stationary ergodic variable-length Markov chain with memory no larger than k, we demonstrate that the null hypothesis of the test—no causal influence—requires a zero transfer entropy rate. The plug-in estimator for this function is identified with the test statistic of the log-likelihood ratios. Since under the null hypothesis, this estimator follows an asymptotic chi-squared distribution, it facilitates the calculation of p-values when applied to empirical data. The efficacy of the hypothesis test is illustrated with data simulated from a neuronal network model, characterized by stochastic neurons with variable-length memory. The test results identify biologically relevant information, validating the underlying theory and highlighting the applicability of the method in understanding effective connectivity between neurons. [ABSTRACT FROM AUTHOR]

This article considers a way to test the hypothesis that two collections of objects are from the same uniform distribution of such objects. The exact p-value is calculated based on the distribution for the observed overlaps. In addition, an interval estimate of the number of distinct objects, when all objects are equally likely, is indicated. [ABSTRACT FROM AUTHOR]

AbstractShape constraints yield flexible middle grounds between fully nonparametric and fully parametric approaches to modeling distributions of data. The specific assumption of log-concavity is motivated by applications across economics, survival modeling, and reliability theory. However, there do not currently exist valid tests for whether the underlying density of given data is log-concave. The recent universal inference methodology provides a valid test. The universal test relies on maximum likelihood estimation (MLE), and efficient methods already exist for finding the log-concave MLE. This yields the first test of log-concavity that is provably valid in finite samples in any dimension, for which we also establish asymptotic consistency results. Empirically, we find that a random projections approach that converts the d-dimensional testing problem into many one-dimensional problems can yield high power, leading to a simple procedure that is statistically and computationally efficient. [ABSTRACT FROM AUTHOR]

AbstractThis article studies the impact of bootstrap procedure on the eigenvalue distributions of the sample covariance matrix under a high-dimensional factor structure. We provide asymptotic distributions for the top eigenvalues of bootstrapped sample covariance matrix under mild conditions. After bootstrap, the spiked eigenvalues which are driven by common factors will converge weakly to Gaussian limits after proper scaling and centralization. However, the largest non-spiked eigenvalue is mainly determined by the order statistics of the bootstrap resampling weights, and follows extreme value distribution. Based on the disparate behavior of the spiked and non-spiked eigenvalues, we propose innovative methods to test the number of common factors. Indicated by extensive numerical and empirical studies, the proposed methods perform reliably and convincingly under the existence of both weak factors and cross-sectionally correlated errors. Our technical details contribute to random matrix theory on spiked covariance model with convexly decaying density and unbounded support, or with general elliptical distributions. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work. [ABSTRACT FROM AUTHOR]

AbstractRegression experts consistently recommend plotting residuals for model diagnosis, despite the availability of many numerical hypothesis test procedures designed to use residuals to assess problems with a model fit. Here we provide evidence for why this is good advice using data from a visual inference experiment. We show how conventional tests are too sensitive, which means that too often the conclusion would be that the model fit is inadequate. The experiment uses the lineup protocol which puts a residual plot in the context of null plots. This helps generate reliable and consistent reading of residual plots for better model diagnosis. It can also help in an obverse situation where a conventional test would fail to detect a problem with a model due to contaminated data. The lineup protocol also detects a range of departures from good residuals simultaneously. Supplemental materials for the article are available online. [ABSTRACT FROM AUTHOR]

The covariance matrix with compound symmetry structure is used in many statistical procedures, as in repeated measures design, in mixed linear or non-linear models, as well as in genetic studies. For making inferences about the compound symmetry structure, the classic original likelihood ratio test (OLRT) is commonly used. The main limitation of this test is the difficulty of establishing an exact distribution for test statistic under the null hypothesis in addition to assuming multivariate normality of the sample data, which makes the test not very robust when this condition is violated. This work aims to propose three robust tests named LRTR, PBTR, and PBTC, which are based on robust estimators and parametric bootstrap methods. Besides that, we intended to compare the performance of the three proposed tests with the classic OLRT and robust MCPT tests that already exist in the literature. We also wanted to check if the proposed tests that are based on the Comedian robust estimators performed better than the OLRT and PBTC when considering or not outliers in the data. Finally, the performance of asymptotic tests was compared to those that are computationally intensive tests. The tests were evaluated using the type I error rate and power in Monte Carlo simulations. We concluded that the Comedian robust estimators did not add improvements to the asymptotic tests or the computationally intensive tests. The PBTC and PBTR performed better than the OLRT, LRTR, and MCTP. Therefore, the PBTC and PBTR outperformed the classic OLRT and the robust MCPT. [ABSTRACT FROM AUTHOR]

For two-sided hypothesis testing in location families, the classical optimality criterion is the one leading to uniformly most powerful unbiased (UMPU) tests. Such optimal tests, however, are constructed in exponential models only. We argue that if the base distribution is symmetric, then it is natural to consider uniformly most powerful symmetric (UMPS) tests, that is, tests that are uniformly most powerful in the class of level- α tests whose power function is symmetric. For single-observation models, we provide a condition ensuring existence of UMPS tests and give their explicit form. When this condition is not met, UMPS tests may fail to exist and we provide a weaker condition under which there exist UMP tests in the class of level- α tests whose power function is symmetric and U-shaped. In the multi-observation case, we obtain results in exponential models that also allow for non-location families. [ABSTRACT FROM AUTHOR]

China's high-speed railway (HSR) construction has gradually extended to earthquake-vulnerable areas in recent years. However, there is currently a lack of studies on the characteristics of earthquake-induced rail irregularities, making it impossible to ascertain the threshold of post-earthquake train running speed. Taking the multi-span HSR simply supported girder bridge of a CRTS II-type track system as the research focus, the distribution models for residual rail irregularity under random seismic actions have been analyzed in this study. The statistical distribution of the evolutionary power spectrum density (EPSD) of the residual rail irregularity set is also explored. Based on the obtained results, the EPSD of earthquake-induced rail geometric irregularity was calculated, and a time-domain sample for earthquake-induced rail geometric irregularity was developed. Finally, the equating method of earthquake-induced rail geometric irregularity under different span numbers was discussed, and a method for fitting earthquake-induced rail geometric irregularity was proposed. [ABSTRACT FROM AUTHOR]

Although qualitative research is often equated with inductive analysis, researchers may also use deductive qualitative approaches for certain types of research questions and purposes. Deductive qualitative research allows researchers to use existing theory to examine meanings, processes, and narratives of interpersonal and intrapersonal phenomena. Deductive qualitative analysis (DQA; Gilgun, 2005, 2019) is one form of deductive qualitative research that is suited to theory application, testing, and refinement. Within DQA, researchers combine deductive and inductive analysis to examine supporting, contradicting, refining, and expanding evidence for the theory or conceptual model being examined, resulting in a theory that better fits the present sample and accounts for increased diversity in the phenomenon being studied. This paper acts as a primer on DQA and presents two worked examples of DQA studies. Our discussion focuses on the five primary components of DQA: selecting a research question and guiding theory, operationalizing theory, collecting a purposive sample, coding and analyzing data, and theorizing. We highlight different ways of operationalizing theory as sensitizing constructs or as working hypotheses and discuss common pitfalls in theory operationalization. We divide the coding and analyzing process into two sections for parsimony: early analysis, focused on familiarity with the data, code generation, and identification of negative cases, and middle analysis, focused on developing a thorough understanding of evidence related to the guiding theory and negative cases that depart from the guiding theory. Theorizing occurs throughout as researchers consider ways in which the theory being examined is supported, refuted, refined, or expanded. We also discuss strengths and limitations of DQA and potential difficulties researchers may experience when utilizing this methodology. [ABSTRACT FROM AUTHOR]

AbstractThis work investigates the problem of testing whether d functional random variables are jointly independent, using a modified estimator of the d-variable Hilbert Schmidt Indepedence Criterion (dHSIC). We then get the asymptotic normality of this estimator both under the joint independence hypothesis and under the alternative hypothesis. A simulation study shows the good performance of the proposed test on a finite sample. [ABSTRACT FROM AUTHOR]

This commentary on one of D. Sinha's articles is organised into three parts. In the first part, the narrowness of the scientific worldview and the limitations of the scientific method and its implication for investigating Indian psychological phenomena have been discussed. The second part discusses the distinct characteristics of the human world and the need for human science to study psychological phenomena. The importance of human science as an antidote to the dark side of scientific modernity has also been highlighted. Extending the discussion of the first two sections, the final (third) section discusses the current status of psychological research in India and suggests measures to improve research practices. [ABSTRACT FROM AUTHOR]

The No Free Lunch Theorem tells us that no algorithm can beat other algorithms on all types of problems. The algorithm selection structure is proposed to select the most suitable algorithm from a set of algorithms for an unknown optimization problem. This paper introduces an innovative algorithm selection approach called the CNN-HT, which is a two-stage algorithm selection framework. In the first stage, a Convolutional Neural Network (CNN) is employed to classify problems. In the second stage, the Hypothesis Testing (HT) technique is used to suggest the best-performing algorithm based on the statistical analysis of the performance metric of algorithms that address various problem categories. The two-stage approach can adapt to different algorithm combinations without the need to retrain the entire model, and modifications can be made in the second stage only, which is an improvement of one-stage approaches. To provide a more general structure for the classification model, we adopt Exploratory Landscape Analysis (ELA) features of the problem as input and utilize feature selection techniques to reduce the redundant ones. In problem classification, the average accuracy of classifying problems using CNN is 96%, which demonstrates the advantages of CNN compared to Random Forest and Support Vector Machines. After feature selection, the accuracy increases to 98.8%, further improving the classification performance while reducing the computational cost. This demonstrates the effectiveness of the first stage of the CNN-HT method, which provides a basis for algorithm selection. In the experiments, CNN-HT shows the advantages of the second stage algorithm as well as good performance with better average rankings in different algorithm combinations compared to the individual algorithms and another algorithm combination approach. [ABSTRACT FROM AUTHOR]

We develop a group of robust, nonparametric hypothesis tests that detect differences between the covariance operators of several populations of functional data. These tests, called functional Kruskal–Wallis tests for covariance, or FKWC tests, are based on functional data depth ranks. FKWC tests work well even when the data are heavy‐tailed, which is shown both in simulation and theory. FKWC tests offer several other benefits: they have a simple asymptotic distribution under the null hypothesis, they are computationally cheap, and they possess transformation‐invariance properties. We show that under general alternative hypotheses, these tests are consistent under mild, nonparametric assumptions. As a result, we introduce a new functional depth function called L2‐root depth that works well for the purposes of detecting differences in magnitude between covariance kernels. We present an analysis of the FKWC test based on L2‐root depth under local alternatives. Through simulations, when the true covariance kernels have an infinite number of positive eigenvalues, we show that these tests have higher power than their competitors while maintaining their nominal size. We also provide a method for computing sample size and performing multiple comparisons. [ABSTRACT FROM AUTHOR]

Classical tests for a difference in means control the Type I error rate when the groups are defined a priori. However, when the groups are instead defined via clustering, then applying a classical test yields an extremely inflated Type I error rate. Notably, this problem persists even if two separate and independent datasets are used to define the groups and to test for a difference in their means. To address this problem, in this article, we propose a selective inference approach to test for a difference in means between two clusters. Our procedure controls the selective Type I error rate by accounting for the fact that the choice of null hypothesis was made based on the data. We describe how to efficiently compute exact p-values for clusters obtained using agglomerative hierarchical clustering with many commonly used linkages. We apply our method to simulated data and to single-cell RNA-sequencing data. for this article are available online. [ABSTRACT FROM AUTHOR]

Numerous testing procedures for directional data have been proposed over the years and a natural question that springs is which to use and when. The aim of this paper is to answer this question, via a large scale Monte Carlo simulation study that covers circular and spherical data for the two mean directions problem. The results evidently signify that tests assuming equal concentration parameters should be avoided as they tend to inflate the test size, while the heterogeneous test that does not make this assumption is to be preferred, but unfortunately only with large sample sizes. Permutation calibration does not improve the performance of any testing procedure, whereas bootstrap does. Specifically, bootstrap calibrated tests exhibited superior performance; they attain the type I error in the vast majority of the case scenarios examined and possess nearly indistinguishable empirical power levels. Finally, examples with real data illustrate the performance of the bootstrap calibrated tests. [ABSTRACT FROM AUTHOR]

In word learning, learners need to identify the referent of words by leveraging the fact that the same word may co‐occur with different sets of objects. This raises the question, what do children remember from "in the moment" that they can use for cross‐situational learning? Furthermore, do children represent pictures of familiar animals versus drawings of non‐existent novel objects as potential referents differently? This study examined these questions by creating learning scenarios with only two potential referents, requiring the least amount of memory to represent all co‐present objects. Across three experiments (n > 250) with 4‐ and 6‐year‐old children, children reliably selected the intended referent from learning at test, though the learning of novel objects was better than familiar objects. When asked for a co‐present object, children of all ages in the study performed at chance in all of the conditions. We discuss the developmental differences in cross‐situational word learning capabilities with regard to representing different stimuli as potential referents. Importantly, all children used a propose‐but‐verify procedure for learning novel words even in the simplest of the learning scenarios given repeated exposure. [ABSTRACT FROM AUTHOR]

Quantile regression has become a widely used tool for analysing competing risk data. However, quantile regression for competing risk data with a continuous mark is still scarce. The mark variable is an extension of cause of failure in a classical competing risk model where cause of failure is replaced by a continuous mark only observed at uncensored failure times. An example of the continuous mark variable is the genetic distance that measures dissimilarity between the infecting virus and the virus contained in the vaccine construct. In this article, we propose a novel mark-specific quantile regression model. The proposed estimation method borrows strength from data in a neighbourhood of a mark and is based on an induced smoothed estimation equation, which is very different from the existing methods for competing risk data with discrete causes. The asymptotic properties of the resulting estimators are established across mark and quantile continuums. In addition, a mark-specific quantile-type vaccine efficacy is proposed and its statistical inference procedures are developed. Simulation studies are conducted to evaluate the finite sample performances of the proposed estimation and hypothesis testing procedures. An application to the first HIV vaccine efficacy trial is provided. [ABSTRACT FROM AUTHOR]

Practical problems with missing data are common, and many methods have been developed concerning the validity and/or efficiency of statistical procedures. On a central focus, there have been longstanding interests on the mechanism governing data missingness, and correctly deciding the appropriate mechanism is crucially relevant for conducting proper practical investigations. In this paper, we present a new hypothesis testing approach for deciding between the conventional notions of missing at random and missing not at random in generalized linear models in the presence of instrumental variables. The foundational idea is to develop appropriate discrepancy measures between estimators whose properties significantly differ only when missing at random does not hold. We show that our testing approach achieves an objective data‐oriented choice between missing at random or not. We demonstrate the feasibility, validity, and efficacy of the new test by theoretical analysis, simulation studies, and a real data analysis. [ABSTRACT FROM AUTHOR]

The median-preserving spread (MPS) ordering for ordinal variables has become ubiquitous in the inequality literature. We devise statistical tests of the hypothesis that a distribution G is not an MPS of a distribution F. Rejecting this hypothesis enables the conclusion that Gis more unequal than F according to the MPS criterion. Monte Carlo simulations and novel graphical techniques show that a simple, asymptotic Z test is sufficient for most applications. We illustrate our tests with two applications: happiness inequality in the US and self-assessed health in Europe. [ABSTRACT FROM AUTHOR]

Generative models have gained significant attention in recent years. They are increasingly used to estimate the underlying structure of high-dimensional data and artificially generate various kinds of data similar to those from the real world. The performance of generative models depends critically on a good set of hyperparameters. Yet, finding the right hyperparameter configuration can be an extremely time-consuming task. In this paper, we focus on speeding up the hyperparameter search through adaptive resource allocation, early stopping underperforming candidates quickly and allocating more computational resources to promising ones by comparing their intermediate performance. The hyperparameter search is formulated as a non-stochastic best-arm identification problem where resources like iterations or training time constrained by some predetermined budget are allocated to different hyperparameter configurations. A procedure which uses hypothesis testing coupled with Successive Halving is proposed to make the resource allocation and early stopping decisions and compares the intermediate performance of generative models by their exponentially weighted Maximum Means Discrepancy (MMD). The experimental results show that the proposed method selects hyperparameter configurations that lead to a significant improvement in the model performance compared to Successive Halving for a wide range of budgets across several real-world applications. [ABSTRACT FROM AUTHOR]

The Non-Informative Nuisance Parameter Principle concerns the problem of how inferences about a parameter of interest should be made in the presence of nuisance parameters. The principle is examined in the context of the hypothesis testing problem. We prove that the mixed test obeys the principle for discrete sample spaces. We also show how adherence of the mixed test to the principle can make performance of the test much easier. These findings are illustrated with new solutions to well-known problems of testing hypotheses for count data. [ABSTRACT FROM AUTHOR]

A quantum channel is sufficient with respect to a set of input states if it can be reversed on this set. In the approximate version, the input states can be recovered within an error bounded by the decrease of the relative entropy under the channel. Using a new integral representation of the relative entropy in Frenkel (Integral formula for quantum relative entropy implies data processing inequality, Quantum 7, 1102 (2023)), we present an easy proof of a characterization of sufficient quantum channels and recoverability by preservation of optimal success probabilities in hypothesis testing problems, equivalently, by preservation of L 1 -distance. [ABSTRACT FROM AUTHOR]

Huisman (Psychonomic Bulletin & Review, 1–10. 2022) argued that a valid measure of evidence should indicate more support in favor of a true alternative hypothesis when sample size is large than when it is small. Bayes factors may violate this pattern and hence Huisman concluded that Bayes factors are invalid as a measure of evidence. In this brief comment we call attention to the following: (1) Huisman's purported anomaly is in fact dictated by probability theory; (2) Huisman's anomaly has been discussed and explained in the statistical literature since 1939; the anomaly was also highlighted in the Psychonomic Bulletin & Review article by Rouder et al. (2009), who interpreted the anomaly as "ideal": an interpretation diametrically opposed to that of Huisman. We conclude that when intuition clashes with probability theory, chances are that it is intuition that needs schooling. [ABSTRACT FROM AUTHOR]

The oriental fruit fly, Bactrocera dorsalis (Hendel) (Diptera: Tephritidae), pupates in the soil, and the average pupation depth increases with the number of concurrently pupating individuals at the same location. This study aimed to explain the density‐dependent pupation depth in B. dorsalis. Previous studies demonstrated that increasing pupation depth has the benefit of reduced parasitism and predation risk and the cost of reduced emergence success (i.e., eclosed adults in the soil fail to reach above ground). It was hypothesized that density‐dependent pupation depth is governed by density‐dependent cost. That is, emergence success of eclosed adults increases with density because the soil is more easily loosened as the number of individuals increases. Pupating larvae can reduce parasitism and predation risk by increasing pupation depth, but only those in high density can afford to pupate at deep depths due to the associated cost. To test the hypothesis, density‐dependent emergence success in B. dorsalis was examined in the laboratory. Newly pupated individuals were buried in peat moss approximately 5 cm below the surface, and the relationship between the number of buried pupae (four levels: 1, 25, 50, and 100 pupae) and their emergence success was recorded. To manipulate the difficulty of emergence, the level of peat moss compaction was also varied. Emergence success was uniformly high when peat moss was not heavily compacted regardless of the number of pupae, but the number of pupae had a positive effect on emergence success when the peat moss was heavily compacted. In addition, the timing of emergence was more synchronized in the highest density than in the lower densities. The results of this study, in combination with the previous findings, support the hypothesis. [ABSTRACT FROM AUTHOR]

This paper treats the problem of constructing confidence interval with massive data. Two methods using the divide and conquer strategy are proposed. The corresponding hypothesis testing problem is also developed. Theoretical and numerical results are presented to illustrate their effectiveness. [ABSTRACT FROM AUTHOR]

The article considers a problem related to testing the hypothesis about the independence of random variables given large amounts of statistical data. The solution to this problem is necessary when estimating probability densities of random variables and synthesizing algorithms for processing information. A nonparametric procedure is proposed for testing the hypothesis about the independence of random variables in a sample containing a large amount of statistical data. The procedure involves the compression of initial statistical data by decomposing the range of values of random variables. The generated data array consists of the centers of sampling intervals and the corresponding frequencies of observations belonging to the original sample. The obtained data was used in the construction of a nonparametric pattern recognition algorithm, which corresponds to the maximum likelihood criterion. The distribution laws in the classes were evaluated assuming the independence and dependence of the compared random variables. When recovering the distribution laws of random variables in the classes, the regression estimates of probability densities were used. For these conditions, the probability of errors in recognizing patterns in the classes was estimated, and decisions about the independence or dependence of random variables were made according to their minimum value. The procedure was used in the analysis of remote sensing data on forest areas; linear and nonlinear relationships between the spectral features of the subject matter of the study were determined. [ABSTRACT FROM AUTHOR]

This paper examines the application of super-superiority margins in study power calculations. Unlike traditional power calculations, which primarily aim to reject the null hypothesis by any margin, a super-superiority margin establishes a clinically significant threshold. Despite potential benefits, this approach, akin to a non-inferiority calculation but in an opposing direction, is rarely used. Implementing a super-superiority margin separates the notion of the likely difference between two groups (the effect size) from the minimum clinically significant difference, without which inconsistent positions could be held. However, these are often used interchangeably. In an audit of 30 recent randomized controlled trial power calculations, four studies utilized the minimal acceptable difference, and nine utilized the expected difference. In the other studies, this was unclarified. In the post hoc scenario, this approach can shed light on the value of undertaking further studies, which is not apparent from the standard power calculation. The acceptance and rejection of the alternate hypothesis for super-superiority, non-inferiority, equivalence, and standard superiority studies have been compared. When a fixed minimal acceptable difference is applied, a study result will be in one of seven logical positions with regards to the simultaneous application of these hypotheses. The trend for increased trial size and the mirror approach of non-inferiority studies implies that newer interventions may be becoming less effective. Powering for superiority could counter this and ensure that a pre-trial evaluation of clinical significance has taken place, which is necessary to con- firm that interventions are beneficial. [ABSTRACT FROM AUTHOR]

This study investigated first‐year undergraduate statistics students' statistical problem‐solving skills on the probability of the union of two events, conditional probability, binomial probability distribution, probabilities for x‐limits using the z‐distribution, x‐limit associated with a given probability for a normal distribution, estimating the y‐value using a regression equation, and hypothesis testing for a single population mean when a population standard deviation is unknown. The study was a descriptive case study and employed a mixed‐method research approach. Data were collected through content analysis of a statistics course examination script of 120 first‐year undergraduate students of statistics in an open distance‐learning university in South Africa. Polya's Model of Problem Solving was used as the framework of analysis. The study revealed that the students, in general, had poor statistical problem‐solving skills. [ABSTRACT FROM AUTHOR]

Conducting research with human subjects can be difficult because of limited sample sizes and small empirical effects. We demonstrate that this problem can yield patterns of results that are practically indistinguishable from flipping a coin to determine the direction of treatment effects. We use this idea of random conclusions to establish a baseline for interpreting effect-size estimates, in turn producing more stringent thresholds for hypothesis testing and for statistical-power calculations. An examination of recent meta-analyses in psychology, neuroscience, and medicine confirms that, even if all considered effects are real, results involving small effects are indeed indistinguishable from random conclusions. [ABSTRACT FROM AUTHOR]

The comparison of Receiver Operating Characteristic (ROC) curves is frequently used in the literature to compare the discriminatory capability of different classification procedures based on diagnostic variables. The performance of these variables can be sometimes influenced by the presence of other covariates, and thus they should be taken into account when making the comparison. A new non-parametric test is proposed here for testing the equality of two or more dependent ROC curves conditioned to the value of a multidimensional covariate. Projections are used for transforming the problem into a one-dimensional approach easier to handle. Simulations are carried out to study the practical performance of the new methodology. The procedure is then used to analyse a real data set of patients with Pleural Effusion to compare the diagnostic capability of different markers. [ABSTRACT FROM AUTHOR]

What drives children to explore and learn when external rewards are uncertain or absent? Across three studies, we tested whether information gain itself acts as an internal reward and suffices to motivate children's actions. We measured 24–56‐month‐olds' persistence in a game where they had to search for an object (animal or toy), which they never find, hidden behind a series of doors, manipulating the degree of uncertainty about which specific object was hidden. We found that children were more persistent in their search when there was higher uncertainty, and therefore, more information to be gained with each action, highlighting the importance of research on artificial intelligence to invest in curiosity‐driven algorithms. Research Highlights: Across three studies, we tested whether information gain itself acts as an internal reward and suffices to motivate preschoolers' actions.We measured preschoolers' persistence when searching for an object behind a series of doors, manipulating the uncertainty about which specific object was hidden.We found that preschoolers were more persistent when there was higher uncertainty, and therefore, more information to be gained with each action.Our results highlight the importance of research on artificial intelligence to invest in curiosity‐driven algorithms. [ABSTRACT FROM AUTHOR]

As edge devices become increasingly powerful, data analytics are gradually moving from a centralized to a decentralized regime where edge computing resources are exploited to process more of the data locally. This regime of analytics is coined as Federated Data Analytics (FDA). Despite the recent success stories of FDA, most literature focuses exclusively on deep neural networks. In this work, we take a step back to develop an FDA treatment for one of the most fundamental statistical models: linear regression. Our treatment is built upon hierarchical modeling that allows borrowing strength across multiple groups. To this end, we propose two federated hierarchical model structures that provide a shared representation across devices to facilitate information sharing. Notably, our proposed frameworks are capable of providing uncertainty quantification, variable selection, hypothesis testing, and fast adaptation to new unseen data. We validate our methods on a range of real-life applications, including condition monitoring for aircraft engines. The results show that our FDA treatment for linear models can serve as a competing benchmark model for the future development of federated algorithms. [ABSTRACT FROM AUTHOR]

The fast generation of values of the beta random variable is a subject of great interest and multiple applications, ranging from purely mathematical and statistical ones to applications in management and production, among others. There are several methods for generating these values, with one of the essential points for their design being the selection of random seeds. Two interesting aspects converge here: the use of sequences as inputs (and the need for them to verify properties such as randomness and uniformity, which are verified through statistical test suites) and the design of the algorithm for the generation of the variable. In this paper, we analyse, in detail, the algorithms that have been developed in the literature, both from a mathematical/statistical and computational point of view. We also provide empirical development using R software, which is currently in high demand and is one of the main novelties with respect to previous comparisons carried out in FORTRAN. We establish which algorithms are more efficient and in which contexts, depending on the different values of the parameters, allowing the user to determine the best method given the experimental conditions. [ABSTRACT FROM AUTHOR]

Approximate Bayesian computation (ABC) is a likelihood-free inference method commonly employed for statistical inference in models with unknown or complex likelihood functions. ABC estimates the posterior distributions of model parameters by comparing summary statistics of the simulated and observed data. However, the selection of informative summary statistics can be challenging in practice. In this study, we propose a summary-statistic-free method called ABC with semiparametric empirical likelihood ratio (ABC-SELR). This method utilises the empirical likelihood within the framework of the semiparametric density ratio model to assess the simulated parameters via testing whether the simulated and observed data conform to the same distribution. By eliminating the need for choosing summary statistics, our approach avoids potential information loss. Furthermore, the proposed method captures the shared characteristics between the simulated and observed data, leading to improved efficiency. We demonstrate the accuracy and efficiency of ABC-SELR by comparing with existing ABC methods through numerical simulations. [ABSTRACT FROM AUTHOR]

Algorithmic stability is a concept from learning theory that expresses the degree to which changes to the input data (e.g. removal of a single data point) may affect the outputs of a regression algorithm. Knowing an algorithm's stability properties is often useful for many downstream applications—for example, stability is known to lead to desirable generalization properties and predictive inference guarantees. However, many modern algorithms currently used in practice are too complex for a theoretical analysis of their stability properties, and thus we can only attempt to establish these properties through an empirical exploration of the algorithm's behaviour on various datasets. In this work, we lay out a formal statistical framework for this kind of black-box testing without any assumptions on the algorithm or the data distribution, and establish fundamental bounds on the ability of any black-box test to identify algorithmic stability. [ABSTRACT FROM AUTHOR]

In the present study, we undertake the task of hypothesis testing in the context of Poissondistributed data. The primary objective of our investigation is to ascertain whether two distinct sets of discrete data share the same Poisson rate. We delve into a comprehensive review and comparative analysis of various frequentist and Bayesian methodologies specifically designed to address this problem. Among these are the conditional test, the likelihood ratio test, and the Bayes factor. Additionally, we employ the posterior predictive p-value in our analysis, coupled with its corresponding calibration procedures. As the culmination of our investigation, we apply these diverse methodologies to test both simulated datasets and real-world data. The latter consists of the offspring distributions linked to COVID-19 cases in two disparate geographies - Hong Kong and Rwanda. This allows us to provide a practical demonstration of the methodologies' applications and their potential implications in the field of epidemiology. [ABSTRACT FROM AUTHOR]

There are several areas of knowledge in which (pseudo-)random numbers are necessary, for example, in statistical–mathematical simulation or in cryptography and system security, among others. Depending on the area of application, it will be necessary that the sequences used meet certain requirements. In general, randomness and uniformity conditions are required in the generated sequences, which are checked with statistical tests, and conditions on sequence unpredictability if the application is in security. In the present work, a literature review on cryptographically secure pseudo-random number generators (CSPRNGs) is carried out, they are implemented, and a critical analysis of their statistical quality and computational efficiency is performed. For this purpose, different programming languages will be used, and the sequences obtained will be checked by means of the NIST Statistical Test Suite (NIST STS). In addition, a user's guide will be provided to allow the selection of one generator over another according to its statistical properties and computational implementation characteristics. [ABSTRACT FROM AUTHOR]

In this study, hypothesis test is investigated based on Bootstrap sample selection methods to compare more than two population means under Ranked Set Sampling. Bootstrap sample selection methods are obtained by adapting Hui’s sample selection methods for confidence interval. We also compare these adapted methods with bootstrap simple random sampling and bootstrap ranked set sampling methods using simulation study. Simulation study shows that adapted methods which proposed in this paper perform quite well. [ABSTRACT FROM AUTHOR]

For gene expression data analysis, an important task is to identify genes that are differentially expressed between two or more groups. Nevertheless, as biological experiments are often measured with a relatively small number of samples, how to accurately estimate the variances of gene expression becomes a challenging issue. To tackle this problem, we introduce a regularized t$$ t $$ distribution and derive its statistical properties including the probability density function and the moment generating function. The noncentral regularized t$$ t $$ distribution is also introduced for computing the statistical power of hypothesis testing. For practical applications, we apply the regularized t$$ t $$ distribution to establish the null distribution of the regularized t$$ t $$ statistic, and then formulate it as a regularized t$$ t $$‐test for detecting the differentially expressed genes. Simulation studies and real data analysis show that our regularized t$$ t $$‐test performs much better than the Bayesian t$$ t $$‐test in the "limma" package, in particular when the sample sizes are small. [ABSTRACT FROM AUTHOR]

In recent years, empirical Bayesian (EB) inference has become an attractive approach for estimation in parametric models arising in a variety of real‐life problems, especially in complex and high‐dimensional scientific applications. However, compared to the relative abundance of available general methods for computing point estimators in the EB framework, the construction of confidence sets and hypothesis tests with good theoretical properties remains difficult and problem specific. Motivated by the Universal Inference framework, we propose a general and universal method, based on holdout likelihood ratios, and utilizing the hierarchical structure of the specified Bayesian model for constructing confidence sets and hypothesis tests that are finite sample valid. We illustrate our method through a range of numerical studies and real data applications, which demonstrate that the approach is able to generate useful and meaningful inferential statements in the relevant contexts. [ABSTRACT FROM AUTHOR]

Biometrical sciences and disease diagnosis in particular, are often concerned with the analysis of associations for cross‐classified data, for which distance association models give us a graphical interpretation for non‐sparse matrices with a low number of categories. In this framework, usually binary exploratory and response variables are present, with analysis based on individual profiles being of great interest. For saturated models, we show the usual linear relationship for log‐linear models is preserved in full dimension for the distance association parameterization. This enables a two‐step procedure to facilitate the analysis and the interpretation of associations in terms of unfolding after the overall and main effects are removed. The proposed procedure can deal with cross‐classified data for profiles by binary variables, and it is easy to implement using traditional statistical software. For disease diagnosis, the problems of a degenerate solution in the unfolding representation, and that of determining significant differences between the profile locations are addressed. A hypothesis test of independence based on odds ratio is considered. Furthermore, a procedure is proposed to determine the causes of the significance of the test, avoiding the problem of error propagation. The equivalence between a test for equality of odds ratio pairs and the test for equality of location for two profiles in the unfolding representation in the disease diagnosis is shown. The results have been applied to a real example on the diagnosis of coronary disease, relating the odds ratios with performance parameters of the diagnostic test. [ABSTRACT FROM AUTHOR]

In this article, a nonparametric lack-of-fit test of nonlinear regression in presence of heteroscedastic variances is proposed. We consider regression models with a discrete or continuous response variable without distributional assumptions so that the test is widely applicable. The test statistic is developed using a k-nearest neighbor augmentation defined through the ranks of the predictor variable. The asymptotic distribution of the test statistic is derived under the null and local alternatives for the case of using fixed number of nearest neighbors. The parametric standardizing rate is achieved for the asymptotic distribution of the proposed test statistic. This allows the proposed test to have faster convergence rate than most of nonparametric methods. Numerical studies show that the proposed test has good power to detect both low and high frequency alternatives even for moderate sample size. The proposed test is applied to an engineering data example. [ABSTRACT FROM AUTHOR]

Abstract Bayes factor, as a measure of the evidence provided by the data in favor of one hypothesis against its alternative, can be highly sensitive to the prior distributions of parameters involved in the hypotheses as well as to the sample size. This may cause a noticeable difference between the Bayesian and classical (frequentist) hypothesis testing results. In the worst-case scenario, the two results are in conflict, which is termed the Jeffreys-Lindley paradox. In this article, we propose a sample size-dependent prior strategy to bridge the Bayesian-frequentist gap from a decision-theoretical perspective. The central idea behind the proposed strategy is to adaptively adjust prior distributions for the parameters in line with the sample size to manage the risk of type I error in Bayesian hypothesis testing at the same level as that prespecified in frequentist hypothesis testing. The proposed strategy is inspired by the work of Maurice Stevenson Bartlett (M.S. Bartlett, A comment on D. V. Lindley’s statistical paradox, Biometrika, 44, 533–534, 1957), who suggested a sample size-dependent prior to make the Bayes factor independent of the sample size. In contrast to his work, we propose a strategy that leverages the use of sample size-dependent priors in Bayesian hypothesis testing and risk management when deciding the two hypotheses. To demonstrate the effectiveness of the proposed strategy, normal mean tests in the cases that (i) the variance is known (z-test) and (ii) the variance is unknown (t-test) are examined. It turns out that the Bayesian testing results coming out from the proposed strategy become consistent with their frequentist counterparts and the Jeffreys-Lindley paradox disappears. [ABSTRACT FROM AUTHOR]

Gini's rank association index is a non parametric measure of association, and is fully described by Genest, Nešlehová and Ben Ghorbal (2010). In this article, we compute the null distribution of this index up to n = 28 where n is the sample size. Our methods are based on permanents and extend the results of Betro (1993). We also discuss approximations to the null distribution for large n. We believe that Gini's rank association index should be more widely used; in particular, it may be preferable to Spearman's rank correlation coefficient if the bivariate distribution is such that outliers are quite likely to occur. [ABSTRACT FROM AUTHOR]

Pediatric patients should have access to medicines that have been appropriately evaluated for safety and efficacy through revised labelling. Given this goal, the adequacy of the pediatric clinical development plan and resulting safety database are critical factors to inform a favorable benefit-risk assessment for the intended use of the medicinal product. While extrapolation from adults can be used to support efficacy of drugs in children, there may be a reluctance to use the same approach in safety assessments, wiping out potential gains in trial efficiency through a reduction of sample size. To address this issue, we explore safety review in pediatric trials, including specific types of safety assessments and precision on the estimation of event rates for specific adverse events (AEs) that can be achieved. In addition, we discuss the assessments which can provide a benchmark for the use of extrapolation of safety that focuses on on-target effects. Finally, we explore a unified approach for understanding precision using Bayesian approaches as the most appropriate methodology to describe or ascertain risk in probabilistic terms for the estimate of the event rate of specific AEs. [ABSTRACT FROM AUTHOR]

With the development of modern data collection techniques, researchers often encounter high-dimensional data across various research fields. An important problem is to determine whether several groups of these high-dimensional data originate from the same population. To address this, this paper presents a novel k-sample test for equal distributions for high-dimensional data, utilizing the Maximum Mean Discrepancy (MMD). The test statistic is constructed using a V-statistic-based estimator of the squared MMD derived for several samples. The asymptotic null and alternative distributions of the test statistic are derived. To approximate the null distribution accurately, three simple methods are described. To evaluate the performance of the proposed test, two simulation studies and a real data example are presented, demonstrating the effectiveness and reliability of the test in practical applications. [ABSTRACT FROM AUTHOR]

The normal distribution has been extensively been used in the statistical inference and decision making problems. One of the main assumptions of the existing tests in classical statistics is that the data should be from normally distributed population.Shapiro- Wilk test is widely used to test the normality of data when the observations are precise or exact in nature. But in many areas including agriculture, engineering and reliability, the data may be in interval form, indeterminate form or uncertain. In such cases, the existed Classical Shapiro- Wilk test fails to test the normality of data. In this paper, we proposed the Shapiro- Wilk test under neutrosophic environment to check whether the uncertain data is from neutrosophic normal distribution or not. The hypothesis testing process is executed on the observations based on lifetime of batteries. The comparative analysis has been done with the existed Shapiro- Wilk test.The comparison shows that the proposed test is efficacious, appropriate and well-suited to be applied in scenarios involving indeterminacy. [ABSTRACT FROM AUTHOR]

Cyber-physical system is an open networked intelligent information system, which is vulnerable to security attack. Injection attack is a kind of communication attack, and injection of false data makes the sensor get wrong measurement value, which leads to system performance deterioration. To solve this problem, this study combines the extended Kalman state estimator and uses the detection scheme of extended Kalman filter state estimation based on the least trace principle to detect the new information sequence in the same scene and judge the system state through hypothesis testing. The simulation experiments on MATLAB show that under the given attack detection rules, the detection scheme can effectively detect the injection attack and reduce the performance loss caused by the wrong measurement value of the sensor. [ABSTRACT FROM AUTHOR]