Test Statistic Research Articles

The Expected Behaviors of Posterior Predictive Tests and Their Unexpected Interpretation.

Poor fit between models of sequence or trait evolution and empirical data is known to cause biases and lead to spurious conclusions about evolutionary patterns and processes. Bayesian posterior prediction is a flexible and intuitive approach for detecting such cases of poor fit. However, the expected behavior of posterior predictive tests has never been characterized for evolutionary models, which is critical for their proper interpretation. Here, we show that the expected distribution of posterior predictive P-values is generally not uniform, in contrast to frequentist P-values used for hypothesis testing, and extreme posterior predictive P-values often provide more evidence of poor fit than typically appreciated. Posterior prediction assesses model adequacy under highly favorable circumstances, because the model is fitted to the data, which leads to expected distributions that are often concentrated around intermediate values. Nonuniform expected distributions of P-values do not pose a problem for the application of these tests, however, and posterior predictive P-values can be interpreted as the posterior probability that the fitted model would predict a dataset with a test statistic value as extreme as the value calculated from the observed data.

An open-source implementation of tree-based scan statistics.

We develop an open-source R package to implement tree-based scan statistics (TBSS) analyses. TBSS are data mining methods used by the United States Food and Drug Administration and the Centers for Disease Control. They simultaneously screen thousands of hierarchically aggregated outcomes to identify unsuspected adverse effects of drugs or vaccines, accounting for multiple comparisons. The general structure of TBSS is highly adaptable, with four essential components: (1) a hierarchical outcome structure, (2) a test statistic to be computed for each element of the hierarchy, (3) an algorithm to generate data replicates under a null distribution, and (4) observed outcomes at the lower level of the hierarchy. We encode the general TBSS framework in a convenient R package that offers user-friendly functions for the most used TBSS methods. To illustrate the performance of our software, we evaluated two examples of archetypical TBSS analyses previously analyzed using proprietary, closed-source TreeScan™ software. The first considers the risk of congenital malformations associated with first-trimester exposure to valproate, and the second compares exposure to newly prescribed canagliflozin with a dipeptidyl peptidase 4 inhibitor in adults affected by type 2 diabetes. The results of the original studies are replicated. The diffusion of an open-source implementation of TBSS can enhance innovation of TBSS methods and foster collaborations. We offer an intuitive R package implementing standard TBSS methods with accompanying tutorials. Our unified object-oriented implementation allows expert users to extend the framework, introduce new features, or enhance existing ones.

Testing Many Zero Restrictions in a High Dimensional Linear Regression Setting

We propose a test of many zero parameter restrictions in a high dimensional linear iid regression model with k ≫ n regressors. The test statistic is formed by estimating key parameters one at a time based on many low dimension regression models with nuisance terms. The parsimoniously parametrized models identify whether the original parameter of interest is or is not zero. Estimating fixed low dimension sub-parameters ensures greater estimator accuracy, it does not require a sparsity assumption nor therefore a regularized estimator, it is computationally fast compared to, e.g., de-biased Lasso, and using only the largest in a sequence of weighted estimators reduces test statistic complexity and therefore estimation error. We provide a parametric wild bootstrap for p-value computation, and prove the test is consistent and has non-trivial n / { ln ( n ) M n } -local-to-null power where M n is the l ∞ covariate fourth moment.

Karate Hakemlerinin Öz Yeterlikleri ile Bilişsel Esneklikleri Arasındaki İlişkinin İncelenmesi

The present study aims to examine the relationship between the self-efficacy and cognitive flexibility of karate referees. A total of 138 referees, 88 male and 50 female, working in the Turkish Karate Federation participated in the study. The mean age of the referees was 38.09±13.43 years, mean body weight was 74.33±13.46 kg, mean height was 170.23±8.09 cm, and mean active refereeing period was 9.95±8.84 years. The Referee Self-Efficacy Scale developed by Myers et al. (2012) and adapted into Turkish by Karaçam and Pulur (2017) as well as the Cognitive Flexibility Scale developed by Bilgin (2009) were applied to the referees. Independent Samples T-test, One-Way ANOVA test, Pearson correlation test and descriptive statistics were applied to the data obtained. According to the results of the Pearson correlation analysis, a significant positive correlation was found between the referees' self-efficacy and cognitive flexibility levels (p<0.05). The results of the independent samples t-test showed that there was a significant difference in the level of self-efficacy between the males and females (p<0.05). Moreover, self-efficacy level was found to be significant in relation to refereeing class (p<0.05). In conclusion, it was determined in the study that the self-efficacy levels of the karate referees increased in parallel with their cognitive flexibility levels, the male participants had higher self-efficacy levels compared to the female participants, and self-efficacy levels increased in parallel with refereeing class.

Tenis Antrenmanlarının Bilişsel Kontrol ve Görsel Uzamsal Beceriler Üzerindeki Etkisi

The aim of this study was to examine the effect of accurate shot exercises in tennis on cognitive control and visuospatial skills. 15 sports science faculty student, 6 females and 9 males, aged between 18-22, with an average age of 18.53 were included in the research. Flanker Task and Spatial Visualization Test were applied to evaluate participants’ cognitive control and visuospatial skills. Tennis training was performed once a week, for half an hour, with 500 hits (forehand and backhand) and an average of 2000 hits in four weeks. After performing the normality test and descriptive statistics, Wilcoxon Signed Rank Test was applied to compare the pre-test and post-test. The findings showed that there were significant differences between pre-test and post-test scores in the spatial visualization test (p = 0.019), correct response rate in the flanker task (p = 0.02=), and difference in reaction time between congruent and incongruent conditions in the flanker task (p = 0.02). Consequently, it can be concluded that tennis training significantly improved participants’ cognitive control and visuospatial skills. The fact that tennis is a sport that requires the use of space and uses open skills may improve individuals’ cognitive control and visuospatial skills.

Two-Stage Limited-Information Estimation for Structural Equation Models of Round-Robin Variables

We propose and demonstrate a new two-stage maximum likelihood estimator for parameters of a social relations structural equation model (SR-SEM) using estimated summary statistics (Σ^) as data, as well as uncertainty about Σ^ to obtain robust inferential statistics. The SR-SEM is a generalization of a traditional SEM for round-robin data, which have a dyadic network structure (i.e., each group member responds to or interacts with each other member). Our two-stage estimator is developed using similar logic as previous two-stage estimators for SEM, developed for application to multilevel data and multiple imputations of missing data. We demonstrate out estimator on a publicly available data set from a 2018 publication about social mimicry. We employ Markov chain Monte Carlo estimation of Σ^ in Stage 1, implemented using the R package rstan. In Stage 2, the posterior mean estimates of Σ^ are used as input data to estimate SEM parameters with the R package lavaan. The posterior covariance matrix of estimated Σ^ is also calculated so that lavaan can use it to calculate robust standard errors and test statistics. Results are compared to full-information maximum likelihood (FIML) estimation of SR-SEM parameters using the R package srm. We discuss how differences between estimators highlight the need for future research to establish best practices under realistic conditions (e.g., how to specify empirical Bayes priors in Stage 1), as well as extensions that would make 2-stage estimation particularly advantageous over single-stage FIML.

Testing covariance structures belonging to a quadratic subspace under a doubly multivariate model

AbstractA hypothesis related to the block structure of a covariance matrix under the doubly multivariate normal model is studied. It is assumed that the block structure of the covariance matrix belongs to a quadratic subspace, and under the null hypothesis, each block of the covariance matrix also has a structure belonging to some quadratic subspace. The Rao score and the likelihood ratio test statistics are derived, and the exact distribution of the likelihood ratio test is determined. Simulation studies show the advantage of the Rao score test over the likelihood ratio test in terms of speed of convergence to the limiting chi-square distribution, while both proposed tests are competitive in terms of their power. The results are applied to both simulated and real-life example data.

A robust likelihood approach to inference for paired multiple binary endpoints data

ABSTRACT We introduce a robust likelihood approach to inference for paired multiple binary endpoints data. One can easily implement the methodology without dealing with the model that incorporates a large number of joint probabilities of no direct relevance to the inference of interest. We present the robust score test statistic for testing the equality of two treatment effects to exemplify the utility and simplicity of the method. Our novel technique is applicable when patients have different numbers of endpoints and for unpaired endpoints. The extension of our robust approach to multiple endpoints data with more categories is straightforward. We use simulations and real data analysis to highlight the efficacy of our robust procedure.

RMST-based multiple contrast tests in general factorial designs.

Several methods in survival analysis are based on the proportional hazards assumption. However, this assumption is very restrictive and often not justifiable in practice. Therefore, effect estimands that do not rely on the proportional hazards assumption are highly desirable in practical applications. One popular example for this is the restricted mean survival time (RMST). It is defined as the area under the survival curve up to a prespecified time point and, thus, summarizes the survival curve into a meaningful estimand. For two-sample comparisons based on the RMST, previous research found the inflation of the type I error of the asymptotic test for small samples and, therefore, a two-sample permutation test has already been developed. The first goal of the present paper is to further extend the permutation test for general factorial designs and general contrast hypotheses by considering a Wald-type test statistic and its asymptotic behavior. Additionally, a groupwise bootstrap approach is considered. Moreover, when a global test detects a significant difference by comparing the RMSTs of more than two groups, it is of interest which specific RMST differences cause the result. However, global tests do not provide this information. Therefore, multiple tests for the RMST are developed in a second step to infer several null hypotheses simultaneously. Hereby, the asymptotically exact dependence structure between the local test statistics is incorporated to gain more power. Finally, the small sample performance of the proposed global and multiple testing procedures is analyzed in simulations and illustrated in a real data example.

Statistical Insights: Analyzing Shock Models, Reliability Operations and Testing Exponentiality for NBRUmgf Class of Life Distributions

This study deals with a novel category of life distributions called the new better than renewal used in moment generating function (NBRUmgf) class. It delves into the connections between this form of aging and established aging categories, along with its relevance in a shock model. Additionally, it explores how this aging concept remains consistent through certain reliability operations which is consider a very important tool in reliability engineering. The research computes Pitman's asymptotic efficiencies for this testing procedure, comparing them with alternative methods. Furthermore, the study furnishes a comprehensive table of percentiles for the test statistic associated with this proposed method. Furthermore, in order to showcase the relevance of the study's conclusions, we utilize distinct real-world datasets, which illustrate the effectiveness of our test across various types of real data.

Inference on order restricted means of inverse Gaussian populations under heteroscedasticity

The hypothesis testing problem of homogeneity of k(≥2) inverse Gaussian means against ordered alternatives is studied when nuisance or scale-like parameters are unknown and unequal. The maximum likelihood estimators (MLEs) of means and scale-like parameters are obtained when means satisfy some simple order restrictions and scale-like parameters are unknown and unequal. An iterative algorithm is proposed for finding these estimators. It has been proved that under a specific condition, the proposed algorithm converges to the true MLEs uniquely. A likelihood ratio test and two simultaneous tests are proposed. Further, an algorithm for finding the MLEs of parameters is given when means are equal but unknown. Using the estimators, the likelihood ratio test is developed for testing against ordered alternative means. Using the asymptotic distribution, the asymptotic likelihood ratio test is proposed. However, for small samples, it does not perform well. Hence, a parametric bootstrap likelihood ratio test (PB LRT) is proposed. Therefore, the asymptotic validity of the bootstrap procedure has been shown. Using the Box-type approximation method, test statistics are developed for the two-sample problem of equality of means when scale-like parameters are heterogeneous. Using these, two PB-based heuristic tests are proposed. Asymptotic null distributions are derived and PB accuracy is also developed. Two asymptotic tests are also proposed using the asymptotic null distributions. To get the critical points and test statistics of the three PB tests and two asymptotic tests, an ‘R’ package is developed and shared on GitHub. Applications of the tests are illustrated using real data.

Weak identification with many instruments

Summary Linear instrumental variable regressions are widely used to estimate causal effects. Many instruments arise from the use of ‘technical’ instruments and more recently from the empirical strategy of ‘judge design’. This paper surveys and summarises ideas from recent literature on estimation and statistical inferences with many instruments for a single endogenous regressor. We discuss how to assess the strength of the instruments and how to conduct weak identification robust inference under heteroscedasticity. We establish new results for a jack-knifed version of the Lagrange Multiplier test statistic. Furthermore, we extend the weak identification robust tests to settings with both many exogenous regressors and many instruments. We propose a test that properly partials out many exogenous regressors while preserving the re-centring property of the jack-knife. The proposed tests have correct size and good power properties.

Maximum-Subsampling Test of Equal Predictive Ability

In comparing the accuracy of any two competing forecasts, under the assumption that the loss differentials are covariance stationary, Diebold and Mariano (DM) proposed a test statistic that is asymptotically normal. This test is further studied by Giacomini and White (GW). However, under the DM-GW framework, the estimator of the variance of the DM test can be inaccurate in small samples, which yields size distortions; see, for example, Coroneo and Iacone (CI). To alleviate this challenge, we propose a maximum-subsampling (MS) test that does not require estimating the long-run variance induced by a number of autocovariances. Accordingly, the MS test is applicable for comparing the predictive ability between two competing forecasts even when the loss differentials are serially correlated with arbitrary autocovariance structures. We demonstrate that the MS test converges to the type I extreme value distribution under the DM-GW null hypothesis with proper conditions. In addition, under a set of alternative hypotheses, we show the MS test is consistent. We further compare the MS test with the DM test and two CI tests via five simulation settings, which are either modified or adapted from McCracken and Coroneo and Iacone. Simulation results show that the MS test performs satisfactorily.

Portmanteau Test for ARCH-Type Models by Using High-Frequency Data

The portmanteau test is an effective tool for testing the goodness of fit of models. Motivated by the fact that high-frequency data can improve the estimation accuracy of models, a modified portmanteau test using high-frequency data is proposed for ARCH-type models in this paper. Simulation results show that the empirical size and power of the modified test statistics of the model using high-frequency data are better than those of the daily model. Three stock indices (CSI 300, SSE 50, CSI 500) are taken as an example to illustrate the practical application of the test.

Joint modeling of an outcome variable and integrated omics datasets using GLM-PO2PLS

In many studies of human diseases, multiple omics datasets are measured. Typically, these omics datasets are studied one by one with the disease, thus the relationship between omics is overlooked. Modeling the joint part of multiple omics and its association to the outcome disease will provide insights into the complex molecular base of the disease. Several dimension reduction methods which jointly model multiple omics and two-stage approaches that model the omics and outcome in separate steps are available. Holistic one-stage models for both omics and outcome are lacking. In this article, we propose a novel one-stage method that jointly models an outcome variable with omics. We establish the model identifiability and develop EM algorithms to obtain maximum likelihood estimators of the parameters for normally and Bernoulli distributed outcomes. Test statistics are proposed to infer the association between the outcome and omics, and their asymptotic distributions are derived. Extensive simulation studies are conducted to evaluate the proposed model. The method is illustrated by modeling Down syndrome as outcome and methylation and glycomics as omics datasets. Here we show that our model provides more insight by jointly considering methylation and glycomics.

Assessment of fit of the time-varying dynamic partial credit model using the posterior predictive model checking method.

Several new models based on item response theory have recently been suggested to analyse intensive longitudinal data. One of these new models is the time-varying dynamic partial credit model (TV-DPCM; Castro-Alvarez etal., Multivariate Behavioral Research, 2023, 1), which is a combination of the partial credit model and the time-varying autoregressive model. The model allows the study of the psychometric properties of the items and the modelling of nonlinear trends at the latent state level. However, there is a severe lack of tools to assess the fit of the TV-DPCM. In this paper, we propose and develop several test statistics and discrepancy measures based on the posterior predictive model checking (PPMC) method (PPMC; Rubin, The Annals of Statistics, 1984, 12, 1151) to assess the fit of the TV-DPCM. Simulated and empirical data are used to study the performance of and illustrate the effectiveness of the PPMC method.

Statistical analysis of air quality dataset of Kathmandu, Nepal, with a New Extended Kumaraswamy Exponential Distribution.

This paper aims to create a new probability distribution and conducts statistical analysis on air quality dataset from Kathmandu. Using this innovative distribution, we have studied the ground reality of air quality conditions of Kathmandu, Nepal. In our research, we have developed a new probability distribution known as the New Extended Kumaraswamy Exponential Distribution by introducing an additional shape parameter to the Extended Kumaraswamy Exponential (EKwE) Distribution. Statistical characteristics such as cumulative distribution function, probability density function, hazard function, reversed hazard function, skewness, kurtosis, survival function, and hazard rate function are studied. The suggested model is non-normal and positively skewed with increasing and inverted bathtub-shaped hazard rate curves. To assess the model's suitability, we utilized a real dataset comprising air quality data from Kathmandu, Nepal, during the year 2021. Study shows that the air quality data exhibit an increasing failure rate, but the P2.5, P10, and total suspended particle concentrations exhibited its lowest levels during the monsoon season and its highest levels during the winter season. Parameters of the model are estimated by using the least square estimation (LSE), maximum likelihood estimation (MLE), and Cramér-von Mises (CVM) approach for P10 at Ratnapark Station, Kathmandu. To assess the model's validity, P-P plots and Q-Q plots are employed. Model comparisons are carried out using Akaike Information Criterion (AIC), Corrected Akaike Information Criterion (CAIC), Bayesian Information Criterion (BIC), and Hannan-Quinn Information Criterion (HQIC). Furthermore, the goodness of fit of the proposed model is evaluated using test statistics such as Anderson-Darling (A2) test, Cramér-von Mises (CVM) test, and the Kolmogorov-Smirnov (KS) test along with their respective p-values. From the findings, we have found that the air quality status of Kathmandu, Nepal, was found to be poor. Proposed distribution provides a better fit with greater flexibility for forecasting air quality data and conducting reliability data analyses. Dataset is analyzed and visualized using R programming.

The Prodigious Need for Fueling South Asian Economies through Sustainable Energies

South Asia is one of the fastest growing regions in the world during the last two decades. This growth momentum has been fuelled by carbon-intensive fossil fuels as reflected through the expansion in fossil fuel utilization in the total energy mix of 60.5 per cent on average for the period 1996-2000 to 70.3 per cent by 2011-2015. Against this backdrop, the study intended to identify the relationship between energy consumption and economic growth in South Asia to recognize the feasibility of promoting low-carbon economic progress in the future. The study employed annual data for the period from 1971-2014 for five selected South Asian countries. The unit root test results indicate that all the variables are stationary at their first difference and the four statistics of the Pedroni cointegration test indicate the existence of a long-run relationship between the variables. The FMOLS estimator implies the significance of the energy consumption in economic growth in the region where one per cent increase in energy consumption leads to a 0.78 per cent increase in economic growth. The study finds a strong bi-directional relationship between the core variables which illustrates the necessity to shift towards sustainable energy sources to achieve an undisrupted economic expansion with a minimum carbon footprint. Thus, the study lays the foundations to identify the aforementioned relationships and encourage the derive of sustainable energy solutions to fuel the growth in the region.

Asymptotics for the conditional self‐weighted M$$ M $$ estimator of GRCA(p$$ p $$) models and its statistical inference

SummaryUnder the ‐order generalised random coefficient autoregressive (GRCA()) model with random coefficients we propose a conditional self‐weighted estimator of . We investigate the asymptotic normality of this estimator with possibly heavy‐tailed random variables. Furthermore, a Wald test statistic is constructed for the linear restriction on the parameters. In addition, the simulation experiments are carried out to assess the finite sample performance of theoretical results. Finally, a real data analysis about the increase (%) in the number of construction projects this year over the same period of last year is provided.

The Macroeconomic Effect of Oil Sector Crisis in Libya

This paper analyses and investigates the impact of the oil sector crisis on the Libyan economy from 2012 Q4 to 2022 Q3, using the Bai-Perron model and a structural vector autoregressive model (SVAR). The findings demonstrate that the multiple structural breaks test statistics approved that nearly all of the study's variables had a structural break at years around political division and political agreement. In contrast to inflation, the results of the impulse response functions (IRFs) indicate that the shock to oil revenue had a considerable negative impact on the money supply and exchange rate. Furthermore, the study reveals that, with the exception of claims on the government with the central bank, shocks to oil revenue are the major contributors to variance decomposition for all variables. The results reveal that oil revenue, in particular, accounts for roughly 16%, 13%, and 16% of the variance decomposition of the money supply, exchange rate, and inflation rate, respectively. As a result, the oil sector crisis is a controlling factor in the explanation of variations in these variables. The study concluded that oil sector revenues have a sensitive impact on the Libyan economy and that the latter has a strong tide with a secure environment and political stability.