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Bootstrap is a widely applicable computational statistical method. The focus of this paper lies in developing a bootstrap method for linear mixed models under homoscedasticity violation (heteroscedasticity) in variance of errors. We assume that the form of heteroscedasticity is unknown. To generate bootstrap response data as close as possible to the actual response data, we transform the marginal residuals to ensure that the variance of the modified marginal residuals in bootstrap samples is an unbiased estimator for the variance of the response variable in the linear mixed models. The consistency is proved, implying that the parameter estimators by the proposed method are asymptotically unbiased. The simulations are conducted with varying error terms and sample sizes to show improvement of the proposed method in parameter estimation. The simulation results are compared to demonstrate that the proposed method outperforms the other considered approaches including the wild method in the heteroscedastic linear mixed models under small samples and performs competitively with the parametric method and both methods outperform the other considered methods in homoscedastic linear mixed models. The proposed bootstrap method is applied to squid data for illustration of its effectiveness. [ABSTRACT FROM AUTHOR]

With clustered data, such as where students are nested within schools or employees are nested within organizations, it is often of interest to estimate and compare associations among variables separately for each level. While researchers routinely estimate between-cluster effects using the sample cluster means of a predictor, previous research has shown that such practice leads to biased estimates of coefficients at the between level, and recent research has recommended the use of latent cluster means with the multilevel structural equation modeling framework. However, the latent cluster mean approach may not always be the best choice as it (a) relies on the assumption that the population cluster sizes are close to infinite, (b) requires a relatively large number of clusters, and (c) is currently only implemented in specialized software such as Mplus. In this paper, we show how using empirical Bayes estimates of the cluster means can also lead to consistent estimates of between-level coefficients, and illustrate how the empirical Bayes estimate can incorporate finite population corrections when information on population cluster sizes is available. Through a series of Monte Carlo simulation studies, we show that the empirical Bayes cluster-mean approach performs similarly to the latent cluster mean approach for estimating the between-cluster coefficients in most conditions when the infinite-population assumption holds, and applying the finite population correction provides reasonable point and interval estimates when the population is finite. The performance of EBM can be further improved with restricted maximum likelihood estimation and likelihood-based confidence intervals. We also provide an R function that implements the empirical Bayes cluster-mean approach, and illustrate it using data from the classic High School and Beyond Study. [ABSTRACT FROM AUTHOR]

Epidemiologic screening programs often make use of tests with small, but nonzero probabilities of misdiagnosis. In this article, we assume the target population is finite with a fixed number of true cases, and that we apply an imperfect test with known sensitivity and specificity to a sample of individuals from the population. In this setting, we propose an enhanced inferential approach for use in conjunction with sampling-based bias-corrected prevalence estimation. While ignoring the finite nature of the population can yield markedly conservative estimates, direct application of a standard finite population correction (FPC) conversely leads to underestimation of variance. We uncover a way to leverage the typical FPC indirectly toward valid statistical inference. In particular, we derive a readily estimable extra variance component induced by misclassification in this specific but arguably common diagnostic testing scenario. Our approach yields a standard error estimate that properly captures the sampling variability of the usual bias-corrected maximum likelihood estimator of disease prevalence. Finally, we develop an adapted Bayesian credible interval for the true prevalence that offers improved frequentist properties (i.e., coverage and width) relative to a Wald-type confidence interval. We report the simulation results to demonstrate the enhanced performance of the proposed inferential methods. [ABSTRACT FROM AUTHOR]

The second version of Kaiser's Measure of Sampling Adequacy (MSA2) has been widely applied to assess the factorability of data in psychological research. The MSA2 is developed in the population and little is known about its behavior in finite samples. If estimated MSA2s are biased due to sampling errors, misleading inferences on the factorability of data are likely to occur. This study investigates the effect of sampling error on MSA2 estimation by systematically examining the accuracy and fluctuations of MSA2 estimates with simulated continuous and ordered categorical data. Features manipulated included the number of factors, number of variables per factor, factor loading, inter-factor correlations, sample size, number of response categories, skewness of variables, and types of correlation analyzed, Pearson and polychoric correlations. Results revealed that the MSA2s were underestimated due to the effect of sampling error. Severely biased MSA2 occurred when analyzing a large number of weakly correlated variables with insufficient participants. The underestimation of MSA2 became worse with categorized data. Polychoric correlations yielded slightly more accurate but relatively unstable MSA2 estimates compared to Pearson correlations. In practice, researchers need to bear in mind the downward bias of MSA2 estimates and interpret the value of sample MSA2s with caution. [ABSTRACT FROM AUTHOR]

In today's steady development of e-commerce, improving enterprise competitiveness is a major challenge that e-commerce enterprises need to face. There are problems with incomplete and inaccurate evaluation systems in commonly used competitiveness evaluation systems. To address these concerns, the study establishes a model for evaluating business-to-business relationships by analyzing indicators of competitiveness. It also examines the algorithm process and neural network structure and incorporates them into the evaluation model. The experiment shows that through training the back propagation neural network, it is discovered that the mean square error of the samples is 9.9869e-06 when the training frequency reaches 3200, resulting in the completion of convergence of the back-propagation neural network. The utilization of back propagation neural networks to enhance the evaluation model of enterprise competitiveness has yielded positive outcomes. Suggestions have been proposed to improve the competitiveness of diverse e-commerce enterprises. This study can furnish enterprise managers with decision support, enhancing enterprise competitiveness and enabling sustainable development. [ABSTRACT FROM AUTHOR]

Over the years, acceptance sampling plans have been crucial to quality assurance in manufacturing. Sample plans are designed using operating characteristic curve conditions to safeguard producers and customers. We propose a conditional probability-based Bayesian generalized multiple-dependent state sampling technique in this paper. The technique relies on Gamma-Poisson distribution. Other performance indicators and acceptance probability are calculated. Also, the new plan's operational method is discussed. The proposed technique is also compared to current attribute sampling schemes for efficacy. Optimal plan parameters for the plan's economic structure are also generated, adding managerial insights to the suggested plan. The entire cost study showed that the suggested plan is cheaper than existing sample plans under identical conditions. To account for inspection flaws, the plan is adjusted. We examine how Type I and Type II errors affect sampling plan outcomes. The plan is demonstrated with numerical examples and a data-driven application. [ABSTRACT FROM AUTHOR]

Detrital zircon (DZ) geochronology is based on a multistage, hierarchical sampling process in which sampling errors (statistical variance) and non-sampling errors (sampling bias) are endemic. Most of these errors are related to 1) initial collection of a non-random grab sample (typically from outcrop); 2) processing the grab sample to obtain a non-random grain-size sample of restricted grain size(s) (effectively a processed population); 3) randomly and/or non-randomly selecting DZs (often based on their size, shape, and colour) from the grain-size sample to obtain a hand-picked sample (effectively an analysed population); and 4) randomly and/or non-randomly radiometrically dating only certain DZs (due to limitations of instrument spot size and grain imperfections) from the hand-picked sample to obtain an analysed sample. Claims that hand-picked samples and analysed samples are randomly chosen are questionable, since these samples likely represent haphazard sampling attempting to emulate randomness. Non-randomness has major implications for calculations that determine sample size and inter-sample 'sameness' comparison, as both techniques generally depend on randomly chosen samples. The use of inter-sample comparison is particularly troublesome in that sameness is determined for the analysed sample, which is not representative of the initial grab sample. Yet more bias occurs with a 'leap of inference', the generalization of DZ ages from the analysed sample to the target population (the strata of interest) or to a general population (DZs derived from ultimate and proximate sources). Sampling bias can be reduced by unambiguously defining the sampled population (the population that inferential statistics apply), selecting representative samples (if possible, randomization should be used at every stage in the sampling process), and preserving the representativeness of subsamples by using correct sampling devices such as a microsplitter. It may be timely for standardized sampling, interpreting, and reporting guidelines so that detrital geochronology data are scientifically meaningful and replicable. [ABSTRACT FROM AUTHOR]

The problem of domain generalization is to learn, given data from different source distributions, a model that can be expected to generalize well on new target distributions which are only seen through unlabeled samples. In this paper, we study domain generalization as a problem of functional regression. Our concept leads to a new algorithm for learning a linear operator from marginal distributions of inputs to the corresponding conditional distributions of outputs given inputs. Our algorithm allows a source distribution-dependent construction of reproducing kernel Hilbert spaces for prediction, and, satisfies finite sample error bounds for the idealized risk. Numerical implementations and source code are available1. [ABSTRACT FROM AUTHOR]

Non-response situations are inevitable in sample survey work, and this is also true in dual sampling frame. In view of this, this study proposes alternative imputation techniques to solve the problem of missing data and further suggests an estimate of the population total in dual sampling frame. The properties of the suggested estimator are analyzed, and its empirical results are compared to the entire response situation. Based on the results obtained, appropriate suggestions have been proposed to survey practitioners and researchers for their practical applications. [ABSTRACT FROM AUTHOR]

"Statistical Methods in Health Disparity Research" by J. Sunil Rao is a comprehensive book that explores statistical methods for estimating health disparities. The book covers various approaches, including non-model and linear-based models, as well as the application of machine learning. It emphasizes the importance of validating findings and discusses the advantages and limitations of each method. The book is divided into seven chapters, which cover topics such as basic concepts of health disparities, estimation of health disparities, domain-specific estimates, causality, moderation, and mediation, machine learning-based approaches, health disparity estimation under a precision medicine paradigm, and extended topics. While the book has some structural inconsistencies, it offers a diverse range of topics and provides in-depth explanations of complex concepts. It is recommended for students, professionals in public health or health policy, researchers, and practitioners working with vulnerable populations. [Extracted from the article]