Parametric Bootstrap Technique Research Articles

Inference on Weibull inverted exponential distribution under progressive first-failure censoring with constant-stress partially accelerated life test

AbstractAccelerated life tests (ALTs) play a pivotal role in life testing experiments as they significantly reduce costs and testing time. Hence, this paper investigates the statistical inference issue for the Weibull inverted exponential distribution (WIED) under the progressive first-failure censoring (PFFC) data with the constant-stress partially ALT (CSPALT) under progressive first-failure censoring (PFFC) data for Weibull inverted exponential distribution (WIED). For classical inference, maximum likelihood (ML) estimates for both the parameters and the acceleration factor are derived. Making use of the Fisher information matrix (FIM), asymptotic confidence intervals (ACIs) are constructed for all parameters. Besides, two parametric bootstrap techniques are implemented. For Bayesian inference based on a proposed technique for eliciting the hyperparameters, the Markov chain Monte Carlo (MCMC) technique is provided to acquire Bayesian estimates. In this context, the Bayesian estimates are obtained under symmetric and asymmetric loss functions, and the corresponding credible intervals (CRIs) are constructed. A simulation study is carried out to assay the performance of the ML, bootstrap, and Bayesian estimates, as well as to compare the performance of the corresponding confidence intervals (CIs). Finally, real-life engineering data is analyzed for illustrative purposes.

Tests under simple order in one‐way ANCOVA

AbstractAnalysis of covariance (ANCOVA) models are used when apart from the main treatments, some covariates also affect the response variable. In this article, the problem of testing the homogeneity of treatment effects against ordered alternatives is addressed in a fixed effects one‐way ANCOVA model when error variances are heterogeneous. The likelihood ratio test (LRT) and two approximate tests based on the asymptotic distributions of some union‐intersection type test statistics are proposed. A parametric bootstrap technique has been used to implement the LRT and its asymptotic validity is proved. A method to construct simultaneous confidence intervals is proposed. All the test procedures are further extended to the case of more than one covariate. The robustness of tests is also studied under departure from normality. Extensive simulation studies show that the proposed test procedures perform well in terms of achieving the nominal size value and good power values.

The Interplay Between Long Memory and Bootstrap Technique in Virtual and Real Currency Markets: The Evidence on the Pre/Post-COVID Era

This article explores the interplay between long memory and the parametric and nonparametric bootstrap techniques in virtual and real currency markets, specifically focusing on Bitcoin and the US dollar (USD) from 2019 to late 2022. The study compares the properties of the bootstrap tests, analyzes long memory effects, and evaluates the significance using P-value plots. Additionally, the research examines the corrected size-power curves to address size distortions. The findings confirm the presence of long memory in the examined currency markets and underscore the importance of accurate bootstrap utilization for robust analysis. The study provides valuable insights for investors and decision-makers in understanding the dynamics of the pre/post-COVID era.

A general modeling framework for quantitative tracking, accurate prediction of ICU, and assessing vaccination for COVID-19 in Chile.

One of the main lessons of the COVID-19 pandemic is that we must prepare to face another pandemic like it. Consequently, this article aims to develop a general framework consisting of epidemiological modeling and a practical identifiability approach to assess combined vaccination and non-pharmaceutical intervention (NPI) strategies for the dynamics of any transmissible disease. Epidemiological modeling of the present work relies on delay differential equations describing time variation and transitions between suitable compartments. The practical identifiability approach relies on parameter optimization, a parametric bootstrap technique, and data processing. We implemented a careful parameter optimization algorithm by searching for suitable initialization according to each processed dataset. In addition, we implemented a parametric bootstrap technique to accurately predict the ICU curve trend in the medium term and assess vaccination. We show the framework's calibration capabilities for several processed COVID-19 datasets of different regions of Chile. We found a unique range of parameters that works well for every dataset and provides overall numerical stability and convergence for parameter optimization. Consequently, the framework produces outstanding results concerning quantitative tracking of COVID-19 dynamics. In addition, it allows us to accurately predict the ICU curve trend in the medium term and assess vaccination. Finally, it is reproducible since we provide open-source codes that consider parameter initialization standardized for every dataset. This work attempts to implement a holistic and general modeling framework for quantitative tracking of the dynamics of any transmissible disease, focusing on accurately predicting the ICU curve trend in the medium term and assessing vaccination. The scientific community could adapt it to evaluate the impact of combined vaccination and NPIs strategies for COVID-19 or any transmissible disease in any country and help visualize the potential effects of implemented plans by policymakers. In future work, we want to improve the computational cost of the parametric bootstrap technique or use another more efficient technique. The aim would be to reconstruct epidemiological curves to predict the combined NPIs and vaccination policies' impact on the ICU curve trend in real-time, providing scientific evidence to help anticipate policymakers' decisions.

Low-Dose Extrapolation Factors Implied by Mortality and Incidence Data from the Japanese Atomic Bomb Survivor Life Span Study Data.

Assessment of the effect of low dose and low-dose-rate exposure depends critically on extrapolation from groups exposed at high dose and high-dose rates such as the Japanese atomic bomb survivor data, and has often been achieved via application of a dose and dose-rate effectiveness factor (DDREF). An important component of DDREF is the factor determining the effect of extrapolation of dose, the so-called low-dose extrapolation factor (LDEF). To assess LDEF models linear (or linear quadratic) in dose are often fitted. In this report LDEF is assessed via fitting relative rate models that are linear or linear quadratic in dose to the latest Japanese atomic bomb survivor data on solid cancer, leukemia and circulatory disease mortality (followed from 1950 through 2003) and to data on solid cancer, lung cancer and urinary tract cancer incidence. The uncertainties in LDEF are assessed using parametric bootstrap techniques. Analysis is restricted to survivors with <3 Gy dose. There is modest evidence for upward curvature in dose response in the mortality data. For leukemia and for all solid cancer excluding lung, stomach and breast cancer there is significant curvature (P < 0.05). There is no evidence of curvature for circulatory disease (P > 0.5). The estimate of LDEF for all solid cancer mortality is 1.273 [95% confidence intervals (CI) 0.913, 2.182], for all solid cancer mortality excluding lung cancer, stomach cancer and breast cancer is 2.183 (95% CI 1.090, >100) and for leukemia mortality is 11.447 (95% CI 2.390, >100). For stomach cancer mortality LDEF is modestly raised, 1.077 (95% CI 0.526, >100), while for lung cancer, female breast cancer and circulatory disease mortality the LDEF does not much exceed 1. LDEF for solid cancer incidence is 1.186 (95% CI 0.942, 1.626) and for urinary tract cancer is 1.298 (95% CI <0, 7.723), although for lung cancer LDEF is not elevated, 0.842 (95% CI 0.344, >100).

Joint test for homogeneity of high-dimensional means and covariance matrices using maximum-type statistics

Several tests for simultaneously checking homogeneity of means and covariance matrices, based on the classical likelihood ratio and sum-of-squares type test statistics, have been proposed in the literature. Despite their usefulness, they tend to have unsatisfactory size performance for either nonnormal high-dimensional data or strongly spiked eigenvalue models. This article proposes a novel high-dimensional nonparametric test using the maximum-type statistics. The limiting null distribution of the proposed test statistic is derived to provide p-values. It turns out that under appropriate conditions, the test is particularly powerful against sparse alternatives. Since the unknown correlations among the data sometimes pose a great challenge toward the accurate p-value calculation of the test, we further use a parametric bootstrap technique to achieve size accuracy. We also prove that the proposed simulation-based testing procedure is asymptotically valid in terms of size and power even if the dimension of the data is much larger than the sample size. We demonstrate the effectiveness of our methods through extensive simulation studies and a real data application.

Does uncertainty in single indicators affect the reliability of composite indexes? An application to the measurement of environmental performances of Italian regions

In recent decades, the measurement and evaluation of important social and natural phenomena has significantly evolved, with many traditional measurements based on single variables increasingly being replaced by multidimensional approaches. One key aspect of these approaches is the development of composite indexes, usually real-value functions of multiple achievements of a group of units. The achievements in each of the selected dimensions are generally synthesised through one or more variables, often referred to as indicators. When indicators are obtained through an estimation process, it is crucial to understand if and how their estimation error – for example, sampling error – affects the resulting composite index.This paper presents a methodology based on a parametric bootstrap technique that evaluates to what extent uncertainty in indicators affects the reliability of the aggregate composite index. The method is applied to four composite indexes measuring the environmental performances of Italian regions based on real population and survey data.To our knowledge, this is the first attempt to measure the impact of indicators’ sampling error on composite indexes. If adequately generalised, our methodology could be used in the presence of measurement errors, non-response issues, or other kinds of non-sampling errors.

Testing Procedure for Item Response Probabilities of 2Class Latent Model

This paper presents Hotelling T2 as a procedure for the testing of significance difference between the item response probabilities (ωij′s) of classes in a Latent Class Model (LCM). Parametric bootstrap technique is used in order to generate samples for ωij′s. These samples are based on the estimated parameters of 2-class latent model. The estimation of parameters in either situation is done using the Expectation Maximization (EM) algorithm through Maximum likelihood method. The hypothesis under consideration is whether the response probabilities (ωij′s) are equal against each item in both the classes. { H0 : ωi1 = ωi2. against H1 : =ωi1 ≠ ωi2}. If the test exhibits significant difference between response probabilities in both classes, it will be a clear indication of a presence of latent variable. We consider both training and testing data sets to develop the test. In order to apply Hotelling T2 test the basic assumptions of normality and homogeneity of variance are also checked. Chi-square goodness of fit test is used for assessing normal distribution to be good fitted on the hypothesized (bootstrap samples) based on 2-class latent model parameters for each data and Bartlett test to check heterogeneity of variances in ωij′s. Moreover, our procedure produces a minimum standard error of estimates as compared to those obtained through the package in R.Gui environment

A Parametric Bootstrap for the Mean Measure of Divergence.

For more than 50 years the Mean Measure of Divergence (MMD) has been one of the most prominent tools used in anthropology for the study of non-metric traits. However, one of the problems, in anthropology including palaeoanthropology (more often there), is the lack of big enough samples or the existence of samples without sufficiently measured traits. Since 1969, with the advent of bootstrapping techniques, this issue has been tackled successfully in many different ways. Here, we present a parametric bootstrap technique based on the fact that the transformed θ, obtained from the Anscombe transformation to stabilize the variance, nearly follows a normal distribution with standard deviation $\sigma = 1 / \sqrt{N + 1/2}$σ=1/N+1/2, where N is the size of the measured trait. When the probabilistic distribution is known, parametric procedures offer more powerful results than non-parametric ones. We profit from knowing the probabilistic distribution of θ to develop a parametric bootstrapping method. We explain it carefully with mathematical support. We give examples, both with artificial data and with real ones. Our results show that this parametric bootstrap procedure is a powerful tool to study samples with scarcity of data.

Scalar dipole dynamical polarizabilities from real Compton scattering data

We present an extraction of the scalar dipole dynamical polarizabilities from proton real Compton scattering (RCS) data below pion-production threshold. The theoretical approach relies on dispersion relations, and on the low-energy expansion and multipole expansion of the scattering amplitude. The statistical analysis is based on the parametric bootstrap technique, that revealed to be crucial to deal with problems inherent to both the low sensitivity of the RCS cross section to the energy dependence of the dynamical polarizabilities and the poor accuracy of the available data sets.

Prediction intervals for penalized longitudinal models with multisource summary measures: An application to childhood malnutrition.

In many global health analyses, it is of interest to examine countries' progress using indicators of socio-economic conditions based on national surveys from varying sources. This results in longitudinal data where heteroscedastic summary measures, rather than individual level data, are available. Administration of national surveys can be sporadic, resulting in sparse data measurements for some countries. Furthermore, the trend of the indicators over time is usually nonlinear and varies by country. It is of interest to track the current level of indicators to determine if countries are meeting certain thresholds, such as those indicated in the United Nations Sustainable Development Goals. In addition, estimation of confidence and prediction intervals are vital to determine true changes in prevalence and where data is low in quantity and/or quality. In this article, we use heteroscedastic penalized longitudinal models with survey summary data to estimate yearly prevalence of malnutrition quantities. We develop and compare methods to estimate confidence and prediction intervals using asymptotic and parametric bootstrap techniques. The intervals can incorporate data from multiple sources or other general data-smoothing steps. The methods are applied to African countries in the UNICEF-WHO-The World Bank joint child malnutrition data set. The properties of the intervals are demonstrated through simulation studies and cross-validation of real data.

On Reliability in a Multicomponent Stress-Strength Model with Power Lindley Distribution

In this paper we study the reliability of a multicomponent stress-strength model assuming that the components follow power Lindley model. The maximum likelihood estimate of the reliability parameter and its asymptotic confidence interval are obtained. Applying the parametric Bootstrap technique, interval estimation of the reliability is presented. Also, the Bayes estimate and highest posterior density credible interval of the reliability parameter are derived using suitable priors on the parameters. Because there is no closed form for the Bayes estimate, we use the Markov Chain Monte Carlo method to obtain approximate Bayes estimate of the reliability. To evaluate the performances of different procedures, simulation studies are conducted and an example of real data sets is provided.

Identifying Aberrant Data in Structural Equation Models With IRLS-ADF

In structural equation models, outliers could result in inaccurate parameter estimates and misleading fit statistics when using traditional methods. To robustly estimate structural equation models, iteratively reweighted least squares (IRLS; Yuan & Bentler, 2000) has been proposed, but not thoroughly examined. We explore the large-sample properties of IRLS and its effect on parameter recovery, model fit, and aberrant data identification. A parametric bootstrap technique is proposed to determine the tuning parameters of IRLS, which results in improved Type I error rates in aberrant data identification, for data sets generated from homogenous populations. Scenarios concerning (a) simulated data, (b) contaminated data, and (c) a real data set are studied. Results indicate good parameter recovery, model fit, and aberrant data identification when noisy observations are drawn from a real data set, but lackluster parameter recovery and identification of aberrant data when the noise is parametrically structured. Practical implications and further research are discussed.

Estimation for coefficient of variation of an extension of the exponential distribution under type-II censoring scheme

AbstractThe coefficient of variation [CV] has several applications in applied statistics. So in this paper, we adopt Bayesian and non-Bayesian approaches for the estimation of CV under type-II censored data from extension exponential distribution [EED]. The point and interval estimate of the CV are obtained for each of the maximum likelihood and parametric bootstrap techniques. Also the Bayesian approach with the help of MCMC method is presented. A real data set is presented and analyzed, hence the obtained results are used to assess the obtained theoretical results.

Improved treatment of non-stationary conditions and uncertainties in probabilistic models of storm wave climate

A framework is presented for the probabilistic modelling of non-stationary coastal storm event sequences. Such modelling is required to integrate seasonal, climatic and long-term non-stationarities into coastal erosion hazard assessments. The framework is applied to a study site on the East Australian Coast where storm waves are found to exhibit non-stationarities related to El Niño-Southern Oscillation (ENSO) and seasonality. The impact of ENSO is most prominent for storm wave direction, long term mean sea level (MSL) and the rate of storms, while seasonal non-stationarity is more ubiquitous, affecting the latter variables as well as storm wave height, duration, period and surge. The probabilistic framework herein separates the modelling of ENSO and seasonal non-stationarity in the storm wave properties from the modelling of their marginal distributions, using copulas. The advantage of this separation is that non-stationarities can be straightforwardly modelled in all storm wave variables, irrespective of whether parametric or non-parametric techniques are used to model their marginal distributions. Storm wave direction and steepness are modelled with non-parametric distributions whereas storm wave height, duration and surge are modelled parametrically using extreme value mixture distributions. The advantage of the extreme value mixture distributions, compared with the standard extreme value distribution for peaks-over-threshold data (Generalized Pareto), is that the statistical threshold becomes a model parameter instead of being fixed, and so uncertainties in the threshold can be straightforwardly integrated into the analysis. Robust quantification of uncertainties in the model predictions is crucial to support hazard applications, and herein uncertainties are quantified using a novel mixture of parametric percentile bootstrap and Bayesian techniques. Percentile bootstrap confidence intervals are shown to non-conservatively underestimate uncertainties in the extremes (e.g. 1% annual exceedance probability wave heights), both in an idealized setting and in our application. The Bayesian approach is applied to the extreme value models to remedy this shortcoming. The modelling framework is applicable to any site where multivariate storm wave properties and timings are affected by seasonal, climatic and long-term non-stationarities, and can be used to account for such non-stationarities in coastal hazard assessments.

Simulation-based hypothesis testing of high dimensional means under covariance heterogeneity.

In this article, we study the problem of testing the mean vectors of high dimensional data in both one-sample and two-sample cases. The proposed testing procedures employ maximum-type statistics and the parametric bootstrap techniques to compute the critical values. Different from the existing tests that heavily rely on the structural conditions on the unknown covariance matrices, the proposed tests allow general covariance structures of the data and therefore enjoy wide scope of applicability in practice. To enhance powers of the tests against sparse alternatives, we further propose two-step procedures with a preliminary feature screening step. Theoretical properties of the proposed tests are investigated. Through extensive numerical experiments on synthetic data sets and an human acute lymphoblastic leukemia gene expression data set, we illustrate the performance of the new tests and how they may provide assistance on detecting disease-associated gene-sets. The proposed methods have been implemented in an R-package HDtest and are available on CRAN.

Evaluation of the ultimate drying shrinkage of cement-based mortars with poroelastic models

In this study, the ultimate drying shrinkage of three different cement-based mortars, with and without supplementary cementitious materials, was investigated. Experimental results were compared to the predicted ultimate shrinkage values obtained by three different poroelastic approaches. The different poroelastic models predict similar ultimate shrinkage as a function of the relative humidity especially in the higher range (above about 50 % RH). The experimentally-measured ultimate drying shrinkage is predicted reasonably well by the different models, with the highest deviations observed for the slag-containing mortars. The most important parameters that influence the predictions are discussed and their effect is quantified. The uncertainty of the shrinkage predictions resulting from error propagation of the input parameters is estimated using a parametric bootstrap technique.

Towards Efficiency in the Residual and Parametric Bootstrap Techniques

There are many bootstrap methods that can be used for statistical analysis especially in econometrics, biometrics, Statistics, Sampling and so on. The sole aim of this paper is to ascertain the accuracy and efficiency of the estimates from the independent and identically distributed (iid) simple linear regression (SLR) model under a variety of assessment conditions using bootstrap techniques. Analysis was carried out using S-plus statistical package on hypothetical data sets from a normal distribution with different group proficiency levels to buttress the arguments in the paper. In the course of the analysis, 268,800 scenarios were replicated 1000 times. The result shows a significant difference between the performances of the bootstrap methods used, namely; residual and parametric bootstrap techniques. From the analysis, the largest bias and standard error were always associated with model HP311 while the smallest bias and standard error values were associated with models HR311. The exception was found in the group proficiency level 3- N (1, 0.25), when the sample sizes were 200, 1000 and 10000 instead of model HR311 producing the smallest bias and standard error, model RP311 did. The significantly better performance of the residual bootstrap indicates the possible use of this technique in assessment of comparative performance and the capability of yielding very accurate, consistent, faster and extra-ordinarily reliable statistical inference under several assessment conditions.

Likelihood Ratio Test for Excess Homozygosity at Marker Loci on X Chromosome.

The assumption of Hardy-Weinberg equilibrium (HWE) is generally required for association analysis using case-control design on autosomes; otherwise, the size may be inflated. There has been an increasing interest of exploring the association between diseases and markers on X chromosome and the effect of the departure from HWE on association analysis on X chromosome. Note that there are two hypotheses of interest regarding the X chromosome: (i) the frequencies of the same allele at a locus in males and females are equal and (ii) the inbreeding coefficient in females is zero (without excess homozygosity). Thus, excess homozygosity and significantly different minor allele frequencies between males and females are used to filter X-linked variants. There are two existing methods to test for (i) and (ii), respectively. However, their size and powers have not been studied yet. Further, there is no existing method to simultaneously detect both hypotheses till now. Therefore, in this article, we propose a novel likelihood ratio test for both (i) and (ii) on X chromosome. To further investigate the underlying reason why the null hypothesis is statistically rejected, we also develop two likelihood ratio tests for detecting (i) and (ii), respectively. Moreover, we explore the effect of population stratification on the proposed tests. From our simulation study, the size of the test for (i) is close to the nominal significance level. However, the size of the excess homozygosity test and the test for both (i) and (ii) is conservative. So, we propose parametric bootstrap techniques to evaluate their validity and performance. Simulation results show that the proposed methods with bootstrap techniques control the size well under the respective null hypothesis. Power comparison demonstrates that the methods with bootstrap techniques are more powerful than those without bootstrap procedure and the existing methods. The application of the proposed methods to a rheumatoid arthritis dataset indicates their utility.

Testing the rate ratio under inverse sampling based on gradient statistic

Inverse sampling is widely applied in studies with dichotomous outcomes, especially when the subjects arrive sequentially or the response of interest is difficult to obtain. In this paper, we investigate the rate ratio test problem under inverse sampling based on gradient statistic with the asymptotic method and parametric bootstrap technique. The gradient statistic has many advantages, for example, it is simple to calculate and competitive with Wald-type, score and likelihood ratio tests in terms of local power. Numerical studies are carried out to evaluate the performance of our gradient test and the existing tests, namely Wald-type, score and likelihood ratio tests. The simulation results suggest that the gradient test based on the parametric bootstrap method has excellent type I error control and large powers even in small sample design. Two real examples, from a heart disease study and a drug comparison study, are applied to illustrate our methods.