Model-robust inference for continuous threshold regression models.

PurposeIn order to develop a feasible and efficient method to acquire the long‐run availability of a parallel system with distribution‐free up and down times, the purpose of this paper is to perform the simulation comparisons on the interval estimations of system availability using four bootstrapping methods.Design/methodology/approachBy using four bootstrap methods; standard bootstrap (SB) confidence interval, percentile bootstrap (PB) confidence interval, bias‐corrected percentile bootstrap (BCPB) confidence interval, and bias‐corrected and accelerated (BCa) confidence interval. A numerical simulation study is carried out in order to demonstrate performance of these proposed bootstrap confidence intervals. Especially, we investigate the accuracy of the four bootstrap confidence intervals by calculating the coverage percentage, the average length, and the relative coverage of confidence intervals.FindingsAmong the four bootstrap confidence intervals, the PB method has the largest relative coverage in most situations. That is, the PB method is the best one made by practitioners who want to obtain an efficient interval estimation of availability.Originality/valueIt is the first time that the relative coverage is introduced to evaluate the performance of estimation method, which is more efficient than the existing measures.

A confidence interval is an interval estimate of a parameter of a population calculated from a sample drawn from the population. Bootstrapping method, which involves producing several new data sets that are resampled from the original data in order to estimate parameter for each newly created data set, allowing an empirical distribution for the parameter to be estimated. Since certain statistics are harder to estimate, confidence intervals are rarely employed. Several statistics might necessitate multi-step formulas assuming that are impractical for calculating confidence intervals. This paper reviews research on the concept of bootstrapping and bootstrap confidence interval. The current narrative analysis was developed to answer the main research question: (1) What is the concept of the bootstrap method and bootstrap confidence interval? (2) What are the methods of bootstrapping to obtain confidence interval? This study has found general bootstrap method idea, various techniques of bootstrap methods, its advantages and disadvantages, and its limitations. There are normal interval method, percentile bootstrap method, basic method, first-order normal approximation method, bias-corrected bootstrap, accelerated bias-corrected bootstrap and bootstrap-t method. This study concludes that the advantages of using bootstrap CI is that it does not require any assumptions about the shape of distribution and universality of the approach. Bootstrapping is a computer-intensive statistical technique that relies significantly on modern high-speed digital computers to do massive computations.

BackgroundSite fidelity is considered as an animal’s tendency to return to a previously occupied place; this is a component of animal behaviour that allows us to understand movement patterns and aspects related to the animal’s life history. Although there are many site fidelity metrics, the lack of standardisation presents a considerable challenge in terms of comparability among studies.MethodsThis investigation focused on the theoretical development of a standardised composite site fidelity index and its statistical distribution in order to obtain reliable population-level site fidelity comparisons. The arithmetic and harmonic means were used as mathematical structures in order to create different indexes by combining the most commonly used indicators for site fidelity such as Occurrence, Permanence and Periodicity. The index performance was then evaluated in simulated populations and one real population of Commerson’s dolphins (Cephalorhynchus commersonii (Lacépède 1804)). In the first case, the indexes were evaluated based on how they were affected by different probability values such as the occurrence of the individual within the study area (φ) and capture probability (p). As a precision measure for the comparison of the indexes, the Wald confidence interval (CI) and the mean square error were applied. Given that there was no previous data concerning the distribution parameters of this population, bootstrap CIs were applied for the study case.ResultsEight alternative indexes were developed. The indexes with an arithmetic mean structure, in general, had a consistently inferior performance than those with a harmonic mean structure. The index IH4, in particular, achieved the best results in all of the scenarios and in the study case. Additionally, this index presented a normal distribution. As such, it was proposed as a standardised measure for site fidelity (Standardised Site Fidelity Index—SSFI).DiscussionThe SSFI is the first standardised metric that quantifies site fidelity at a populational level. It is an estimator that varies between zero and one and works in situations where detection is not perfect and effort can be constant or not. Moreover, it has an associated CI that allows users to make comparisons.

Blood culture contamination is a common problem in the emergency department (ED) that leads to unnecessary patient morbidity and health care costs. The study objective was to develop and evaluate the effectiveness of a quality improvement (QI) intervention for reducing blood culture contamination in an ED. The authors developed a QI intervention to reduce blood culture contamination in the ED and then evaluated its effectiveness in a prospective interrupted times series study. The QI intervention involved changing the technique of blood culture specimen collection from the traditional clean procedure to a new sterile procedure, with standardized use of sterile gloves and a new materials kit containing a 2% chlorhexidine skin antisepsis device, a sterile fenestrated drape, a sterile needle, and a procedural checklist. The intervention was implemented in a university-affiliated ED and its effect on blood culture contamination evaluated by comparing the biweekly percentages of blood cultures contaminated during a 48-week baseline period (clean technique) and 48-week intervention period (sterile technique), using segmented regression analysis with adjustment for secular trends and first-order autocorrelation. The goal was to achieve and maintain a contamination rate below 3%. During the baseline period, 321 of 7,389 (4.3%) cultures were contaminated, compared to 111 of 6,590 (1.7%) during the intervention period (p < 0.001). In the segmented regression model, the intervention was associated with an immediate 2.9% (95% confidence interval [CI] = 2.2% to 3.2%) absolute reduction in contamination. The contamination rate was maintained below 3% during each biweekly interval throughout the intervention period. A QI assessment of ED blood culture contamination led to development of a targeted intervention to convert the process of blood culture collection from a clean to a fully sterile procedure. Implementation of this intervention led to an immediate and sustained reduction of contamination in an ED with a high baseline contamination rate.

The generalized Pareto distribution (GPD) is a two-parameter family of distributions which can be used to model exceedances over a threshold. We compare the empirical coverage of some standard bootstrap and likelihood-based confidence intervals for the parameters and upper p-quantiles of the GPD. Simulation results indicate that none of the bootstrap methods give satisfactory intervals for small sample sizes. By applying a general method of D. N. Lawley, correction factors for likelihood ratio statistics of parameters and quantiles of the GPD have been calculated. Simulations show that for small sample sizes accuracy of confidence intervals can be improved by incorporating the computed correction factors to the likelihood-based confidence intervals. While the modified likelihood method has better empirical coverage probability, the mean length of produced intervals are not longer than corresponding bootstrap confidence intervals. This article also investigates the performance of some bootstrap methods for estimation of accuracy measures of maximum likelihood estimators of parameters and quantiles of the GPD.

PurposeThe study based on the estimation of the stress–strength reliability parameter plays a vital role in showing system efficiency. In this paper, considering independent strength and stress random variables distributed as inverted exponentiated Rayleigh model, the author have developed estimation procedures for the stress–strength reliability parameter R = P(X>Y) under Type II hybrid censored samples.Design/methodology/approachThe maximum likelihood and Bayesian estimates of R based on Type II hybrid censored samples are evaluated. Because there is no closed form for the Bayes estimate, the author use the Metropolis–Hastings algorithm to obtain approximate Bayes estimate of the reliability parameter. Furthermore, the author construct the asymptotic confidence interval, bootstrap confidence interval and highest posterior density (HPD) credible interval for R. The Monte Carlo simulation study has been conducted to compare the performance of various proposed point and interval estimators. Finally, the validity of the stress–strength reliability model is demonstrated via a practical case.FindingsThe performance of various point and interval estimators is compared via the simulation study. Among all proposed estimators, Bayes estimators using MHG algorithm show minimum MSE for all considered censoring schemes. Furthermore, the real data analysis indicates that the splashing diameter decreases with the increase of MPa under different hybrid censored samples.Originality/valueThe frequentist and Bayesian methods are developed to estimate the associated parameters of the reliability model under the hybrid censored inverted exponentiated Rayleigh distribution. The application of the proposed stress–strength reliability model will help the reliability engineers and also other scientists to estimate the system reliability.

This paper assesses the bootstrap confidence intervals of a newly proposed process capability index (PCI) for Weibull distribution, using the logarithm of the analyzed data. These methods can be applied when the quality of interest has non-symmetrical distribution. Bootstrap confidence intervals, which consist of standard bootstrap (SB), percentile bootstrap (PB), and bias-corrected percentile bootstrap (BCPB) confidence interval are constructed for the proposed method. A Monte Carlo simulation study is used to determine the efficiency of newly proposed index C p k w over the existing method by addressing the coverage probabilities and average widths. The outcome shows that the BCPB confidence interval is recommended. The methodology of the proposed index has been explained by using the real data of breaking stress of carbon fibers.

The study focused on estimating the reliability index using confidence interval by comparing the Fishers Z and the bootstrap confidence interval methods. The rational for the study was to examine the bootstrap and the Fisher –Z methods and finding out the better of the two. The population of the study consists of the senior secondary school students in Egor local government area, Edo State. There are a total of 12 school with 8,207 students. A sample size of 410 representing 5% of the total population of students were randomly selected from the 12 schools. The instrument for data collection was the Open Hemisphere Brain Dominance Scale 1.0 (OHBDS) a personality scale designed by Eric Jorgenson (2015). It was adapted for the study. The instrument was validated. The reliability was part of the issues raised in the study. The data were analyzed using the Pearson Product-Moment Correlation Coefficient to determine the reliability. The Fishers Z 95% and the Bootstrap (percentile and bias corrected and accelerated) confidence interval were also used. The findings revealed that as the sample size became large, the length of the interval became narrower; the three methods utilized in this study yielded the same length of the interval (width) when the same size was 100 and 150; and as the sample size increases, the bias corrected and accelerated bootstrap gave a shorter interval length, thereby becoming the best of the three method considered in the study. It was therefore recommended that reporting reliability should be based on interval estimation as against the point estimate, the sample size should be at least 100 and the bootstrap confidence interval should be adopted as it is not liable to the normality condition associated with the classical statistics.

Time-to-event analysis of sexually transmitted infection data is often complicated by the existence of nonproportional hazards and nonlinear independent variable effects. Methods without the proportional hazards assumption, such as threshold regression models, have been successfully used in many applications. This paper seeks to extend the existing threshold regression models to accommodate the nonlinear independent variable effects. Specifically, we incorporated penalized and regression splines to the threshold regression models for added modeling flexibility. Cross validation methods were used for the selection of the number of knots and for the determination of smoothing parameters. Variance estimates were proposed for inference purposes. Simulation results showed that the proposed methods were able to achieve nonparametric function and parametric coefficient estimates that are close to their true values. Simulation also demonstrated satisfactory performance of variance estimates. Using the proposed methods, we analyzed time from sexual debut to the first infection with Chlamydia trachomatis infection in a group of young women. Analysis shows that the lifetime number of sexual partners has a nonlinear effect on the risk of C. trachomatis infection and the infection risks were differential by ethnicity and age of sexual debut.

PurposeThis study examines the impact of structural shocks and policy interventions on the India/US exchange rate post the 1991 economic reforms in India. The study aims to improve forecasting accuracy by incorporating macroeconomic and microeconomic factors into the analysis using the threshold regression model (TRM), a nonlinear approach to estimation.Design/methodology/approachExtending Dornbusch’s (1976) overshooting model, the study incorporates micro factors, such as investor behaviour, beliefs and preferences, alongside traditional macroeconomic variables. Additionally, it introduces a capital control variable to assess monetary policy interventions. Using quarterly data from 1996Q2 to 2019Q3, TRM identifies two distinct economic regimes, providing a comprehensive understanding of India’s exchange rate dynamics.FindingsThe study reveals that macro and micro factors have varying effects on the exchange rate across regimes, reflecting India’s different economic conditions and policies. Furthermore, the TRM-based model achieves superior out-of-sample forecasting accuracy compared to the random walk model across all forecast horizons.Originality/valueUnlike prior studies, where not all variables were deemed significant, our analysis demonstrates that all factors significantly influence the exchange rate. The innovative use of TRM deepens understanding of exchange rate behaviour, particularly in response to structural shocks and policy shifts. By identifying distinct economic regimes, the model offers insights into targeted policy measures tailored to India’s economic conditions, a previously unexplored perspective.

Interval estimation of multicomponent stress–strength reliability based on inverse Weibull distribution

Theory: Bootstrapping is a nonparametric approach to statistical inference that relies on large amounts of computation rather than mathematical analysis and distributional assumptions of traditional parametric inference. It has been shown to provide asymptotically accurate inferences for a wide variety of statistics. Hypothesis: Bootstrapping may make more accurate inferences than the parametric approach under two general circumstances: 1) when the assumptions of parametric inference are not tenable, and 2) when no parametric alternative exists for a problem. Methods: Monte Carlo simulation is used to test the performance of bootstrap and parametric confidence intervals for both types of situations in which bootstrapping is hypothesized to be superior to parametric inference. A single data example is used to illustrate the use of the bootstrap: a seats/votes model of U.S. House elections from 1932 to 1988. Results: My central conclusions are that in the cases examined: 1) bootstrap confidence intervals are at least as good as the parametric confidence interval and sometimes better, 2) OLS parametric confidence intervals do not perform too badly when the model error is non-normal, especially as sample size increases, and 3) when no parametric alternative exists, the bootstrap provides a reasonable method of making statistical inferences.

Process capability indices (PCIs) are most effective devices/techniques used in industries for determining the quality of products and performance of manufacturing processes. In this article, we consider the process capability index which is based on an asymmetric loss function (linear exponential) and is applicable to normally as well as non-normally distributed processes. In order to estimate the PCI when the process follows exponentiated exponential distribution, we have used ten classical methods of estimation and the performances of these classical estimates for the index are compared in terms of mean squared errors (MSEs) through simulation study. Also, the confidence intervals for the index are constructed based on four bootstrap confidence interval (BCIs) methods. A simulation study is performed in order to compare the performance of these four BCIs in terms of average width and coverage probabilities. We use two published data sets related to electronic and food industries to illustrate the performance of the proposed methods of estimation and BCIs. All the data sets show that width of bias-corrected accelerated bootstrap interval is the lowest among all other considered BCIs.

In this article, we consider six process capability indices (PCIs) whose quality characteristics have a normal distribution, out of which first PCI 𝒞 p {\mathcal{C}_{p}} was developed in [J. M. Juran, Juran’s Quality Control Handbook, 3rd ed., McGraw-Hill, New York, 1974], next PCI 𝒞 p ⁢ m {\mathcal{C}_{pm}} was developed in [T. C. Hsiang and G. Taguchi, A tutorial on quality control and assurance, Annual Meeting on the American Statistical Association, Las Vegas 1985], third PCI 𝒞 p ⁢ m ⁢ c {\mathcal{C}_{pmc}} was developed in [M. Saha, S. Dey and L. Wang, Parametric inference of the loss based index C p ⁢ m C_{pm} for normal distribution, Qual. Reliab. Eng. Int. 38 2022, 10.1002/qre.2987], fourth PCI 𝒞 p ⁢ m ′ {\mathcal{C}^{\prime}_{pm}} was developed in [S. Dey, W. Wang and M. Saha, Modified estimation and confidence intervals of an asymmetric loss based process capability index 𝒞 p ⁢ m ′ \mathcal{C}^{\prime}_{pm} , Qual. Reliab. Eng. Int. 38 2022, 8, 4033–4048], fifth PCI 𝒞 p ⁢ c {\mathcal{C}_{pc}} and sixth one 𝒞 p ⁢ m ⁢ c ′ {\mathcal{C}^{\prime}_{pmc}} are newly proposed in the paper. Next, we estimate the cited process capability indices using the method of moment estimation (MOM) approach when the underlying process follows normal distribution. A simulation study is conducted to evaluate the performance of these indices with respect to their mean squared errors. Additionally, confidence intervals are constructed using the asymptotic confidence interval (ACI), the generalized confidence interval (GCI) and parametric bootstrap confidence interval (BCI). Using Monte Carlo simulation, the performance of the GCI and BCI is compared in terms of average width and associated coverage probabilities. Finally, four data sets, two related to electronic industries and two related to food industries are re-analyzed to show the applicability’s of the suggested indices, MOM estimation, GCI and BCI.

Maastricht convergence and real convergence: European evidence from threshold and smooth transition regression models