Bootstrapping endpoint

Weighted Approximations of Tail Copula Processes with Application to Testing the Multivariate Extreme Value Condition

A stress and strain partition theory for two phase alloys was developed on the basis of the modified rules of mixtures. The extreme value condition of macroscopic strain energy density was found through Lagrangian multiplier method. Expressions for macroscopic elastic constants of two phase alloys were derived from the extreme value condition by assuming the strain linearity between constituent phases. Governing equation for stress and strain partition in plastic deformation was also obtained from the extreme value condition. The calculated elastic constants of WC-Co alloys fell invariably within the Hashin and Shtrikman's bounds. According to the governing equation the stress ratio between constituent phases was plotted as a function of strain increment ratio. By applying the governing equation to spheroidized carbon steel and duplex stainless steel, it was shown that the stress ratios, strain ratios, macroscopic stress-strain curves, and internal stresses could be evaluated from thein situ stress-strain curves of constituent phases.

Doubly truncated data consist of samples whose observed values fall between the right- and left- truncation limits. With such samples, the distribution function of interest is estimated using the nonparametric maximum likelihood estimator (NPMLE) that is obtained through a self-consistency algorithm. Owing to the complicated asymptotic distribution of the NPMLE, the bootstrap method has been suggested for statistical inference. This paper proposes a closed-form estimator for the asymptotic covariance function of the NPMLE, which is computationally attractive alternative to bootstrapping. Furthermore, we develop various statistical inference procedures, such as confidence interval, goodness-of-fit tests, and confidence bands to demonstrate the usefulness of the proposed covariance estimator. Simulations are performed to compare the proposed method with both the bootstrap and jackknife methods. The methods are illustrated using the childhood cancer dataset.

هدف از پژوهش کنونی بررسی دورنمایی از اثرات احتمالی تغییر اقلیم بر جابه‌جایی زمانی تاریخ وقوع اولین و آخرین یخبندان‌های پاییزه و بهارۀ ایران است. بدین منظور از داده‌های دیده‌بانی 43 ایستگاه همدید کشور (1981-2010) و داده‌های شبیه‌سازی شدۀ LARS WG در دو مدل آب‌وهوای جهانی GFCM21 و HadCM3 در بازه‌های زمانی (2065-2046) و (2099-2080)، تحت سه سناریوی انتشار A1B، A2 و B1استفاده گردید. نتایج، بیانگر جابه‌جایی اولین یخبندان پاییزه‌ به سمت اوایل زمستان و جابه‌جایی آخرین یخبندان بهاره به‌سوی اواخر زمستان در گسترۀ ایران است. پراکنش زمانی-مکانی تغییرات متفاوت است؛ به‌گونه‌ای که بیشترین جابه‌جایی‌های مثبت در رخداد اولین یخبندان پاییزه در دورۀ (2065-2046) در ایستگاه‌هایی چون خرم‌‌آباد، رشت و گرگان مشاهده می‌شود. میزان تغییرات در ایستگاه‌های شمال شرقی (سبزوار و سمنان)، نیمۀ جنوبی (کرمان، بم و آباده) و بیشتر ایستگاه‌های شمال‌غرب نسبت به دیگر مناطق کمتر است. در دورۀ (2080-2099) بیشترین روند منفی در ایستگاه‌های گرگان، رشت، اردبیل و شهرکرد خواهد بود. خوی، قزوین، بم و کاشان کمترین جابه‌جایی منفی خواهند داشت.

In the present paper we develop second-order theory using the subsample bootstrap in the context of Pareto index estimation. We show that the bootstrap is not second-order accurate, in the sense that it fails to correct the first term describing departure from the limit distribution. Worse than this, even when the subsample size is chosen optimally, the error between the subsample bootstrap approximation and the true distribution is often an order of magnitude larger than that oi tue asymptotic approximation. To overcome this deficiency, we show that an extrapolation method, based quite literally on a mixture of asymptotic and subsample bootstrap methods, can lead to second-order correct confidence intervals for the Pareto index.

To evaluate the fatigue reliability of the excavator working device, the fatigue tests of 2 sets of moving arm and bucket rod of medium-sized excavators with self-weight of 26000 kgwere carried out. The virtual augmented sample method (VASM) combined with Bootstrap method was used to analyze the reliability of the excavator working device under extreme small samples, and the interval and point estimations of life parameters were obtained. Based on the lognormal distribution of the excavator working device, the reliability evaluation model of the excavator working device was established, and reliability indexes, such as reliability function, failure distribution function, inefficiency function, reliable life and so on, were obtained. And the results of fatigue safety life under different confidence and reliability were calculated. The evaluation results show that the average failure time of the excavator working device is 6124 hours under the confidence of 75%, which provides an important reference for the design, the safety inspection and maintenance decision of the excavator working device.

Potential competing interests: No potential competing interests to declare

Review of: "Variable selection in generalized extreme value regression model using Bootstrap method"

Potential competing interests: No potential competing interests to declare.The presented methodology combines the Generalized Extreme Value (GEV) regression model with bootstrapping for variable selection and model assessment, aiming to develop a predictive model for rare and extreme events.While the approach appears promising, there are several points that needs to address.

It is well known that the standard independent, identically distributed (iid) bootstrap of the mean is inconsistent in a location model with infinite variance (α-stable) innovations. This occurs because the bootstrap distribution of a normalised sum of infinite variance random variables tends to a random distribution. Consistent bootstrap algorithms based on subsampling methods have been proposed but have the drawback that they deliver much wider confidence sets than those generated by the iid bootstrap owing to the fact that they eliminate the dependence of the bootstrap distribution on the sample extremes. In this paper we propose sufficient conditions that allow a simple modification of the bootstrap (Wu, 1986) to be consistent (in a conditional sense) yet to also reproduce the narrower confidence sets of the iid bootstrap. Numerical results demonstrate that our proposed bootstrap method works very well in practice delivering coverage rates very close to the nominal level and significantly narrower confidence sets than other consistent methods.

Over the last four decades, the bootstrap method has been considered so as to define data‐driven bandwidth selectors for nonparametric curve estimation. An extensive and updated review of bootstrap methods used to select the smoothing parameter for the nonparametric estimation of several curves has been carried out. Different data generating processes have been profoundly reviewed, such as the classical independent and identically distributed setup as well as dependent, censored, length‐biased, grouped, missing or directional data, among others. Several curves have also been considered, such as the density, regression, hazard rate, intensity, latency, incidence, or distribution functions, among many others. It is worth mentioning that there exist situations where Monte Carlo methods are not needed when using the bootstrap for bandwidth selections. This idea has also been exploited to find closed expressions for the bootstrap version of criterion functions for some proxy of the real curve estimator.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bootstrap and Resampling Statistical and Graphical Methods of Data Analysis > Nonparametric Methods Statistical and Graphical Methods of Data Analysis > Density Estimation

On goodness-of-fit and the bootstrap

It is important to examine the symmetry of an underlying distribution before applying some statistical procedures to a data set. For example, in the Zuni School District case, a formula originally developed by the Department of Education trimmed 5% of the data symmetrically from each end. The validity of this procedure was questioned at the hearing by Chief Justice Roberts. Most tests of symmetry (even nonparametric ones) are not distribution free in finite sample sizes. Hence, using asymptotic distribution may not yield an accurate type I error rate or/and loss of power in small samples. Bootstrap resampling from a symmetric empirical distribution function fitted to the data is proposed to improve the accuracy of the calculated p-value of several tests of symmetry. The results show that the bootstrap method is superior to previously used approaches relying on the asymptotic distribution of the tests that assumed the data come from a normal distribution. Incorporating the bootstrap estimate in a recently proposed test due to Miao, Gel and Gastwirth (2006) preserved its level and shows it has reasonable power properties on the family of distribution evaluated.

ABSTRACTIn this study, we consider an entropy-type goodness-of-fit (GOF) test based on integrated distribution functions. We first construct the test for the simple vs. simple hypothesis and then extend it to the composite hypothesis case. It is shown that under regularity conditions, the null limiting distribution of the proposed test is a function of a Brownian bridge. A bootstrap method is also considered and is shown to be weakly consistent. A simulation study and real data analysis are conducted for illustration.

We evaluated 12 types of bootstrap methods for estimating the confidence intervals of percentiles predicted from a dataset containing nondetected (ND) results of Monte Carlo simulation. The bootstrap prediction process, which computes the confidence intervals, comprises three steps: resampling, calculating bootstrap parameters and computing confidence intervals. We selected several methods—parametric or nonparametric methods for resampling, lognormal or truncated lognormal for parent distribution, and ‘percentile’, ‘bootstrap‐t’ or ‘BCa’ methods for computing the confidence intervals. The reliabilities of these bootstrap methods were compared. In addition, we used environmental monitoring data, which were obtained in 2002 from various rivers in Japan for the verification of the bootstrap methods. The bootstrap confidence intervals for the five proposed methods were compared from the viewpoint of reliability. Based on the results computed by the ‘lognormal, parametric, bootstrap‐t’ method (LN‐P‐Bt)—the most reliable method—95% of the upper confidence limits of the 95th percentiles were from 1.7 to 2.1 times greater than the 95th percentiles directly predicted from the actual sample, and the logarithmic ranges for 90% of the bootstrap confidence intervals varied from 3.0 to 4.4. With regard to the maximum value among the five applied methods, the 95% upper confidence limits of the 95th percentiles were from 3.5 to 7.0 times greater than the 95th percentiles. The parent distribution cannot be assumed to randomly conform to a parametric distribution function particularly in the case of environmental monitoring data. For the conservative estimates, the confidence limits should be comprehensively evaluated from the values estimated by several methods that are established on the basis of different assumptions. Copyright © 2006 John Wiley & Sons, Ltd.