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An active learning multi-fidelity metamodeling method based on the bootstrap estimator

AEROSPACE SCIENCE AND TECHNOLOGY 2020年 106卷 106116-106116页

作者： Wu, Yuda Hu, Jiexiang Zhou, Qi Wang, Shengyi Jin, Peng Huazhong Univ Sci & Technol Sch Aerosp Engn Wuhan 430074 Hubei Peoples R China

Multi-fidelity (MF) metamodel has attracted significant attention recently in simulation-based design and optimization. It can achieve a desirable modeling accuracy with relatively lower simulation cost by making use of the data from both low-fidelity (LF) and high-fidelity (HF) simulations. To facilitate the usage of MF metamodel, there are still challenging issues on (1) how to determine the location of sample points, and (2) how to allocate the limited computational budget to HF and LF simulations. In this study, a bootstrap-based sequential multi-fidelity (BB-SMF) metamodeling method is proposed for data regression of computationally expensive black-box problems. First, constrained optimization problems with the goal of reducing the global predicted error of the MF metamodel are constructed to obtain the candidates for HF and LF simulations, respectively. Specifically, the predicted error of the MF metamodel is evaluated by a developed MF bootstrap estimator. Second, a criterion based on the uncertainty of pseudo-updated MF metamodel is developed to determine whether one HF sample or several LF sample points with the equivalent computational budget are selected to update the MF metamodel. To demonstrate the performance of the proposed method, two analytical functions and a maximum stress prediction problem of the micro-aerial vehicle (MAV) fuselage are adopted. Different test conditions are also discussed, such as different correlation level, initial sample sizes, and cost ratios. Results show that the proposed BB-SMF metamodel is more accurate and robust than the compared methods. (C) 2020 Elsevier Masson SAS. All rights reserved.

关键词： Multi-fidelity metamodel bootstrap estimator Sequential sampling Simulation-based design Micro-aerial vehicle

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A nonlinear quantile regression for accelerated destructive degradation testing data

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IISE TRANSACTIONS 2025年第6期57卷 621-638页

作者： Bae, Suk Joo Lim, Munwon Hanyang Univ Dept Ind Engn Seoul South Korea

Traditional regression approaches to Accelerated Destructive Degradation test (ADDT) data have modeled the mean curve as being representative. However, maximum likelihood estimates of the mean model are likely to be biased when the data are non-Gaussian or highly skewed. The median model can be an alternative for skewed degradation data. In this work, we introduce a nonlinear Quantile Regression (QR) approach for estimating quantile curves of ADDT data. We propose an iterative QR algorithm that uses the generalized expectation-maximization framework to estimate the parameters of the nonlinear QR ADDT model, based on the asymmetric Laplace distribution to accommodate non-Gaussian and skewed errors. Using the asymptotic properties of the QR parameter estimates, we estimate variance-covariance matrix for the tau th QR parameters using order statistics and bootstrap methods. We propose a new prediction method of the quantile of the failure-time distribution in the normal use condition. Confidence intervals for the quantiles of the failure-time distribution are constructed using the parametric bootstrap method. The proposed model is illustrated using an industrial application and compared with the existing model. Various quantile curve estimates derived using the QR ADDT model provide a more flexible modeling framework than the traditional mean ADDT modeling approach.

关键词： Accelerated destructive degradation test asymmetric Laplace distribution bootstrap estimator generalized EM algorithm order statistic estimator

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Semiparametric Estimation in Transformation Models with Cure Fraction

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2010年第18期39卷 3371-3388页

作者： Zhao, Xiaobing Zhou, Xian Macquarie Univ Dept Actuarial Studies Sydney NSW 2109 Australia Zhejiang Univ Finance & Econ Sch Management & Stat Hangzhou Zhejiang Peoples R China

Semiparametric transformation model has been extensively investigated in the literature. The model, however, has little dealt with survival data with cure fraction. In this article, we consider a class of semi-parametric transformation models, where an unknown transformation of the survival times with cure fraction is assumed to be linearly related to the covariates and the error distributions are parametrically specified by an extreme value distribution with unknown parameters. estimators for the coefficients of covariates are obtained from pseudo Z-estimator procedures allowing censored observations. We show that the estimators are consistent and asymptotically normal. The bootstrap estimation of the variances of the estimators is also investigated.

关键词： bootstrap estimator Cure fraction Pseudo Z-estimator Semi-parametric transformation models

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On the validity of the residual-based bootstrap for the unit root test statistic with long memory observations

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2023年第2期52卷 309-319页

作者： Fu, Ke-Ang Li, Jie Zhejiang Univ City Coll Dept Stat Hangzhou 310015 Peoples R China Zhejiang Univ Finance & Econ Sch Data Sci Hangzhou Peoples R China

Consider the AR(1) model, X-t = theta Xt-1 + u(t), where {u(t), t >= 1} is a sequence of long memory processes with possibly infinite variance. In this paper, we propose to use a residual-based m-out-of-n bootstrap procedure to approximate the distribution of a least-squares estimator for the autoregressive parameter when this parameter is equal to unity, and its asymptotic validity is also proved.

关键词： Asymptotic distribution bootstrap estimator long memory unit root

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VARIANCE ESTIMATES IN LOGISTIC-REGRESSION USING THE bootstrap

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 1995年第2期24卷 473-486页

作者： FRIEDL, H TILG, N GRAZ TECH UNIV INST STATA-8010 GRAZAUSTRIA

Large-sample confidence intervals for the parameter beta under the binomial and extra-binomial variance model are presented. Alternative estimates of Var() are discussed, which all have a nice bootstrap interpretation... 详细信息

Large-sample confidence intervals for the parameter beta under the binomial and extra-binomial variance model are presented. Alternative estimates of Var(<(beta)over cap>) are discussed, which all have a nice bootstrap interpretation in the context of resampling from residuals or score components. The latter approach yields both a model-based and a robust estimate. Some properties of these estimates and their corresponding confidence intervals are also discussed. In an extensive simulation study we compare the coverage probabilities of the intervals supposing binomial variation as well as overdispersion.

关键词： BINARY REGRESSION OVERDISPERSION MAXIMUM-LIKELIHOOD estimator bootstrap estimator

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Estimation of the incidence of inefficiency using bootstrap and Bayesian estimators

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2024年

作者： Unsal, Mehmet Guray Friesner, Daniel Rosenman, Robert Edward Orkcu, Mediha Baskent Univ Fac Business & Adm Sci Dept Technol & Knowledge Management Baglica CampusEskisehir Rd 7th km Ankara Turkiye Univ Akron Coll Hlth & Human Sci Akron OH USA Washington State Univ Sch Econ Sci Pullman WA USA Gazi Univ Fac Sci Dept Math Ankara Turkiye

This paper compares estimates from nonparametric bootstrapping to Bayesian methods for the incidence of inefficiency (IOI) from Data Envelopment Analysis when applied to finite populations. We find for extremely simple production technologies (one input, one output, and a single ray production technology) with large sample sizes, nonparametric bootstrapping yields better estimates of the IOI compared to Bayesian methods that do and do not account for the latent aspect of the true IOI. As the production process becomes more complex, Bayesian methods, especially those that account for a latent IOI, outperform nonparametric bootstrapping methods. Our conclusion is that Bayesian methods are superior for estimating the IOI.

关键词： Bayesian estimator bootstrap estimator Incidence of Inefficiency Simulation

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Bias, precision, and accuracy of four measures of species richness

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ECOLOGICAL APPLICATIONS 1999年第3期9卷 824-834页

作者： Hellmann, JJ Fowler, GW Univ Michigan Sch Nat Resources & Environm Ann Arbor MI 48109 USA

Species richness is a widely used surrogate for the more complex concept of biological diversity. Because species richness is often central to ecological study and the establishment of conservation priorities, the biases and merits of richness measurements demand evaluation. The jackknife and bootstrap estimators can be used to compensate for the underestimation associated with simple richness estimation (or the sum of species courted in a sample). Using data from five forest communities, we analyzed the simple measure of richness, the first- and second-order jackknife, and the bootstrap estimators with simulation and resampling methods to examine the effects of sample size on estimator performance. Performance parameters examined were systematic under- or overestimation (bias), ability to estimate consistently (precision), and ability to estimate true species richness (accuracy). For small sample sizes in all studied communities (less than similar to 25% of the total community), the least biased estimator was the second-order jackknife, followed by the first-order jackknife, the bootstrap, and the simple richness estimator. However, with increases in sample size, the second-order jackknife, followed by the first-order jackknife and the bootstrap, became positively biased. The simple richness estimator was the most precise estimator in all studied communities, but it yielded the largest underestimate of species richness at all sample sizes. The relative precision of the four estimators did not differ across communities, but the magnitude of estimator variance is dependent on the sampled community. Differences in accuracy among the estimators were not independent of community, and accuracy patterns were associated with community species diversity. The results of this study can assist policy makers, researchers, and managers in the selection of appropriate sample sizes and estimators for richness estimation and should facilitate the ongoing assessment of local, and ul

关键词： biological diversity bootstrap estimator jackknife estimator, first- and second-order Monte Carlo simulation quadrat sampling resampling procedures sample size determination simple richness estimator species diversity species richness

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Permutation tests using least distance estimator in the multivariate regression model

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COMPUTATIONAL STATISTICS 2012年第2期27卷 191-201页

作者： Sohn, Sooncheol Jung, Byoung Cheol Jhun, Myoungshic Korea Univ Dept Stat Seoul 136701 South Korea Univ Seoul Dept Stat Seoul 130743 South Korea

This paper proposes two permutation tests based on the least distance estimator in a multivariate regression model. One is a type of t test statistic using the bootstrap method, and the other is a type of F test statistic using the sum of distances between observed and predicted values under the full and reduced models. We conducted a simulation study to compare the power of the proposed permutation tests with that of the parametric tests based on the least squares estimator for three types of hypotheses in several error distributions. The results indicate that the power of the proposed permutation tests is greater than that of the parametric tests when the error distribution is skewed like the Wishart distribution, has a heavy tail like the Cauchy distribution, or has outliers.

关键词： Least distance estimator Least squares estimator Permutation test bootstrap estimator

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SINGH THEOREM IN THE LATTICE CASE

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STATISTICS & PROBABILITY LETTERS 1988年第3期7卷 201-205页

作者： WOODROOFE, M JHUN, M Department of Statistics The University of Michigan 1444 Mason Hall Ann Arbor MI 48109-1027 USA

The asymptotic behavior of the parametric bootstrap estimator of the sampling distribution of a maximum likelihood estimator is investigated in a simple lattice case, integer valued random variables whose distributions form an exponential family. The expected value of the bootstrap estimator is compared with an Edgeworth expansion, less the continuity correction.

关键词： bootstrap estimator Edgeworth expansions fractional part maximum likelihood estimator very weak expansions

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An Efficient estimator for the Error Rate in Discriminant Analysis

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Statistics 1985年第1期16卷 107-119页

作者： Läuter, Henning Institut für Mathematik AdW der DDR DDR - 1086 Berlin Mohrenstr. 39 Germany

In this paper we discuss different approaches to the estimation of error rates in discriminant analysis. Especially we prove the asymptotic efficiency of an estimator of the bootstrap type and give some numerical results for the comparison of the resubstitution, the jackknife and the asymptotically efficient estimator. © 1985, Taylor & Francis Group, LLC. All rights reserved.

关键词： Asymptotic efficiency bootstrap estimator Error rates in discriminant analysis Lachenbruch estimator Resubstitution estimator U-statistics

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