Block Bootstrap Method Research Articles

Small data reliability analysis in concrete three-point bending tests: A Weibull mixture model approach based on Weibull fracture theory

Due to the high costs and time-consuming nature of experiments, data from concrete three-point bending tests are usually limited. Additionally, the performance of concrete is influenced by various factors such as mix composition and sample preparation methods, leading to significant variability in test results. This poses a major challenge for the reliability analysis of small data from repeated tests. In reliability analysis, statistical models are particularly important as they allow for the prediction of performance and failure probabilities based on existing data. However, traditional statistical methods require a large number of similar samples for data processing and may need specific adjustments due to the diversity of practical applications. To address these issues, this study proposes a mixture model that combines domain knowledge of concrete with Weibull fracture theory and uses the Clustering-Circular Block Bootstrap method for sample augmentation. By analyzing real data obtained from concrete three-point bending tests, we accurately estimated the failure probability of concrete. Additionally, the study uses Gaussian process regression with a spectral mixture kernel function to fit the threshold fracture strength of concrete and estimate failure probabilities. The results show that the proposed method can accurately fit small datasets, with a RMSE of 0.320 and a MAPE of 0.100. The nominal bending strength range at a 5% failure probability is 2.0 MPa to 6.5 MPa, depending on the sample height and pre-crack length. Statistical learning demonstrates that the proposed method excels in fitting small datasets, providing a solid framework for predicting concrete strength and reliability.

On Sample Size Needed for Block Bootstrap Confidence Intervals to Have Desired Coverage Rates

Block bootstrap is widely used in constructing confidence intervals for parameters estimated from stationary time series. Theoretically, the method should provide valid confidence intervals as the length of the time series goes to infinity. In practice, however, it is necessary to know how large of a finite sample is required for block bootstrap confidence intervals to work well. This study aims to answer this question in a simple simulation setting where the data are generated from a first-order autoregressive process. The empirical coverage rates of several commonly used bootstrap confidence intervals for the mean, standard deviation, and the lag-1 autocorrelation coefficient are compared. A quite large sample is found necessary for the intervals to have the right coverage rates even when estimating a simple parameter like the mean. Some block bootstrap methods could fail when estimating the lag-1 autocorrelation. It is surprising that the coverage property even deteriorates as the sample size increases with some commonly used block bootstrap confidence intervals including the percentile intervals and bias-corrected intervals. KEYWORDS: Autocorrelation; Bias-Correction; Centering; Dependent Data; Percentile; Resampling; Simulation; Time Series

Modified Block Bootstrap Testing for Persistence Change in Infinite Variance Observations

This paper investigates the properties of the change in persistence detection for observations with infinite variance. The innovations are assumed to be in the domain of attraction of a stable law with index κ∈(0,2]. We provide a new test statistic and show that its asymptotic distribution under the null hypothesis of non-stationary I(1) series is a functional of a stable process. When the change point in persistence is not known, the consistency is always given under the alternative, either from stationary I(0) to non-stationary I(1) or vice versa. The proposed tests can be used to identify the direction of change and do not over-reject against constant I(0) series, even in relatively small samples. Furthermore, we also consider the change point estimator which is consistent and the asymptotic behavior of the test statistic in the case of near-integrated time series. A block bootstrap method is suggested to determine critical values because the null asymptotic distribution contains the unknown tail index, which results in critical values depending on it. The simulation study demonstrates that the block bootstrap-based test is robust against change in persistence for heavy-tailed series with infinite variance. Finally, we apply our methods to the two series of the US inflation rate and USD/CNY exchange rate, and find significant evidence for persistence changes, respectively, from I(0) to I(1) and from I(1) to I(0).

Normality of the T-tests for Buy and Sell Days from Moving Average Trading Rules on the NASDAQ

In this article, we examine the sampling distributions of the T-ratios commonly used to support the exam of the market efficiency. From the p-values and the fixed block bootstrap methods, it shows that those T-ratios are far from the standard normal distribution claimed by numerous previous studies. Therefore, the T-ratios should not be used to test whether or not the market is efficient.

Remaining Useful Life Prediction of PV Systems Under Dynamic Environmental Conditions

Solar power is one of the least carbon-intensive approaches for electricity generation, and so photovoltaic (PV) systems have great potential as a low-carbon technology during their long lifecycle. Consequently, remaining useful life (RUL) prediction is critical for the prognostics and health management of PV systems, potentially preventing unexpected failure and maintenance due to PV degradation. One of the major root causes of PV degradation is the dynamic environmental conditions associated with PV outdoor operation. However, RUL prediction under such dynamic environmental conditions remains challenging. This article presents a semiparametric prognostic framework for PV systems under dynamic environmental conditions. The quantitative relationship between PV degradation and environmental conditions is established to integrate environmental condition information into RUL prediction, combining the cumulative damage model with multivariate Bernstein bases. The block bootstrap method is used to estimate future environmental conditions as inputs for RUL prediction. The least-squares estimators of the model parameters can be obtained through the block coordinate descent method. Finally, applications to field data of Australian PV systems are presented to demonstrate the effectiveness of the proposed method. The proposed framework is applicable to most PV technologies.

Bootstrapping the Seasonal Means and the Overall Mean in Rainfall Time Series

Several bootstrap methods have been studied nowadays for estimating the parameters in periodic data and it is important to consider the periodicity present in choosing the right bootstrap method. In this study we conducted a comparison of the performance of several block bootstrap methods designed for dependent data in the case of a real data time series with periodic structure such as the rainfall time series that is a time series with meteorological data collected monthly in a region in Albania. R programming language is used to perform the bootstrap and to obtain the results. We proposed a block bootstrap procedure in the case of estimating the seasonal means and the overall mean in the time series studied and based on the results obtained we notice a good performance of our proposed bootstrap procedure compared with other procedures considered.
 
 Received: 12 January 2023 / Accepted: 16 March 2023 / Published: 20 March 2023

Chaotic diffusion of the fundamental frequencies in the Solar System (Corrigendum)

The long-term variations in the orbit of the Earth govern the insolation on its surface and hence its climate. The use of the astronomical signal, whose imprint has been recovered in the geological records, has revolutionized the determination of the geological timescales. However, the orbital variations beyond 60 Myr cannot be reliably predicted because of the chaotic dynamics of the planetary orbits in the Solar System. Taking this dynamical uncertainty into account is necessary for a complete astronomical calibration of geological records. Our work addresses this problem with a statistical analysis of 120 000 orbital solutions of the secular model of the Solar System ranging from 500 Myr to 5 Gyr. We obtain the marginal probability density functions of the fundamental secular frequencies using kernel density estimation. The uncertainty of the density estimation is also obtained here in the form of confidence intervals determined by the moving block bootstrap method. The results of the secular model are shown to be in good agreement with those of the direct integrations of a comprehensive model of the Solar System. Application of our work is illustrated on two geological data sets: the Newark-Hartford records and the Libsack core.

Reliability in Portfolio Optimization using Uncertain Estimates

Portfolio optimization problems are rather easy to solve if one assumes normality of the (joint) distribution of returns with given parameters and a linear objective function, subject to some risk constraints. Higher degrees of complexities arise when taking into account (i) non- linear asset classes, (ii) non-normal distributions, (iii) constraints on lot size, portfolio shares etc., and (iv) uncertainty of parameter estimates. In this paper a Reliability-Based Design Optimization (RBDO) framework is developed to tackle the last two issues, namely, to solve portfolio optimization problems, taking into account the constraints on lot sizes, portfolio shares, etc., and the uncertainty of parameter estimates (i.e., return and risk). Thereby, standard methods and heuristics, available in the literature for handling reliability-based constraints, are adopted. The Block-Bootstrap method is used to obtain estimates of the uncertainty of parameter estimates. For an application to stocks which are components of the DAX, efficient portfolios are obtained taking into account the trade-off between optimal values of the objective function and the reliability of results.

Robust market timing tests of Canadian hybrid mutual funds

PurposePrior research has documented inconclusive and/or mixed empirical evidence on the timing performance of hybrid funds. Their performance inferences generally do not efficiently control for fixed-income exposure, conditioning information, and cross-correlations in fund returns. This study examines the stock and bond timing performances of hybrid funds while controlling and accounting for these important issues. It also discusses the inferential implications of using alternative bootstrap resampling approaches.Design/methodology/approachWe examine the stock and bond timing performances of hybrid funds using (un)conditional multi-factor benchmark models with robust estimation inferences. We also rely on the block bootstrap method to account for cross-correlations in fund returns and to separate the effects of luck or sampling variation from manager skill.FindingsWe find that the timing performance of portfolios of funds is neutral and sensitive to controlling for fixed-income exposures and choice of the timing measurement model. The block-bootstrap analyses of funds in the tails of the distributions of stock timing performances suggest that sampling variation explains the underperformance of extreme left tail funds and confirms the good and bad luck in the bond timing management of tail funds. We report inference changes based on whether the Kosowski et al. or the Fama and French bootstrap approach is used.Originality/valueThis study provides extensive and robust evidence on the stock and bond timing performances of hybrid funds and their sensitivity based on (un)conditional linear multi-factor benchmark models. It examines the timing performances in the extreme tails funds using the block bootstrap method to efficiently identify (un)skilled fund managers. It also highlights the sensitivity of inferences to the choice of testing methodology.

Application of dynamic mode decomposition to Rossi-α method in a critical state using file-by-file moving block bootstrap method

ABSTRACT Prompt neutron decay constant in a critical state is useful information to validate the numerically predicted ratio of the point kinetics parameters , where and are the effective delayed neutron fraction and prompt neutron lifetime, respectively. To directly measure in a target critical system, this study proposes the application of the dynamic mode decomposition (DMD) to the reactor noise analysis based on the Rossi- method. The DMD-based Rossi- method enables us to robustly estimate the fundamental mode component of from the Rossi- histograms measured using multiple neutron detectors. Furthermore, the file-by-file moving block bootstrap method is newly proposed for the statistical uncertainty quantification of to prevent huge memory usage when the neutron count rate is high and/or the total measurement time is long. A critical experiment has been conducted at Kyoto University Critical Assembly to demonstrate the proposed method. As a result, the proposed method can uniquely determine the value of which the statistical uncertainty is smallest. By utilizing this experimental result of , numerical results of ratio using the continuous energy Monte Carlo code MCNP6.2 with recent nuclear data libraries, which are processed by the nuclear data processing code FRENDY, are validated.

Applying block bootstrap methods in silver prices forecasting

Applying block bootstrap methods in silver prices forecasting

Chaotic diffusion of the fundamental frequencies in the Solar System

The long-term variations in the orbit of the Earth govern the insolation on its surface and hence its climate. The use of the astronomical signal, whose imprint has been recovered in the geological records, has revolutionized the determination of the geological timescales. However, the orbital variations beyond 60 Myr cannot be reliably predicted because of the chaotic dynamics of the planetary orbits in the Solar System. Taking this dynamical uncertainty to account is necessary for a complete astronomical calibration of geological records. Our work addresses this problem with a statistical analysis of 120 000 orbital solutions of the secular model of the Solar System ranging from 500 Myr to 5 Gyr. We obtain the marginal probability density functions of the fundamental secular frequencies using kernel density estimation. The uncertainty of the density estimation is also obtained here in the form of confidence intervals determined by the moving block bootstrap method. The results of the secular model are shown to be in good agreement with those of the direct integrations of a comprehensive model of the Solar System. Application of our work is illustrated on two geological data sets: the Newark-Hartford records and the Libsack core.

On the Construction of Bootstrap Confidence Intervals for Estimating the Correlation Between Two Time Series Not Sampled on Identical Time Points

Two important issues characterize the design of bootstrap methods to construct confidence intervals for the correlation between two time series sampled (unevenly or evenly spaced) on different time points: (i) ordinary block bootstrap methods that produce bootstrap samples have been designed for time series that are coeval (i.e., sampled on identical time points) and must be adapted; (ii) the sample Pearson correlation coefficient cannot be readily applied, and the construction of the bootstrap confidence intervals must rely on alternative estimators that unfortunately do not have the same asymptotic properties. In this paper it is argued that existing proposals provide an unsatisfactory solution to issue (i) and ignore issue (ii). This results in procedures with poor coverage whose limitations and potential applications are not well understood. As a first step to address these issues, a modification of the bootstrap procedure underlying existing methods is proposed, and the asymptotic properties of the estimator of the correlation are investigated. It is established that the estimator converges to a weighted average of the cross-correlation function in a neighborhood of zero. This implies a change in perspective when interpreting the results of the confidence intervals based on this estimator. Specifically, it is argued that with the proposed modification of the bootstrap, the existing methods have the potential to provide a useful lower bound for the absolute correlation in the non-coeval case and, in some special cases, confidence intervals with approximately the correct coverage. The limitations and implications of the results presented are demonstrated with a simulation study. The extension of the proposed methodology to the problem of estimating the cross-correlation function is straightforward and is illustrated with a real data example. Related applications include the estimation of the autocorrelation function and the periodogram of a time series.

Models for Expected Returns with Statistical Factors

In this paper, we propose multifactor models for the pan-European Equity Market using a block-bootstrap method and compare the results with those of traditional inferential techniques. The new factors are built from statistical measurements on stock prices—in particular, coefficient of variation, skewness, and kurtosis. Data come from Reuters, correspond to nearly 2000 EU companies, and span from January 2008 to February 2018. Regarding methodology, we propose a non-parametric resampling procedure that accounts for time dependency in order to test the validity of the model and the significance of the parameters involved. We compare our bootstrap-based inferential results with classical proposals (based on F-statistics). Methods under assessment are time-series regression, cross-sectional regression, and the Fama–MacBeth procedure. The main findings indicate that the two factors that better improve the Capital Asset Pricing Model with regard to the adjusted R2 in the time-series regressions are the skewness and the coefficient of variation. For this reason, a model including those two factors together with the market is thoroughly studied. We also observe that our block-bootstrap methodology seems to be more conservative with the null of the GRS test than classical procedures.

A note on stationary bootstrap variance estimator under long-range dependence

The stationary bootstrap method is popularly used to compute the standard errors or confidence regions of estimators, generated from time processes exhibiting weakly dependent stationarity. Most previous stationary bootstrap methods have focused on studying large-sample properties of stationary bootstrap inference about a sample mean under short-range dependence. For long-range dependence, recent studies have investigated the properties of block bootstrap methods using overlapping and non-overlapping blocking techniques with fixed block lengths. However, the characteristics of a stationary bootstrap with random block lengths are less well-known under long-range dependence. We investigate the asymptotic property of a stationary bootstrap variance estimator for a sample mean under long-range dependence. Our theoretical and simulation results indicate that the stationary bootstrap method does not have n−consistency for stationary and long-range dependent time processes.

Varying Coefficient Panel Data Model with Interactive Fixed Effects

In this paper, we propose a varying coefficient panel data model with unobservable multiple interactive fixed effects that are correlated with the regressors. We approximate each coefficient function by B-spline, and propose a robust nonlinear iteration scheme based on the least squares method to estimate the coefficient functions of interest. We also establish the asymptotic theory of the resulting estimators under certain regularity assumptions, including the consistency, the convergence rate and the asymptotic distribution. Furthermore, we develop a least squares dummy variable method to study an important special case of the proposed model: the varying coefficient panel data model with additive fixed effects. To construct the pointwise confidence intervals for the coefficient functions, a residual-based block bootstrap method is proposed to reduce the computational burden as well as to avoid the accumulative errors. Simulation studies and a real data analysis are also carried out to assess the performance of our proposed methods.

Phase Relation Between Large and Simple Sunspot Groups in Solar Cycles 22 – 24

In order to investigate the phase relation between the temporal variations of sunspot groups of various classes, firstly we use the separation scheme that was introduced by Kilcik et al. (Solar Phys.289, 4365, 2014b) to separate sunspot groups into large sunspot groups (D, E, and F classes in the modified Zurich classification) and simple sunspot groups (A and B classes) in Solar Cycles 22 – 24 collected by the United States Air Force/Mount Wilson Observatory (USAF/MWL). Then, using lagged-cross-correlation analysis and the block-bootstrap method, we calculate the correlation coefficients against time lags and determine the statistical significance of phase relation between large and simple sunspot groups in Solar Cycles 22 – 24, respectively. The main results that we obtained are summarized as follows: i) During Solar Cycles 22 and 24, the results – large sunspot groups lead or lag simple sunspot groups – are statistically insignificant and large sunspot groups should be in phase with simple sunspot groups. ii) During Solar Cycle 23, large sunspot groups statistically significantly lag simple sunspot groups in temporal phase.

A Probabilistic Uncertainty Estimation Method for Turbulence Parameters Measured by Hot-Wire Anemometry in Short-Duration Wind Tunnels

Abstract A robust and complete uncertainty estimation method is developed to quantify the uncertainty of turbulence quantities measured by hot-wire anemometry (HWA) at the inlet of a short-duration turbine test rig. The uncertainty is categorized into two macro-uncertainty sources: the measurement-related uncertainty (the uncertainty of each instantaneous velocity sample) and the uncertainty stemming from the statistical treatment of the time series. The former is addressed by the implementation of a Monte Carlo (MC) method. The latter, which is directly related to the duration of the acquired signal, is estimated using the moving block bootstrap (MBB) method, a nonparametric resampling algorithm suitable for correlated time series. This methodology allows computing the confidence intervals of the spanwise distributions of mean velocity, turbulence intensity, length scales, and other statistical moments at the inlet of the turbine test section.

Accurate experimental benchmark study of a catamaran in regular and irregular head waves including uncertainty quantification

Irregular wave experiments are essential to assess the statistics of ship responses in realistic operating conditions and to validate the associated numerical simulations. The cost and time required to achieve statistically-converged results are usually high (both experimentally and computationally). For these reasons, high-quality statistically-converged irregular wave studies are limited in the literature and models to reduce the experimental/computational costs are highly desirable. Here, a statistically-converged experimental benchmark study of a catamaran in irregular waves is presented, along with regular-wave Uncertainty Quantification (UQ) model used to approximate the relevant statistical estimators. The statistical assessment is achieved through recently-developed approaches based on the analysis of the autocovariance function of the ship response, along with block-bootstrap and bootstrap methods. The validation variables are the wave elevation, axial force, heave and pitch motions, vertical acceleration of the bridge and vertical velocity of the flight-deck. Values from the time series are addressed as primary variables, whereas heights associated to mean-crossing waves are referred to as secondary variables. The statistical uncertainty related to Expected Value (EV) and Standard Deviation (SD) of primary variables is evaluated through autocovariance analysis and block-bootstrap methods. The latter are used to assess also the quantile function. EV, SD, and quantile function of secondary variables are then assessed by the bootstrap method. Regular-wave models assess the EV of the axial force, and single significant amplitudes (twice the SD) of pitch, acceleration, and velocity, as relevant merit factors used for design optimization in earlier studies.

Moving block and tapered block bootstrap for functional time series with an application to the $K$-sample mean problem

We consider infinite-dimensional Hilbert space-valued random variables that are assumed to be temporal dependent in a broad sense. We prove a central limit theorem for the moving block bootstrap and for the tapered block bootstrap, and show that these block bootstrap procedures also provide consistent estimators of the long run covariance operator. Furthermore, we consider block bootstrap-based procedures for fully functional testing of the equality of mean functions between several independent functional time series. We establish validity of the block bootstrap methods in approximating the distribution of the statistic of interest under the null and show consistency of the block bootstrap-based tests under the alternative. The finite sample behaviour of the procedures is investigated by means of simulations. An application to a real-life dataset is also discussed.