Moving Block Bootstrap Method Research Articles

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.

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.

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.

Experimental validation of unique combination numbers for third- and fourth-order neutron correlation factors of zero-power reactor noise

ABSTRACT Zero-power reactor noise is useful for subcriticality measurements. Based on the nuclear reactor physics and the theory of neutron detection, this paper theoretically clarifies that the third- and fourth-order neutron correlation factors and can be expressed as functions of the second-order neutron correlation factor . In particular, if the neutron-counting gate width is sufficiently large, the saturation values and are almost equal to the unique combination numbers, ‘3’ and ‘15,’ for a source-driven subcritical system, where the subcriticality is less than 10,000 pcm. These unique combination numbers, ‘3’ and ‘15,’ for and were validated using actual zero-power reactor noise measurements carried out at the Kyoto University Criticality Assembly. In this study, the estimation of statistical errors and correlations between different gate widths owing to the bunching method was achieved by the moving block bootstrap method. For a sufficiently long measured reactor noise in a steady and unperturbed state, a statistical test for the evaluation of the critical state and the absolute measurement of subcriticality can be carried out by statistically quantifying the difference between the measurement value of and the unique combination number.

Bootstrap for almost cyclostationary processes with jitter effect

In this paper we consider almost cyclostationary processes with jitter effect. We propose a bootstrap approach based on the Moving Block Bootstrap method to construct pointwise and simultaneous confidence intervals for the Fourier coefficients of the autocovariance function of such processes. In the simulation study we show how our results can be used to detect the significant frequencies of the autocovariance function. We compare the behavior of our approach for jitter effects caused by perturbations from two distributions, namely uniform and truncated normal. Moreover, we present a real data application of our methodology.

Robust to noise and outliers estimator of correlation dimension

The estimation of correlation dimension of continuous and discreet deterministic chaotic processes corrupted by an additive noise and outliers observations is investigated. In this paper we propose a new estimator of correlation dimension based on similarity between the evolution of Gaussian kernel correlation sum (Gkcs) and that of modified Boltzmann sigmoidal function (mBsf), this estimator is given by the maximum value of the first derivative of logarithmic transform of Gkcs against logarithmic transform of bandwidth, so the proposed estimator is independent of the choice of regression region like other regression estimators of correlation dimension. Simulation study indicates the robustness of proposed estimator to the presence of different types of noise such us independent Gaussian noise, non independent Gaussian noise and uniform noise for high noise level, moreover, this estimator is also robust to presence of 60% of outliers observations. Application of this new estimator with determination of their confidence interval using the moving block bootstrap method to adjusted closed price of S&P500 index daily time series revels the stochastic behavior of such financial time series.

Wind power prediction interval estimation method using wavelet-transform neuro-fuzzy network

Wind power point forecasting is the primary method to deal with its uncertainty. However, in many applications, the probabilistic interval of wind power is more useful than traditional point forecasting. Methods to determine the probabilistic interval of wind power point forecasting value is very essential to power system operations. Based on the bootstrap method, this paper proposed a wavelet transform combined with a neuro-fuzzy network model to estimate the prediction interval of wind power. In the model, to account for the ramp event of wind power series, a wavelet-based ramp event was used and the moving block bootstrap method, which considers the dependence of wind power series, was used to construct sampling datasets. Then, the bootstrapped datasets were estimated by a neuro-fuzzy network inference system. A case study provided a 90% confidence level of prediction intervals, which was constructed to examine the effectiveness of the model.

Testing cointegration relationship in a semiparametric varying coefficient model

In this paper, we develop two cointegration tests for two varying coefficient cointegration regression models, respectively. Our test statistics are residual based. We derive the asymptotic distributions of test statistics under the null hypothesis of cointegration and show that they are consistent against the alternative hypotheses. We also propose a wild bootstrap procedure companioned with the continuous moving block bootstrap method proposed in Paparoditis and Politis (2001) and Phillips (2010) to rectify severe distortions found in simulations when the sample size is small. We apply the proposed test statistic to examine the purchasing power parity (PPP) hypothesis between the US and Canada. In contrast to the existing results from linear cointegration tests, our varying coefficient cointegration test does not reject that PPP holds between the US and Canada.

Dynamic GSCA (Generalized Structured Component Analysis) with Applications to the Analysis of Effective Connectivity in Functional Neuroimaging Data

We propose a new method of structural equation modeling (SEM) for longitudinal and time series data, named Dynamic GSCA (Generalized Structured Component Analysis). The proposed method extends the original GSCA by incorporating a multivariate autoregressive model to account for the dynamic nature of data taken over time. Dynamic GSCA also incorporates direct and modulating effects of input variables on specific latent variables and on connections between latent variables, respectively. An alternating least square (ALS) algorithm is developed for parameter estimation. An improved bootstrap method called a modified moving block bootstrap method is used to assess reliability of parameter estimates, which deals with time dependence between consecutive observations effectively. We analyze synthetic and real data to illustrate the feasibility of the proposed method.

Dlouhá paměť a její vývoj ve výnosech burzovního indexu PX v letech 1997-2009

Long-term memory processes have been extensively examined in recent literature as they provide simple way to test for predictabilty in the underlying process. However, most of the literature interprets the results of estimated Hurst exponent simply by its comparison to its asymptotic limit of 0.5. Therefore, we use moving block bootstrap method for rescaled range and periodogram method. In our analysis of evolution of Hurst exponent between 1997 and 2009, we show that PX experienced persistent behavior which weakened in time. Nevertheless, the returns of PX remain close to confidence interval separating independent and persistent behavior.

A comparison of block and semi-parametric bootstrap methods for variance estimation in spatial statistics

Efron (1979) introduced the bootstrap method for independent data but it cannot be easily applied to spatial data because of their dependency. For spatial data that are correlated in terms of their locations in the underlying space the moving block bootstrap method is usually used to estimate the precision measures of the estimators. The precision of the moving block bootstrap estimators is related to the block size which is difficult to select. In the moving block bootstrap method also the variance estimator is underestimated. In this paper, first the semi-parametric bootstrap is used to estimate the precision measures of estimators in spatial data analysis. In the semi-parametric bootstrap method, we use the estimation of the spatial correlation structure. Then, we compare the semi-parametric bootstrap with a moving block bootstrap for variance estimation of estimators in a simulation study. Finally, we use the semi-parametric bootstrap to analyze the coal-ash data.

Uncovering Gene Regulatory Networks from Time-Series Microarray Data with Variational Bayesian Structural Expectation Maximization

We investigate in this paper reverse engineering of gene regulatory networks from time-series microarray data. We apply dynamic Bayesian networks (DBNs) for modeling cell cycle regulations. In developing a network inference algorithm, we focus on soft solutions that can provide a posteriori probability (APP) of network topology. In particular, we propose a variational Bayesian structural expectation maximization algorithm that can learn the posterior distribution of the network model parameters and topology jointly. We also show how the obtained APPs of the network topology can be used in a Bayesian data integration strategy to integrate two different microarray data sets. The proposed VBSEM algorithm has been tested on yeast cell cycle data sets. To evaluate the confidence of the inferred networks, we apply a moving block bootstrap method. The inferred network is validated by comparing it to the KEGG pathway map.