A WILD BOOTSTRAP FOR DEPENDENT DATA

Econometric Theory ◽

10.1017/s0266466621000487 ◽

2021 ◽

pp. 1-26

Author(s):

Ulrich Hounyo

Keyword(s):

Smooth Function ◽

Bootstrap Method ◽

Confidence Regions ◽

Heterogeneous Data ◽

Stationary Time Series ◽

Dependent Data ◽

Wild Bootstrap ◽

Finite Sample ◽

Bootstrap Methods ◽

Sample Mean

This paper introduces a novel wild bootstrap for dependent data (WBDD) as a means of calculating standard errors of estimators and constructing confidence regions for parameters based on dependent heterogeneous data. The consistency of the bootstrap variance estimator for smooth function of the sample mean is shown to be robust against heteroskedasticity and dependence of unknown form. The first-order asymptotic validity of the WBDD in distribution approximation is established when data are assumed to satisfy a near epoch dependent condition and under the framework of the smooth function model. The WBDD offers a viable alternative to the existing non parametric bootstrap methods for dependent data. It preserves the second-order correctness property of blockwise bootstrap (provided we choose the external random variables appropriately), for stationary time series and smooth functions of the mean. This desirable property of any bootstrap method is not known for extant wild-based bootstrap methods for dependent data. Simulation studies illustrate the finite-sample performance of the WBDD.

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Confidence Regions for Parameters in Stationary Time Series Models With Gaussian Noise

Frontiers in Physics ◽

10.3389/fphy.2021.801692 ◽

2022 ◽

Vol 9 ◽

Author(s):

Xiuzhen Zhang ◽

Riquan Zhang ◽

Zhiping Lu

Keyword(s):

Time Series ◽

Empirical Likelihood ◽

Long Memory ◽

Score Function ◽

Real Data ◽

Confidence Regions ◽

Stationary Time Series ◽

Time Series Models ◽

Finite Sample ◽

Memory Time

This article develops two new empirical likelihood methods for long-memory time series models based on adjusted empirical likelihood and mean empirical likelihood. By application of Whittle likelihood, one obtains a score function that can be viewed as the estimating equation of the parameters of the long-memory time series model. An empirical likelihood ratio is obtained which is shown to be asymptotically chi-square distributed. It can be used to construct confidence regions. By adding pseudo samples, we simultaneously eliminate the non-definition of the original empirical likelihood and enhance the coverage probability. Finite sample properties of the empirical likelihood confidence regions are explored through Monte Carlo simulation, and some real data applications are carried out.

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k-NEAREST NEIGHBOR ESTIMATION OF INVERSE-DENSITY-WEIGHTED EXPECTATIONS WITH DEPENDENT DATA

Econometric Theory ◽

10.1017/s026646661100079x ◽

2012 ◽

Vol 28 (4) ◽

pp. 769-803 ◽

Cited By ~ 6

Author(s):

Ba Chu ◽

David T. Jacho-Chávez

Keyword(s):

Nearest Neighbor ◽

Time Series Data ◽

Asymptotic Variance ◽

Stationary Time Series ◽

Dependent Data ◽

Series Data ◽

Finite Sample ◽

K Nearest Neighbor ◽

Monte Carlo Experiments ◽

Unknown Density

This paper considers the problem of estimating expected values of functions that are inversely weighted by an unknown density using the k-nearest neighbor (k-NN) method. It establishes the $\root \of T $-consistency and the asymptotic normality of an estimator that allows for strictly stationary time-series data. The consistency of the Bartlett estimator of the derived asymptotic variance is also established. The proposed estimator is also shown to be asymptotically semiparametric efficient in the independent random sampling scheme. Monte Carlo experiments show that the proposed estimator performs well in finite sample applications.

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Mean Empirical Likelihood Inference for Response Mean with Data Missing at Random

Discrete Dynamics in Nature and Society ◽

10.1155/2020/8893594 ◽

2020 ◽

Vol 2020 ◽

pp. 1-12

Author(s):

Hanji He ◽

Guangming Deng

Keyword(s):

Empirical Likelihood ◽

Missing At Random ◽

Confidence Regions ◽

Likelihood Inference ◽

High Dimensional ◽

Finite Sample ◽

The Mean ◽

Data Missing ◽

Consistency And Asymptotic Normality ◽

The Impact

We extend the mean empirical likelihood inference for response mean with data missing at random. The empirical likelihood ratio confidence regions are poor when the response is missing at random, especially when the covariate is high-dimensional and the sample size is small. Hence, we develop three bias-corrected mean empirical likelihood approaches to obtain efficient inference for response mean. As to three bias-corrected estimating equations, we get a new set by producing a pairwise-mean dataset. The method can increase the size of the sample for estimation and reduce the impact of the dimensional curse. Consistency and asymptotic normality of the maximum mean empirical likelihood estimators are established. The finite sample performance of the proposed estimators is presented through simulation, and an application to the Boston Housing dataset is shown.

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Evaluation of Inter-Observer Reliability of Animal Welfare Indicators: Which Is the Best Index to Use?

Animals ◽

10.3390/ani11051445 ◽

2021 ◽

Vol 11 (5) ◽

pp. 1445

Author(s):

Mauro Giammarino ◽

Silvana Mattiello ◽

Monica Battini ◽

Piero Quatto ◽

Luca Maria Battaglini ◽

...

Keyword(s):

Animal Welfare ◽

Confidence Intervals ◽

Bootstrap Method ◽

Dairy Goat ◽

Microsoft Excel ◽

Bootstrap Methods ◽

Welfare Indicators ◽

Observer Reliability ◽

High Concordance ◽

Variance Estimates

This study focuses on the problem of assessing inter-observer reliability (IOR) in the case of dichotomous categorical animal-based welfare indicators and the presence of two observers. Based on observations obtained from Animal Welfare Indicators (AWIN) project surveys conducted on nine dairy goat farms, and using udder asymmetry as an indicator, we compared the performance of the most popular agreement indexes available in the literature: Scott’s π, Cohen’s k, kPABAK, Holsti’s H, Krippendorff’s α, Hubert’s Γ, Janson and Vegelius’ J, Bangdiwala’s B, Andrés and Marzo’s ∆, and Gwet’s γ(AC1). Confidence intervals were calculated using closed formulas of variance estimates for π, k, kPABAK, H, α, Γ, J, ∆, and γ(AC1), while the bootstrap and exact bootstrap methods were used for all the indexes. All the indexes and closed formulas of variance estimates were calculated using Microsoft Excel. The bootstrap method was performed with R software, while the exact bootstrap method was performed with SAS software. k, π, and α exhibited a paradoxical behavior, showing unacceptably low values even in the presence of very high concordance rates. B and γ(AC1) showed values very close to the concordance rate, independently of its value. Both bootstrap and exact bootstrap methods turned out to be simpler compared to the implementation of closed variance formulas and provided effective confidence intervals for all the considered indexes. The best approach for measuring IOR in these cases is the use of B or γ(AC1), with bootstrap or exact bootstrap methods for confidence interval calculation.

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Parametric Bootstrap Methods for Estimating Model Parameters of Non-homogeneous Gamma Process

International Journal of Mathematical Engineering and Management Sciences ◽

10.33889/ijmems.2018.3.2-013 ◽

2018 ◽

Vol 3 (2) ◽

pp. 167-176 ◽

Cited By ~ 1

Author(s):

Yasuhiro Saito ◽

Tadashi Dohi

Keyword(s):

Confidence Intervals ◽

Bootstrap Method ◽

Parametric Bootstrap ◽

Gamma Process ◽

Estimation Accuracy ◽

Model Parameters ◽

Trend Function ◽

Bootstrap Methods ◽

Parametric Bootstrapping ◽

Simulation Based

Non-Homogeneous Gamma Process (NHGP) is characterized by an arbitrary trend function and a gamma renewal distribution. In this paper, we estimate the confidence intervals of model parameters of NHGP via two parametric bootstrap methods: simulation-based approach and re-sampling-based approach. For each bootstrap method, we apply three methods to construct the confidence intervals. Through simulation experiments, we investigate each parametric bootstrapping and each construction method of confidence intervals in terms of the estimation accuracy. Finally, we find the best combination to estimate the model parameters in trend function and gamma renewal distribution in NHGP.

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