scholarly journals Using Bootstrap Method to Evaluate the Power of Tests for Non-Linearity in Asymmetric Price Relationship

2013 ◽  
Vol 5 (4) ◽  
pp. 237-241
Author(s):  
Henry De-Graft Acquah
Keyword(s):  
Sample Size ◽  
Bootstrap Method ◽  
Complex Model ◽  
Model Complexity ◽  
Bootstrap Sample ◽  
Power Of The Test ◽  
Data Generating Process ◽  
Price Relationship ◽  
False Null Hypothesis ◽  
The Bootstrap Method

This paper introduces and applies the bootstrap method to compare the power of the test for asymmetry in the Granger and Lee (1989) and Von Cramon-Taubadel and Loy (1996) models. The results of the bootstrap simulations indicate that the power of the test for asymmetry depends on various conditions such as the bootstrap sample size, model complexity, difference in adjustment speeds and the amount of noise in the data generating process used in the application. The true model achieves greater power when compared with the complex model. With small bootstrap sample size or large noise, both models display low power in rejecting the (false) null hypothesis of symmetry.

scholarly journals Estimation of sensitivity and specificity and calculation of sample size for a validation study with stratified sampling

2020 ◽  
Author(s):  
Kiyoshi Kubota ◽  
Masao Iwagami ◽  
Takuhiro Yamaguchi
Keyword(s):  
Sample Size ◽  
Sensitivity And Specificity ◽  
Validation Study ◽  
Predictive Value ◽  
Validation Studies ◽  
Bootstrap Method ◽  
Stratified Sampling ◽  
Delta Method ◽  
Estimate Sample Size ◽  
The Bootstrap Method

Abstract Background:We propose and evaluate the approximation formulae for the 95% confidence intervals (CIs) of the sensitivity and specificity and a formula to estimate sample size in a validation study with stratified sampling where positive samples satisfying the outcome definition and negative samples that do not are selected with different extraction fractions. Methods:We used the delta method to derive the approximation formulae for estimating the sensitivity and specificity and their CIs. From those formulae, we derived the formula to estimate the size of negative samples required to achieve the intended precision and the formula to estimate the precision for a negative sample size arbitrarily selected by the investigator. We conducted simulation studies in a population where 4% were outcome definition positive, the positive predictive value (PPV)=0.8, and the negative predictive value (NPV)=0.96, 0.98 and 0.99. The size of negative samples, n0, was either selected to make the 95% CI fall within ± 0.1, 0.15 and 0.2 or set arbitrarily as 150, 300 and 600. We assumed a binomial distribution for the positive and negative samples. The coverage of the 95% CIs of the sensitivity and specificity was calculated as the proportion of CIs including the sensitivity and specificity in the population, respectively. For selected studies, the coverage was also estimated by the bootstrap method. The sample size was evaluated by examining whether the observed precision was within the pre-specified value.Results:For the sensitivity, the coverage of the approximated 95% CIs was larger than 0.95 in most studies but in 9 of 18 selected studies derived by the bootstrap method. For the specificity, the coverage of the approximated 95% CIs was approximately 0.93 in most studies, but the coverage was more than 0.95 in all 18 studies derived by the bootstrap method. The calculated size of negative samples yielded precisions within the pre-specified values in most of the studies.Conclusion:The approximation formulae for the 95% CIs of the sensitivity and specificity for stratified validation studies are presented. These formulae will help in conducting and analysing validation studies with stratified sampling.

scholarly journals Influence Function and Bootstrap Methods of Estimating the Standard Errors of the Estimators of Mixture Exponential Distribution Parameter

2021 ◽  
pp. 113-136
Author(s):  
J. I. Udobi ◽  
G. A. Osuji ◽  
S. I. Onyeagu ◽  
H. O. Obiora-Ilouno
Keyword(s):  
Sample Size ◽  
Standard Error ◽  
Influence Function ◽  
Bootstrap Method ◽  
Standard Errors ◽  
Sample Sizes ◽  
Trimmed Mean ◽  
Contamination Levels ◽  
M Estimate ◽  
The Bootstrap Method

This work estimated the standard error of the maximum likelihood estimator (MLE) and the robust estimators of the exponential mixture parameter (θ) using the influence function and the bootstrap approaches. Mixture exponential random samples of sizes 10, 15, 20, 25, 50, and 100 were generated using 3 mixture exponential models at 2%, 5% and 10% contamination levels. The selected estimators namely: mean, median, alpha-trimmed mean, Huber M-estimate and their standard errors (Tn ) were estimated using the two approaches at the indicated sample sizes and contamination levels. The results were compared using the coefficient of variation, confidence interval and the asymptotic relative efficiency of Tn in order to find out which approach yields the more reliable, precise and efficient estimate of Tn. The results of the analysis show that the two approaches do not equally perform at all conditions. From the results, the bootstrap method was found to be more reliable and efficient method of estimating the standard error of the arithmetic mean at all sample sizes and contamination levels. In estimating the standard error of the median, the influence function method was found to be more effective especially when the sample size is small and yet contamination is high. The influence function based approach yielded more reliable, precise and efficient estimates of the standard errors of the alpha-trimmed mean and the Huber M-estimate for all sample sizes and levels of contamination although the reliability of the bootstrap method improved better as sample size increased to 50 and above. All simulations and analysis were carried out in R programming language.

scholarly journals Effect of plot size and plant spatial arrangement on the efficiency of family selection in sugarcane

2021 ◽  
Vol 53 (2) ◽  
pp. 1-10
Author(s):  
Aparecido De Moraes ◽  
Matheus Henrique Silveira Mendes ◽  
Mauro Sérgio de Oliveira Leite ◽  
Regis De Castro Carvalho ◽  
Flávia Maria Avelar Gonçalves
Keyword(s):  
Sample Size ◽  
Bootstrap Method ◽  
Spatial Arrangement ◽  
Family Selection ◽  
Plot Size ◽  
Stalk Diameter ◽  
New Varieties ◽  
Selection Of ◽  
The Bootstrap Method ◽  
The Ideal

The purpose of this study was to identify the ideal sample size representing a family in its potential, to identify superior families and, in parallel, determine in which spatial arrangement they may have a better accuracy in the selection of new varieties of sugarcane. For such purpose, five families of full-sibs were evaluated, each with 360 individuals, in the randomized blocks design, with three replications in three different spacing among plants in the row (50 cm, 75 cm, and 100 cm) and 150 cm between the rows. To determine the ideal sample size, as well as the better spacing for evaluation, the bootstrap method was adopted. It was observed that 100 cm spacings provided the best average for the stalk numbers, stalk diameter and for estimated weight of stalks in the stool. The spacing of 75 cm between the plants allowed a better power of discrimination among the families for all characters evaluated. At this 75 cm spacing  was also possible to identify superior families with a sample of 30 plants each plot and 3 reps in the trial. Highlights The bootstrap method was efficient to determine the ideal sample size, as well as the best spacing for evaluation. The 75-cm spacing had the highest power of discrimination among families, indicating that this spacing is the most efficient in evaluating sugarcane families for selection purposes. From all the results and considering selective accuracy as the guiding parameter for decision making, the highest values obtained considering the number of stalks and weight of stalks in the stools were found at the 75-cm spacing.

scholarly journals A Bootstrap Approach to Evaluating the Power of the Houck’s Test for Asymmetry

2013 ◽  
Vol 4 (2) ◽  
pp. 69-73
Author(s):  
Henry de-Graft Acquah
Keyword(s):  
Low Power ◽  
Noise Level ◽  
Null Hypothesis ◽  
Parametric Bootstrap ◽  
Bootstrap Sample ◽  
Power Of The Test ◽  
Bootstrap Simulation ◽  
Bootstrap Approach ◽  
Data Generating Process ◽  
S Model

The power of the conventional Houck’s model of asymmetry is examined via parametric bootstrap simulation. The results of the bootstrap simulations indicate that the Houck’s model has low power in rejecting the null of symmetric adjustment. The power of the test depends on the bootstrap sample size, level of asymmetry and the amount of noise in the data generating process used in an application. With a small bootstrap sample and large noise level, the Houck’s model display low power in rejecting the null hypothesis of symmetry.

scholarly journals A Weighted Residual Bootstrap Method for Multilevel Modeling with Sampling Weights

2021 ◽  
Author(s):  
Wen Luo ◽  
Hok Chio Lai
Keyword(s):  
Sample Size ◽  
Multilevel Modeling ◽  
Bootstrap Method ◽  
Intraclass Correlation ◽  
R Package ◽  
Sampling Weights ◽  
Multistage Sampling ◽  
The Impact ◽  
Level 2 ◽  
The Bootstrap Method

Multilevel modeling is often used to analyze survey data collected with a multistage sampling design. When the selection is informative, sampling weights need to be incorporated in the estimation. We propose a weighted residual bootstrap method as an alternative to the multilevel pseudo-maximum likelihood (MPML) estimators. In a Monte Carlo simulation using two-level linear mixed effects models, the bootstrap method showed advantages over MPML for the estimates and the statistical inferences of the intercept, the slope of the level-2 predictor, and the variance components at level-2. The impact of sample size, selection mechanism, intraclass correlation (ICC), and distributional assumptions on the performance of the methods were examined. The performance of MPML was suboptimal when sample size and ICC were small and when the normality assumption was violated. The bootstrap estimates performed generally well across all the simulation conditions, but had notably suboptimal performance in estimating the covariance component in a random slopes model when sample size and ICCs were large. As an illustration, the bootstrap method is applied to the American data of the OECD’s Program for International Students Assessment (PISA) survey on math achievement using the R package bootmlm.

scholarly journals Statistical Estimates of the Pulsar Glitch Activity

Universe ◽  
2021 ◽  
Vol 7 (1) ◽  
pp. 8
Author(s):  
Alessandro Montoli ◽  
Marco Antonelli ◽  
Brynmor Haskell ◽  
Pierre Pizzochero
Keyword(s):  
Linear Regression ◽  
Upper Bound ◽  
Bootstrap Method ◽  
Waiting Times ◽  
Statistical Estimates ◽  
Equal Variance ◽  
Linear Fit ◽  
The Moment ◽  
The Bootstrap Method

A common way to calculate the glitch activity of a pulsar is an ordinary linear regression of the observed cumulative glitch history. This method however is likely to underestimate the errors on the activity, as it implicitly assumes a (long-term) linear dependence between glitch sizes and waiting times, as well as equal variance, i.e., homoscedasticity, in the fit residuals, both assumptions that are not well justified from pulsar data. In this paper, we review the extrapolation of the glitch activity parameter and explore two alternatives: the relaxation of the homoscedasticity hypothesis in the linear fit and the use of the bootstrap technique. We find a larger uncertainty in the activity with respect to that obtained by ordinary linear regression, especially for those objects in which it can be significantly affected by a single glitch. We discuss how this affects the theoretical upper bound on the moment of inertia associated with the region of a neutron star containing the superfluid reservoir of angular momentum released in a stationary sequence of glitches. We find that this upper bound is less tight if one considers the uncertainty on the activity estimated with the bootstrap method and allows for models in which the superfluid reservoir is entirely in the crust.

scholarly journals Reliability estimation for drive axle of wheel loader under extreme small sample

2019 ◽  
Vol 11 (3) ◽  
pp. 168781401983684 ◽  
Author(s):  
Leilei Cao ◽  
Lulu Cao ◽  
Lei Guo ◽  
Kui Liu ◽  
Xin Ding
Keyword(s):  
Sample Size ◽  
Promising Result ◽  
Small Sample Size ◽  
Bootstrap Method ◽  
Estimation Method ◽  
Small Sample ◽  
Reliability Estimation ◽  
Fatigue Reliability ◽  
Drive Axle ◽  
Semi Empirical

It is difficult to have enough samples to implement the full-scale life test on the loader drive axle due to high cost. But the extreme small sample size can hardly meet the statistical requirements of the traditional reliability analysis methods. In this work, the method of combining virtual sample expanding with Bootstrap is proposed to evaluate the fatigue reliability of the loader drive axle with extreme small sample. First, the sample size is expanded by virtual augmentation method to meet the requirement of Bootstrap method. Then, a modified Bootstrap method is used to evaluate the fatigue reliability of the expanded sample. Finally, the feasibility and reliability of the method are verified by comparing the results with the semi-empirical estimation method. Moreover, from the practical perspective, the promising result from this study indicates that the proposed method is more efficient than the semi-empirical method. The proposed method provides a new way for the reliability evaluation of costly and complex structures.

The Bootstrap-Method: Discussion and Proposal for Improvement / Das bootstrap-Verfahren: Diskussion und Verbesserungsvorschlag

1998 ◽  
Vol 217 (1) ◽  
Author(s):  
Hans Schneeberger
Keyword(s):  
Bootstrap Method ◽  
Law School ◽  
Mean Deviation ◽  
Alternative Method ◽  
Doubling Method ◽  
The Mean ◽  
The Bootstrap Method

SummaryWith Efron’s law-school example the bootstrap method is compared with an alternative method, called doubling. It is shown, that the mean deviation of the estimator is always smaller for the doubling method.

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