ASYMPTOTIC SIZE AND A PROBLEM WITH SUBSAMPLING AND WITH THE m OUT OF n BOOTSTRAP

2009 ◽  
Vol 26 (2) ◽  
pp. 426-468 ◽  
Author(s):  
Donald W.K. Andrews ◽  
Patrik Guggenberger
Keyword(s):  
Limit Distribution ◽  
Test Statistic ◽  
Nominal Level ◽  
Asymptotic Size ◽  
Bootstrap Tests ◽  
Exact Size ◽  
High Level

This paper considers inference based on a test statistic that has a limit distribution that is discontinuous in a parameter. The paper shows that subsampling and m out of n bootstrap tests based on such a test statistic often have asymptotic size—defined as the limit of exact size—that is greater than the nominal level of the tests. This is due to a lack of uniformity in the pointwise asymptotics. We determine precisely the asymptotic size of such tests under a general set of high-level conditions that are relatively easy to verify. The results show that the asymptotic size of subsampling and m out of n bootstrap tests is distorted in some examples but not in others.

scholarly journals Testing in Nonparametric Accelerated Life Time Models

2016 ◽  
Vol 37 (1) ◽  
Author(s):  
Hannelore Liero
Keyword(s):  
Limit Distribution ◽  
Goodness Of Fit ◽  
Bootstrap Method ◽  
Life Time ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Time Model ◽  
Power Of The Test ◽  
Accelerated Life ◽  
Type Test

A goodness-of-fit test for testing the acceleration function in a nonparametric life time model is proposed. For this aim the limit distribution of an L2-type test statistic is derived. Furthermore, a bootstrap method is considered and the power of the test is studied.

scholarly journals Quantile treatment effects and bootstrap inference under covariate‐adaptive randomization

2020 ◽  
Vol 11 (3) ◽  
pp. 957-982
Author(s):  
Yichong Zhang ◽  
Xin Zheng
Keyword(s):  
Propensity Score ◽  
Quantile Regression ◽  
Standard Error ◽  
Wald Test ◽  
Estimation Methods ◽  
Compact Set ◽  
Nominal Level ◽  
Adaptive Randomization ◽  
Asymptotic Size ◽  
Quantile Treatment Effect

In this paper, we study the estimation and inference of the quantile treatment effect under covariate‐adaptive randomization. We propose two estimation methods: (1) the simple quantile regression and (2) the inverse propensity score weighted quantile regression. For the two estimators, we derive their asymptotic distributions uniformly over a compact set of quantile indexes, and show that, when the treatment assignment rule does not achieve strong balance, the inverse propensity score weighted estimator has a smaller asymptotic variance than the simple quantile regression estimator. For the inference of method (1), we show that the Wald test using a weighted bootstrap standard error underrejects. But for method (2), its asymptotic size equals the nominal level. We also show that, for both methods, the asymptotic size of the Wald test using a covariate‐adaptive bootstrap standard error equals the nominal level. We illustrate the finite sample performance of the new estimation and inference methods using both simulated and real datasets.

scholarly journals Fractional Entropy-Based Test of Uniformity with Power Comparisons

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Mohamed S. Mohamed ◽  
Haroon M. Barakat ◽  
Salem A. Alyami ◽  
Mohamed A. Abd Elgawad
Keyword(s):  
Simulation Study ◽  
Limit Distribution ◽  
Residual Entropy ◽  
Test Statistic ◽  
Percentage Points ◽  
Entropy Measures ◽  
Cumulative Residual Entropy ◽  
Power Comparisons ◽  
Fractional Entropy ◽  
Cumulative Residual

In the present paper, we use the fractional and weighted cumulative residual entropy measures to test the uniformity. The limit distribution and an approximation of the distribution of the test statistic based on the fractional cumulative residual entropy are derived. Moreover, for this test statistic, percentage points and power against seven alternatives are reported. Finally, a simulation study is carried out to compare the power of the proposed tests and other tests of uniformity.

A Note on Bootstrapping Generalized Method of Moments Estimators

1996 ◽  
Vol 12 (1) ◽  
pp. 187-197 ◽  
Author(s):  
Jinyong Hahn
Keyword(s):  
New York ◽  
Limit Distribution ◽  
Generalized Method Of Moments ◽  
Test Statistic ◽  
Percentile Method ◽  
Coverage Probabilities ◽  
Bootstrap Percentile ◽  
Nominal Coverage ◽  
Moments Estimators ◽  
Bootstrap Distribution

Recently, Arcones and Giné (1992, pp. 13–47, in R. LePage & L. Billard [eds.], Exploring the Limits of Bootstrap, New York: Wiley) established that the bootstrap distribution of the M-estimator converges weakly to the limit distribution of the estimator in probability. In contrast, Brown and Newey (1992, Bootstrapping for GMM, Seminar note) discovered that the bootstrap distribution of the GMM overidentification test statistic does not converge weakly to the x2 distribution. In this paper, it is shown that the bootstrap distribution of the GMM estimator converges weakly to the limit distribution of the estimator in probability. Asymptotic coverage probabilities of the confidence intervals based on the bootstrap percentile method are thus equal to their nominal coverage probability.

scholarly journals Pengaruh Gaya Kepemimpinan Transformasional Terhadap Kinerja Karyawan

2016 ◽  
Vol 2 (1) ◽  
pp. 54
Author(s):  
Repin Ali Rahman ◽  
Ermina Tiorida
Keyword(s):  
Transformational Leadership ◽  
Leadership Style ◽  
Employee Performance ◽  
Descriptive Analysis ◽  
Coefficient Of Determination ◽  
Test Statistic ◽  
Green Hotel ◽  
Organization Leadership ◽  
Transformational Leadership Style ◽  
High Level

The style of leadership is an important element in a business organization. Leadership style described by Bass consists of transformational leadership and transactional leadership. This study aims to determine how well the transformational leadership style towards employee performance in Kamojang Green Hotel & Resort, in addition to this study, aims to determine the relationship between leadership style with employee performance employee in Kamojang Green Hotel & Resort. This study uses qualitative methods with data collection through questionnaires distributed randomly to employees who work in Kamojang Green Hotel & Resort. The phenomenon happens in Kamojang Green Hotel & Resort is a high level of employee come late due to lack of supervision of the leaders and the lack of punishment that makes a deterrent to employees.To achieve the objectives that have been outlined previously, researchers used several tests such as the test statistic descriptive analysis, correlation, regression and the coefficient of determination. The result is a style of leadership transformational and employees in Kamojang Green Hotel & Resort is good, style of leadership significant positive effect on employee performance, Y = 3,529+0,231𝑋𝑋 a regression coefficient after regression testing against the influence of transformational leadership style on employee performance in Kamojang Green Hotel & Resort.

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