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.

Bootstrapping Quantile Regression Estimators

1995 ◽  
Vol 11 (1) ◽  
pp. 105-121 ◽  
Author(s):  
Jinyong Hahn
Keyword(s):  
Quantile Regression ◽  
Limit Distribution ◽  
Asymptotic Variance ◽  
Regression Estimator ◽  
Variance Matrix ◽  
Percentile Method ◽  
Coverage Probabilities ◽  
Regression Estimators ◽  
Bootstrap Percentile ◽  
Bootstrap Distribution

The asymptotic variance matrix of the quantile regression estimator depends on the density of the error. For both deterministic and random regressors, the bootstrap distribution is shown to converge weakly to the limit distribution of the quantile regression estimator in probability. Thus, the confidence intervals constructed by the bootstrap percentile method have asymptotically correct coverage probabilities.

scholarly journals Generalized Inference on Stress-Strength Reliability in Generalized Pareto Model

2021 ◽  
Author(s):  
Sanju Scaria ◽  
Seemon Thomas ◽  
Sibil Jose
Keyword(s):  
Simulation Studies ◽  
Strength Data ◽  
Percentile Method ◽  
Generalized Pareto ◽  
Variable Approach ◽  
Pareto Model ◽  
Coverage Probabilities ◽  
Generalized Inference ◽  
Bootstrap Percentile ◽  
Generalized Variable Approach

The article focuses on the inference of stress-strength reliability in generalized Pareto model using the generalized variable approach and bootstrap percentile method. Simulation studies are conducted to obtain expected lengths and coverage probabilities of confidence intervals constructed using the generalized variable and the bootstrap percentile methods. An example consisting of real stress-strength data is also presented for illustrative purposes.

scholarly journals Bootstrap Methods in Econometrics

2019 ◽  
Vol 11 (1) ◽  
pp. 193-224 ◽  
Author(s):  
Joel L. Horowitz
Keyword(s):  
Asymptotic Distribution ◽  
Confidence Intervals ◽  
Test Statistic ◽  
Bootstrap Methods ◽  
First Order ◽  
Coverage Probabilities ◽  
Asymptotic Distribution Theory ◽  
Nominal Coverage ◽  
Distributional Approximations ◽  
Approximations To Distributions

The bootstrap is a method for estimating the distribution of an estimator or test statistic by resampling one's data or a model estimated from the data. Under conditions that hold in a wide variety of econometric applications, the bootstrap provides approximations to distributions of statistics, coverage probabilities of confidence intervals, and rejection probabilities of hypothesis tests that are more accurate than the approximations of first-order asymptotic distribution theory. The reductions in the differences between true and nominal coverage or rejection probabilities can be very large. In addition, the bootstrap provides a way to carry out inference in certain settings where obtaining analytic distributional approximations is difficult or impossible. This article explains the usefulness and limitations of the bootstrap in contexts of interest in econometrics. The presentation is informal and expository. It provides an intuitive understanding of how the bootstrap works. Mathematical details are available in the references that are cited.

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.

Bootstrap Standard Error Estimates and Inference

Econometrica ◽  
2021 ◽  
Vol 89 (4) ◽  
pp. 1963-1977 ◽  
Author(s):  
Jinyong Hahn ◽  
Zhipeng Liao
Keyword(s):  
Weak Convergence ◽  
Error Estimates ◽  
Limit Distribution ◽  
Standard Error ◽  
Asymptotic Variance ◽  
Theory And Practice ◽  
Second Moment ◽  
Theoretical Literature ◽  
Bootstrap Distribution

Asymptotic justification of the bootstrap often takes the form of weak convergence of the bootstrap distribution to some limit distribution. Theoretical literature recognized that the weak convergence does not imply consistency of the bootstrap second moment or the bootstrap variance as an estimator of the asymptotic variance, but such concern is not always reflected in the applied practice. We bridge the gap between the theory and practice by showing that such common bootstrap based standard error in fact leads to a potentially conservative inference.

Estimating Dynamic Panel Data Models in Political Science

2002 ◽  
Vol 10 (1) ◽  
pp. 25-48 ◽  
Author(s):  
Gregory Wawro
Keyword(s):  
Panel Data ◽  
Political Science ◽  
Dynamic Models ◽  
Party Identification ◽  
Generalized Method Of Moments ◽  
Dynamic Panel Data ◽  
Panel Data Models ◽  
Dynamic Panel ◽  
Cross Sectional ◽  
Moments Estimators

Panel data are a very valuable resource for finding empirical solutions to political science puzzles. Yet numerous published studies in political science that use panel data to estimate models with dynamics have failed to take into account important estimation issues, which calls into question the inferences we can make from these analyses. The failure to account explicitly for unobserved individual effects in dynamic panel data induces bias and inconsistency in cross-sectional estimators. The purpose of this paper is to review dynamic panel data estimators that eliminate these problems. I first show how the problems with cross-sectional estimators arise in dynamic models for panel data. I then show how to correct for these problems using generalized method of moments estimators. Finally, I demonstrate the usefulness of these methods with replications of analyses in the debate over the dynamics of party identification.

Sign in / Sign up

Export Citation Format

Share Document