scholarly journals Exogeneity Tests, Incomplete Models, Weak Identification and Non-Gaussian Distributions: Invariance and Finite-Sample Distributional Theory

2016 ◽  
Author(s):  
Firmin Doko Tchatoka ◽  
Jean-Marie Dufour
Keyword(s):  
Finite Sample ◽  
Gaussian Distributions ◽  
Weak Identification ◽  
Exogeneity Tests ◽  
Non Gaussian ◽  
Incomplete Models

scholarly journals Emergence of skewed non-Gaussian distributions of velocity increments in isotropic turbulence

2019 ◽  
Vol 4 (6) ◽  
Author(s):  
W. Sosa-Correa ◽  
R. M. Pereira ◽  
A. M. S. Macêdo ◽  
E. P. Raposo ◽  
D. S. P. Salazar ◽  
...  
Keyword(s):  
Isotropic Turbulence ◽  
Gaussian Distributions ◽  
Velocity Increments ◽  
Non Gaussian

scholarly journals DETERMINING SOURCE CUMULANTS IN FEMTOSCOPY WITH GRAM–CHARLIER AND EDGEWORTH SERIES

2011 ◽  
Vol 26 (24) ◽  
pp. 1771-1782 ◽  
Author(s):  
H. C. EGGERS ◽  
M. B. DE KOCK ◽  
J. SCHMIEGEL
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Fourth Order ◽  
Momentum Space ◽  
Crucial Role ◽  
Gaussian Distributions ◽  
Edgeworth Series ◽  
The Central Limit Theorem ◽  
Non Gaussian

Lowest-order cumulants provide important information on the shape of the emission source in femtoscopy. For the simple case of noninteracting identical particles, we show how the fourth-order source cumulant can be determined from measured cumulants in momentum space. The textbook Gram–Charlier series is found to be highly inaccurate, while the related Edgeworth series provides increasingly accurate estimates. Ordering of terms compatible with the Central Limit Theorem appears to play a crucial role even for non-Gaussian distributions.

scholarly journals On uniform asymptotic risk of averaging GMM estimators

10.3982/qe711 ◽  
2019 ◽  
Vol 10 (3) ◽  
pp. 931-979 ◽  
Author(s):  
Xu Cheng ◽  
Zhipeng Liao ◽  
Ruoyao Shi
Keyword(s):  
Nonlinear Models ◽  
Sufficient Conditions ◽  
Risk Difference ◽  
Upper And Lower Bounds ◽  
Quadratic Loss ◽  
Finite Sample ◽  
Moment Conditions ◽  
Gmm Estimator ◽  
Asymptotic Risk ◽  
Non Gaussian

This paper studies the averaging GMM estimator that combines a conservative GMM estimator based on valid moment conditions and an aggressive GMM estimator based on both valid and possibly misspecified moment conditions, where the weight is the sample analog of an infeasible optimal weight. We establish asymptotic theory on uniform approximation of the upper and lower bounds of the finite‐sample truncated risk difference between any two estimators, which is used to compare the averaging GMM estimator and the conservative GMM estimator. Under some sufficient conditions, we show that the asymptotic lower bound of the truncated risk difference between the averaging estimator and the conservative estimator is strictly less than zero, while the asymptotic upper bound is zero uniformly over any degree of misspecification. The results apply to quadratic loss functions. This uniform asymptotic dominance is established in non‐Gaussian semiparametric nonlinear models.

Control charts for non-Gaussian distributions

2007 ◽  
Author(s):  
Florina Babus ◽  
Abdessamad Kobi ◽  
Th. Tiplica ◽  
Ioan Bacivarov ◽  
Angelica Bacivarov
Keyword(s):  
Control Charts ◽  
Gaussian Distributions ◽  
Non Gaussian

Reliability-Based Design Optimization With Confidence Level for Non-Gaussian Distributions Using Bootstrap Method

2011 ◽  
Vol 133 (9) ◽  
Author(s):  
Yoojeong Noh ◽  
Kyung K. Choi ◽  
Ikjin Lee ◽  
David Gorsich ◽  
David Lamb
Keyword(s):  
Statistical Model ◽  
Design Optimization ◽  
Confidence Intervals ◽  
Confidence Level ◽  
Bootstrap Method ◽  
Random Variables ◽  
Reliability Based Design Optimization ◽  
Gaussian Distributions ◽  
Reliability Based Design ◽  
Non Gaussian

For reliability-based design optimization (RBDO), generating an input statistical model with confidence level has been recently proposed to offset inaccurate estimation of the input statistical model with Gaussian distributions. For this, the confidence intervals for the mean and standard deviation are calculated using Gaussian distributions of the input random variables. However, if the input random variables are non-Gaussian, use of Gaussian distributions of the input variables will provide inaccurate confidence intervals, and thus yield an undesirable confidence level of the reliability-based optimum design meeting the target reliability βt. In this paper, an RBDO method using a bootstrap method, which accurately calculates the confidence intervals for the input parameters for non-Gaussian distributions, is proposed to obtain a desirable confidence level of the output performance for non-Gaussian distributions. The proposed method is examined by testing a numerical example and M1A1 Abrams tank roadarm problem.

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