Analysis of critical-exponent data using Efron’s bootstrap technique

1987 ◽  
Vol 35 (4) ◽  
pp. 2102-2104 ◽  
Author(s):  
S. B. Crary ◽  
D. A. Fahey
Keyword(s):  
Critical Exponent ◽  
Bootstrap Technique ◽  
Efron’S Bootstrap ◽  
Efron's Bootstrap

scholarly journals A PARAMETRIC BOOTSTRAP FOR HEAVY-TAILED DISTRIBUTIONS

2014 ◽  
Vol 31 (3) ◽  
pp. 449-470 ◽  
Author(s):  
Adriana Cornea-Madeira ◽  
Russell Davidson
Keyword(s):  
Domain Of Attraction ◽  
Parametric Bootstrap ◽  
Limiting Distribution ◽  
Infinite Variance ◽  
Heavy Tailed Distributions ◽  
The Mean ◽  
Heavy Tailed ◽  
Efron’S Bootstrap ◽  
Efron's Bootstrap

It is known that Efron’s bootstrap of the mean of a distribution in the domain of attraction of the stable laws with infinite variance is not consistent, in the sense that the limiting distribution of the bootstrap mean is not the same as the limiting distribution of the mean from the real sample. Moreover, the limiting bootstrap distribution is random and unknown. The conventional remedy for this problem, at least asymptotically, is either the m out of n bootstrap or subsampling. However, we show that both these procedures can be unreliable in other than very large samples. We introduce a parametric bootstrap that overcomes the failure of Efron’s bootstrap and performs better than the m out of n bootstrap and subsampling. The quality of inference based on the parametric bootstrap is examined in a simulation study, and is found to be satisfactory with heavy-tailed distributions unless the tail index is close to 1 and the distribution is heavily skewed.

scholarly journals Efron's bootstrap

Significance ◽  
2010 ◽  
Vol 7 (4) ◽  
pp. 186-188 ◽  
Author(s):  
Dennis Boos ◽  
Leonard Stefanski
Keyword(s):  
Efron’S Bootstrap ◽  
Efron's Bootstrap

scholarly journals A survey of limit laws for bootstrapped sums

2003 ◽  
Vol 2003 (45) ◽  
pp. 2835-2861 ◽  
Author(s):  
Sándor Csörgő ◽  
Andrew Rosalsky
Keyword(s):  
Limit Theorems ◽  
Open Problems ◽  
Limit Laws ◽  
First Order ◽  
Efron’S Bootstrap ◽  
The Relationship ◽  
Efron's Bootstrap ◽  
Independent And Identically Distributed

Concentrating mainly on independent and identically distributed (i.i.d.) real-valued parent sequences, we give an overview of first-order limit theorems available for bootstrapped sample sums for Efron's bootstrap. As a light unifying theme, we expose by elementary means the relationship between corresponding conditional and unconditional bootstrap limit laws. Some open problems are also posed.

scholarly journals Bootstrap and Order Statistics for Quantifying Thermal-Hydraulic Code Uncertainties in the Estimation of Safety Margins

2008 ◽  
Vol 2008 ◽  
pp. 1-9 ◽  
Author(s):  
Enrico Zio ◽  
Francesco Di Maio
Keyword(s):  
Confidence Interval ◽  
Order Statistics ◽  
Nuclear Reactor ◽  
Safety Margin ◽  
Fuel Cladding ◽  
Complete Group ◽  
Bootstrap Technique ◽  
Safety Margins ◽  
Group Distribution

In the present work, the uncertainties affecting the safety margins estimated from thermal-hydraulic code calculations are captured quantitatively by resorting to the order statistics and the bootstrap technique. The proposed framework of analysis is applied to the estimation of the safety margin, with its confidence interval, of the maximum fuel cladding temperature reached during a complete group distribution blockage scenario in a RBMK-1500 nuclear reactor.

scholarly journals Multiple solutions for critical Choquard-Kirchhoff type equations

2020 ◽  
Vol 10 (1) ◽  
pp. 400-419 ◽  
Author(s):  
Sihua Liang ◽  
Patrizia Pucci ◽  
Binlin Zhang
Keyword(s):  
Critical Exponent ◽  
Critical Exponents ◽  
Sobolev Inequality ◽  
Multiple Solutions ◽  
Concentration Compactness ◽  
Positive Real ◽  
Multiplicity Results ◽  
Kirchhoff Type ◽  
Concentration Compactness Principle ◽  
Compactness Principle

Abstract In this article, we investigate multiplicity results for Choquard-Kirchhoff type equations, with Hardy-Littlewood-Sobolev critical exponents, $$\begin{array}{} \displaystyle -\left(a + b\int\limits_{\mathbb{R}^N} |\nabla u|^2 dx\right){\it\Delta} u = \alpha k(x)|u|^{q-2}u + \beta\left(\,\,\displaystyle\int\limits_{\mathbb{R}^N}\frac{|u(y)|^{2^*_{\mu}}}{|x-y|^{\mu}}dy\right)|u|^{2^*_{\mu}-2}u, \quad x \in \mathbb{R}^N, \end{array}$$ where a > 0, b ≥ 0, 0 < μ < N, N ≥ 3, α and β are positive real parameters, $\begin{array}{} 2^*_{\mu} = (2N-\mu)/(N-2) \end{array}$ is the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality, k ∈ Lr(ℝN), with r = 2∗/(2∗ − q) if 1 < q < 2* and r = ∞ if q ≥ 2∗. According to the different range of q, we discuss the multiplicity of solutions to the above equation, using variational methods under suitable conditions. In order to overcome the lack of compactness, we appeal to the concentration compactness principle in the Choquard-type setting.

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