Random weighting estimation of stable exponent

Metrika ◽  
2013 ◽  
Vol 77 (4) ◽  
pp. 451-468 ◽  
Author(s):  
Gaoge Hu ◽  
Shesheng Gao ◽  
Yongmin Zhong ◽  
Chengfan Gu
Entropy ◽  
2021 ◽  
Vol 24 (1) ◽  
pp. 38
Author(s):  
Marcel Ausloos ◽  
Philippe Bronlet

We recall the historically admitted prerequisites of Economic Freedom (EF). We have examined 908 data points for the Economic Freedom of the World (EFW) index and 1884 points for the Index of Economic Freedom (IEF); the studied periods are 2000–2006 and 1997–2007, respectively, thereby following the Berlin wall collapse, and including 11 September 2001. After discussing EFW index and IEF, in order to compare the indices, one needs to study their overlap in time and space. That leaves 138 countries to be examined over a period extending from 2000 to 2006, thus 2 sets of 862 data points. The data analysis pertains to the rank-size law technique. It is examined whether the distributions obey an exponential or a power law. A correlation with the country’s Gross Domestic Product (GDP), an admittedly major determinant of EF, follows, distinguishing regional aspects, i.e., defining 6 continents. Semi-log plots show that the EFW-rank relationship is exponential for countries of high rank (≥20); overall the log–log plots point to a behaviour close to a power law. In contrast, for the IEF, the overall ranking has an exponential behaviour; but the log–log plots point to the existence of a transitional point between two different power laws, i.e., near rank 10. Moreover, log–log plots of the EFW index relationship to country GDP are characterised by a power law, with a rather stable exponent (γ≃0.674) as a function of time. In contrast, log–log plots of the IEF relationship with the country’s gross domestic product point to a downward evolutive power law as a function of time. Markedly the two studied indices provide different aspects of EF.


Author(s):  
Yalin Jiao ◽  
Yongmin Zhong ◽  
Shesheng Gao ◽  
Bijan Shirinzadeh

This paper presents a new random weighting method for estimation of one-sided confidence intervals in discrete distributions. It establishes random weighting estimations for the Wald and Score intervals. Based on this, a theorem of coverage probability is rigorously proved by using the Edgeworth expansion for random weighting estimation of the Wald interval. Experimental results demonstrate that the proposed random weighting method can effectively estimate one-sided confidence intervals, and the estimation accuracy is much higher than that of the bootstrap method.


2021 ◽  
pp. 438-470
Author(s):  
James Davidson

This chapter focuses largely on methods of proof of the strong law, building on the fundamental convergence lemma. It covers Kolmogorov's three‐series theorem, strong laws for martingales, and random weighting. Then a range of strong laws are proved for mixingales and for near‐epoch dependent and mixing processes.


2013 ◽  
Vol 55 (1) ◽  
pp. 43-53 ◽  
Author(s):  
Shesheng Gao ◽  
Yongmin Zhong ◽  
Chengfan Gu

Sign in / Sign up

Export Citation Format

Share Document