A simple note on some empirical stochastic process as a tool in uniform L-statistics weak laws

Lo, Gane Samb

doi:10.4314/afst.v5i1.71058

Cited by 4 publications

(7 citation statements)

References 7 publications

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“…Here and in the sequel, K is a generic constant eventually taking different values from one formula to another. Next, we find in [12], that (…”

Section: K T H T K T H T H T K Tmentioning

confidence: 85%

“…We still need a thorough study of (11) and its connection with , t n α while the computation of the variance and covariance function. This is done separately in [12] to avoid lengthy papers. Now, we use these tools to give first, general laws for the WMLG statistic below and then for the Kakwani class of indices in Section 2.2 and for the Shorrocks-Thon indices in Section 3.…”

Section: K T H T K T H T H T K Tmentioning

confidence: 99%

“…The computation of the limiting Gaussian process requires heavy calculations done in [12]. The proof ends with providing the covariance function 1 Γ of ( )…”

Section: Y T Y T Smentioning

confidence: 99%

See 2 more Smart Citations

Functional Weak Laws for the Weighted Mean Losses or Gains and Applications

Lo¹,

Sall²,

Mergane³

2015

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In this paper, we show that many risk measures arising in Actuarial Sciences, Finance, Medicine, Welfare analysis, etc. are gathered in classes of Weighted Mean Loss or Gain (WMLG) statistics. Some of them are Upper Threshold Based (UTH) or Lower Threshold Based (LTH). These statistics may be time-dependent when the scene is monitored in the time and depend on specific functions w and d. This paper provides time-dependent and uniformly functional weak asymptotic laws that allow temporal and spatial studies of the risk as well as comparison among statistics in terms of dependence and mutual influence. The results are particularized for usual statistics like the Kakwani and Shorrocks ones that are mainly used in welfare analysis. Data-driven applications based on pseudo-panel data are provided.

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“…Here and in the sequel, K is a generic constant eventually taking different values from one formula to another. Next, we find in [12], that (…”

Section: K T H T K T H T H T K Tmentioning

confidence: 85%

Section: K T H T K T H T H T K Tmentioning

confidence: 99%

See 1 more Smart Citation

Functional Weak Laws for the Weighted Mean Losses or Gains and Applications

Lo¹,

Sall²,

Mergane³

2015

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“…Proof. To prove (a), we use the method described in Lo (2010), itself based on the functional empirical process described above. The method of Subsection 3.1 and Lemma 2 are repeatedly used below.…”

Section: Asymptotic Joint Multinormal Law Of the Pair Of Moments Estimentioning

confidence: 99%

Statistical tests for the Pseudo-Lindley distribution and applications

Lo¹,

Kpanzou²,

Haidara³

2019

JAS

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The pseudo-Lindley distribution was introduced as a useful generalization of the Lindley distribution in Zeghdoudi and Nedjar (2016) who showed interesting properties of their new law, in particular its efficiency in modeling data in Reliability and Survival Analysis. In this paper we study the estimators of the pair of parameters and determine their asymptotic law from which a chi-square law is derived. From both asymptotic laws, statistical tests are built. Simulation studies on the tests conclude to their efficiency for data sizes generally used in Reliability. Related VB6 codes related to statistical analysis on that law are given

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“…We may easily find the functions g and  for the most common members of the GPI family (see [25,28]) in Table 1. In this case, let Where …”

Section: Representation Of Some Poverty Indicesmentioning

confidence: 99%

On the Functional Empirical Process and Its Application to the Mutual Influence of the Theil-Like Inequality Measure and the Growth

Mergane¹,

Lo²

2013

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We set in this paper a coherent theory based on functional empirical processes that allows to consider both the poverty and the inequality indices in one Gaussian field in which the study of the influence of the one over the other is done. We use the General Poverty Index (GPI), that is a class of poverty indices gathering the most common ones and a functional class of inequality measures including the Entropy Measure, the Mean Logarithmic Deviation, the different inequality measures of Atkinson, Champernowne, Kolm and Theil called Theil-Like Inequality Measures (TLIM). Our results are given in a unified approach with respect to the two classes instead of their particular elements. We provide the asymptotic laws of the variations of each class over two given periods and the ratio of the variation and derive confidence intervals for them. Although the variances may seem somehow complicated, we provide R codes for their computations and apply the results for the pseudo-panel data for Senegal with a simple analysis.

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A simple note on some empirical stochastic process as a tool in uniform L-statistics weak laws

Cited by 4 publications

References 7 publications

Functional Weak Laws for the Weighted Mean Losses or Gains and Applications

Functional Weak Laws for the Weighted Mean Losses or Gains and Applications

Statistical tests for the Pseudo-Lindley distribution and applications

On the Functional Empirical Process and Its Application to the Mutual Influence of the Theil-Like Inequality Measure and the Growth

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