Asymptotic representation theorems for poverty indices

Lo, Gane Samb; Sall, Serigne Touba

doi:10.4314/afst.v5i1.71052

Cited by 7 publications

(16 citation statements)

References 10 publications

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“…Our results will rely on the representation of Theorem [11], which in turn will need the following assumptions.…”

Section: Our Resultsmentioning

confidence: 99%

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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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“…Our results will rely on the representation of Theorem [11], which in turn will need the following assumptions.…”

Section: Our Resultsmentioning

confidence: 99%

“…This theorem expresses our studied time-dependent statistics as the sum of a functional empirical process and the stochastic process (11). It will be seen, for a fixed time, that ( )…”

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

confidence: 96%

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

Lo¹,

Sall²,

Mergane³

2015

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“…Under some conditions (see Lo [5]), (2) may be uniformly approximated by the representation, as n → ∞,…”

Section: Introductionmentioning

confidence: 99%

“…Statistics like (2) thus are present in many situations in connection with L-Statistics (see Helmers and Ruymgaart [1], Helmers et al [2,3]) and naturally occur is Actuarial Sciences and in inequality measures (see Puri et al [4]), and more recently in poverty measures (see Lo [5], Lo et al [8]). In all these fields, we may be faced not to find simple asymptotic normality results, but to derive uniform asymptotic laws for the time-dependant statistics (with the parameter t ∈ [0, T ]) and functional asymptotic laws with respect to the class of functions…”

Section: Introductionmentioning

confidence: 99%

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

Lo¹

2011

afst

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Abstract. In this paper, we are concerned with the stochastic processwhere for n ≥ 1 and T > 0, the sequences, and finally q t is a bounded real function defined on R. This process appears when investigating some time-dependent L-Statistics which are expressed as a function of some functional empirical process and the process (A). Since the functional empirical process is widely investigated in the literature, the process reveals itself as an important key for L-Statistics laws. In this paper, we state an extended study of this process, give complete calculations of the first moments, the covariance function and find conditions for asymptotic tightness.Résumé. Nous nous interéssons dans ce papier au processus stochastique suivant

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“…In Section 2, we remind key definitions and properties for functional empirical processes, and we state the asymptotic representation of the GPI of Sall and Lo [25] stated in Theorem 1 that will be used later on. In Section 3, we give our main results and make some commentaries and data driven applications to Senegalese pseudo-panel data are considered while the proofs and the tables are postponed in an appendix Section 5.…”

Section:   mentioning

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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Asymptotic representation theorems for poverty indices

Cited by 7 publications

References 10 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

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

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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