Strassen's LIL for the Lorenz Curve
Copyright policy )Strassen's LIL for the Lorenz Curve
The authors prove Strassen's law of the iterated logarithm for the Lorenz process assuming that the underlying d.f. \(F\) and its inverse \(F^{-1}\) are continuous and the moment \(EX^{2+u}\) is finite for some \(u>0\). Previously, the first author, \textit{S. Csörgö} and \textit{L. Horváth} [``An asymptotic theory for empirical reliability and concentration processes'' (1986; Zbl 0605.62105)] and \textit{R. C. Rao} and \textit{L. C. Zhao} [J. Multivariate Anal. 54, No. 2, 239-252 (1995)] proved strong invariance principle for Lorenz process using stronger assumptions on \(f\) and \(F\). Using a limit theorem for the general integrated empirical difference process and techniques of \textit{W. Vervaat} [Z. Wahrscheinlichkeitstheorie Verw. Geb. 23, 245-253 (1972; Zbl 0238.60018)] and \textit{Polonik} (Shorack and Wellner, 1986), the authors are able to obtain sharper results for Lorenz process.
- Carleton University Canada
Statistics and Probability, integrated empirical difference process, redudancy process, Numerical Analysis, total time on test function, Strong limit theorems, Functional limit theorems; invariance principles, Applications of renewal theory (reliability, demand theory, etc.), quantile process, mean residual life process, Strassen's law of the iterated logarithm, empirical process, Shannon process, Lorenz process of orderν, Lorenz curve, strong invariance principle, Lorenz process, Vervaat process, relative compactness, Statistics, Probability and Uncertainty
Statistics and Probability, integrated empirical difference process, redudancy process, Numerical Analysis, total time on test function, Strong limit theorems, Functional limit theorems; invariance principles, Applications of renewal theory (reliability, demand theory, etc.), quantile process, mean residual life process, Strassen's law of the iterated logarithm, empirical process, Shannon process, Lorenz process of orderν, Lorenz curve, strong invariance principle, Lorenz process, Vervaat process, relative compactness, Statistics, Probability and Uncertainty
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