Browsing by Author "Ibragimov, Rustam"
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Efficiency of linear estimators under heavytailedness: convolutions of [alpha]symmetric distributions.
Ibragimov, Rustam (Cambridge University Press, 2007)This paper focuses on the analysis of efficiency, peakedness, and majorization properties of linear estimators under heavytailedness assumptions. We demonstrate that peakedness and majorization properties of logconcavely ... 
The exact constant in the Rosenthal inequality for random variables with mean zero
Ibragimov, Rustam; Sharakhmetov, Shaturgun (Society for Industrial and Applied Mathematics, 2002)Let $\xi_1, \ldots, \xi_n$ be independent random variables with ${\bf E}\xi_i=0,$ ${\bf E}\xi_i^t<\infty$, $t>2$, $i=1,\ldots, n,$ and let $S_n=\sum_{i=1}^n \xi_i.$ In the present paper we prove that the exact constant ... 
Heavytailedness and Threshold Sex Determination.
Ibragimov, Rustam (Elsevier, 2008)This paper studies the properties of the sex ratio in twoperiod models of threshold (e.g., polygenic or temperaturedependent) sex determination under heavytailedness in the framework of possibly skewed stable distributions ... 
The limits of diversification when losses may be large.
Ibragimov, Rustam; Walden, Johan (Elsevier, 2007)Recent results in value at risk analysis show that, for extremely heavytailed risks with unbounded distribution support, diversification may increase value at risk, and that generally it is difficult to construct an ... 
Market Demand Elasticity and Income Inequality
Ibragimov, Rustam; Ibragimov, Marat (Springer Verlag, 2007)This paper deals with the analysis of the relation between aggregate demand for a consumption good and the distribution of income across consumers. We obtain sufficient conditions under which changes in income inequality ... 
On Extremal Distributions and Sharp L[sub]pBounds For Sums of Multilinear Forms.
de la Peña, Victor H.; Ibragimov, Rustam; Sharakhmetov, Shaturgun (The Institute of Mathematical Statistics, 2003)In this paper we present a study of the problem of approximating the expectations of functions of statistics in independent and dependent random variables in terms of the expectations of functions of the component random ... 
Optimal Constants in the Rosenthal Inequality for Random Variables with Zero Odd Moments.
Ibragimov, Rustam; Ibragimov, Marat (Elsevier Science B.V., Amsterdam, 2008)We obtain estimates for the best constant in the Rosenthal inequality View the MathML source for independent random variables ξ1,…,ξn with l zero first odd moments, lgreaterorequal, slanted1. The estimates are sharp in ... 
Portfolio Diversification under Local and Moderate Deviations from Power Laws.
Ibragimov, Rustam; Walden, Johan (Elsevier, 2008)This paper analyzes portfolio diversification for nonlinear transformations of heavytailed risks. It is shown that diversification of a portfolio of convex functions of heavytailed risks increases the portfolio’s riskiness ... 
Regression asymptotics using martingale convergence methods.
Ibragimov, Rustam; Phillips, Peter C.B. (Cambridge University Press, 2008)Weak convergence of partial sums and multilinear forms in independent random variables and linear processes and their nonlinear analogues to stochastic integrals now plays a major role in nonstationary time series and has ... 
A Tale of Two Tails: Peakedness Properties in Inheritance Models of Evolutionary Theory.
Ibragimov, Rustam (Springer International, 2008)In this paper, we study transmission of traits through generations in multifactorial inheritance models with sex and timedependent heritability. We further analyze the implications of these models under heavytailedness ... 
Thou shalt not diversity: Why "Two of Every Sort"?
Ibragimov, Rustam (Apt (Applied Probability Trust), 2007)This paper presents a study of the intertemporal propagation of distributional properties of phenotypes in general polygenic multisex inheritance models with sex and timedependent heritabilities. It further analyzes the ...