INFERENCE UNDER PEAKEDNESS RESTRICTIONS
Javier Rojo, José Luis Batún-Cutz, Ramón Durazo-Arvizú · 2007
A distribution function F is more about a known point a than the distribution G is about the known point b if F((x + a) − ) F( x + a) � G((x + b) − ) G( x + b) for every x. The statistical concept of dispersion plays an important role in the theory and practice of statistics. For example, in statis- tical genetics, the effect of a gene on a phenotype of interest can be ascertained by regressing the squared phenotypical differences on the proportion of identical by descent alleles shared by pairs of siblings (Haseman-Elston (1972)). This paper proposes estimators for the distribution functions F and/or G, when F is more peaked than G. The estimators are shown to be strongly uniformly consistent, their asymptotic distribution theory is discussed, and an asymptotic test for equal- ity in peakedness is provided. The case of censored data is also considered. Data from various national and international studies are used to illustrate the new pro- cedures.