A note on estimating distribution functions

A Note on Misspecified Estimating Functions

We consider the use of estimating functions that are not unbiased. Typically, to result in consistent estimators, unbiasedness of estimating functions is a pre-requisite. However, it is sometimes easier to find a useful estimating function that is biased, especially in the presence of missing data or misclassified observations. We show that the root of the estimating function can be modified to...

A Note on Estimating Distribution Functions1

In this note we consider the problem of estimating the distribution function Fiy) in terms of the sequence of numbers {a»}, and the sequence of functions/B(y). To this end we consider, for each positive integer ra, a system of equations and inequalities. We construct a distribution function £n(y) in terms of any solution of this system, and show that limnH.,0 £.(y) = £(y) for every continuity p...

A Note on Conjugate Functions

1. Statement of results. The purpose of this note is to discuss as simply as possible a generalization of the classical theorem of M. Riesz2 on the integrability of the conjugate functions of functions in LP, and to point out some of the consequences for Fourier series. Suppose that(t) is a non-negative, convex function defined for t^O with (2t) ̂K<p(t) ior some constant K. Th...

A Note on Convex Functions

In this paper, we give twoweak conditions for a lower semi-continuous function on the n-dimensional Euclidean space Rn to be a convex function. We also present some results for convex functions, strictly convex functions, and quasi-convex functions.

A Note on SpanP Functions