Estimation of a certain functional of a probability density function
- 1 January 1969
- journal article
- research article
- Published by Taylor & Francis in Scandinavian Actuarial Journal
- Vol. 1969 (3-4) , 201-206
- https://doi.org/10.1080/03461238.1969.10404595
Abstract
In nonparametric inference, the importance of the functional Δ(F)=∫−∞∞ ƒ2(x)dx, where F is the population cdf with density f, could hardly be overemphasized. It is a fundamental quantity involved in the expressions for the asymptotic efficiency of rank tests for many problems like location shift, regression, dependence, analysis of variance, etc. Also in some cases, point as well as interval estimates derived from rank tests have asymptotic efficiency involving the above functional. By a variational argument, Dodges and LehmannKeywords
This publication has 4 references indexed in Scilit:
- On a Distribution-free Method of Estimating Asymptotic Efficiency of a Class of Non-parametric TestsThe Annals of Mathematical Statistics, 1966
- Nonparametric Confidence Intervals for a Shift ParameterThe Annals of Mathematical Statistics, 1963
- On Estimation of a Probability Density Function and ModeThe Annals of Mathematical Statistics, 1962
- The Efficiency of Some Nonparametric Competitors of the $t$-TestThe Annals of Mathematical Statistics, 1956