Logarithmic quantile estimation and its applications to nonparametric factorial designs
Penn State University
The logarithmic quantile estimation for rank statistics estimates quantiles based on the almost sure central limit theorem for linear rank statistics for samples with continuous distribution functions. The logarithmic quantile estimation for rank statistics is a procedure that estimates quantiles directly from the data and not using the asymptotic distributions or estimations of unknown variances, covariances or eigenvalues of covariance matrices. In this talk we show how the logarithmic quantile estimation is derived from the almost sure central limit theorem and how it is applied to nonparametric factorial designs.
As an application, we consider the c-sample problem, when the samples may be dependent and the asymptotic distribution is unknown. In this case the logarithmic quantile estimation is applicable to the Kruskal-Wallis statistic and we illustrate this using the data set from Boos (1986). Another application is the “shoulder tip pain study” that appears in Lumley (1996) and that can be analyzed using a combination of logarithmic quantile estimation and an ANOVA type statistic.
This is joint work with Manfred Denker.