ABSTRACT
This chapter introduces the rank and signed rank statistics to test two types of experiments. The most popular simple linear rank statistic is the Wilcoxon statistic. The main attractive feature of signed rank statistics is their simplicity and distribution freeness over the set of all symmetric distributions. Sufficient statistics make a problem simple by reducing the sample space. Test statistics based on efficient central sequences are only valid under correctly specified radial densities. The study of the asymptotic properties is a fundamental and essential part of nonparametric statistics. Many authors have contributed to the development, and numerous theorems have been formulated to show the asymptotic normality of a properly normalized rank order statistic in many testing problems. In many financial applications, a modeling of the time varying conditional covariance matrix for asset returns is widely invoked. The chapter proposes two different multivariate rank-based portfolio estimations.
