New semiparametric and nonparametric bootstrap tests for Spearman's rho

In this paper we propose two bootstrap-based tests for Spearman's rho. The first is a semiparametric test based on copulas, while the second is a nonparametric test. The efficiency of the tests are investigated by means of a Monte-Carlo study. It is found that they perform very satisfactorily as far as size and power are concerned

Three methods to apply the bootstrap correctly to hypothesis testing

In this paper we discuss three methods to apply the bootstrap correctly to hypothesis testing. For each of these methods a simple example is considered, namely testing the variance of a population. The shortcoming associated with implementing bootstrap testing procedures incorrectly is analysed by making use of this example. Some theoretical properties of the corresponding bootstrap critical values are derived. The results of a simulation study are presented to provide empirical comparison between the different methods and to substantiate the theoretical finding

Some new results on the empirical copula estimator with applications

We derive the joint distribution of the ranks associated with a given bivariate random sample. Using these results, exact non-asymptotic expressions and asymptotic expansions for the mean and variance of the classical empirical copula estimator are obtained. An explicit expression of the coefficient appearing in the O(1/n)-term for the mean can, for example, be found; a result that apparently does not appear in the existing literature. Furthermore, it is shown that similar explicit non-asymptotic expressions as well as asymptotic expansions can be derived for the rank-based Bernstein copula estimatorNational Research Foundation of South Afric

Comments: a review of testing procedures based on the characteristic function

First of all, we would like to congratulate the author for writing this interesting and timely review paper on testing procedures based on the empirical characteristic function. The exposition of the ideas and methods is necessarily brief, given the wide scope of the paper. So, we strongly encourage the author to write a monograph on the topic, where main procedures can be developed in detail. Although it is really hard to add something interesting to this review, we would like to comment on three issues. The author provides a very limited discussion on the first, but did not consider the second and third in his pape