Extreme values and tests for randomness

Nonparametric Tests for Randomness

To decide whether a given sequence is “truely” random, or independent and identically distributed, we need to resort to nonparametric tests for randomness. Six tests: the ordinary run test, the sign test, the runs up and down test, the Mann-Kendall test, the Bartels’ rank test and the test based on entropy estimators are introduced in this report and their weaknesses are analyzed. Combining the...

Comparison of Some Tests of Sample Censoring of Extreme Values

Rank Tests for Independence and Randomness

This chapter concerns rank tests for independence of two random variables. A form of locally most powerful test against particular alternative is derived and the most often used variants of this test are mentioned, namely the test of van der Waerden type, Spearman rank correlation coefficient, the quadrant test and the Kendall rank correlation coefficient, a member of non-linear rank statistics...

Hierarchies of Randomness Tests

It is well known that Martin-Löf randomness can be characterized by a number of equivalent test concepts, based either on effective nullsets (Martin-Löf and Solovay tests) or on prefix-free Kolmogorov complexity (lower and upper entropy). These equivalences are not preserved as regards the partial randomness notions induced by effective Hausdorff measures or partial incompressibility. Tadaki [2...

Calibration Weighting to Compensate for Extreme Values, Non-response and Non-coverage in Labor Force Survey

Frame imperfection, non-response and unequal selection probabilities always affect survey results. In order to compensate for the effects of these problems, Devill and Särndal (1992) introduced a family of estimators called calibration estimators. In these estimators we look for weights that have minimum distance with design weights based on a distance function and satisfy calibration equa...