Inhaltszusammenfassung

Many test procedures with correlated chi-square statistics from the diagonal of a Wishart matrix use conservative probability inequalities for small “p-values”, mostly based on low dimensional marginal distributions. Here, some upper tail approximations are presented for the distribution of the maximum of such chi-square or gamma random variables. Frequently, much more accurate results are obtained than by any other known methods. Moreover, in many examples, this method provides still conserv...Many test procedures with correlated chi-square statistics from the diagonal of a Wishart matrix use conservative probability inequalities for small “p-values”, mostly based on low dimensional marginal distributions. Here, some upper tail approximations are presented for the distribution of the maximum of such chi-square or gamma random variables. Frequently, much more accurate results are obtained than by any other known methods. Moreover, in many examples, this method provides still conservative values. The approximations are suitable for correlation matrices allowing - after a permutation of the random variables - a partition into blocks with diagonal blocks tending to contain larger correlations with a rather moderate variability and positive means. The “probability contributions” of the individual diagonal blocks are approximated by Taylor polynomials of 2nd degree w.r.t. the deviations between the correlations and their means or sometimes computed exactly. The contribution of the off-diagonal blocks is estimated by replacing the correlations by means.» weiterlesen» einklappen

Autoren

Klassifikation

DFG Fachgebiet:
Mathematik

DDC Sachgruppe:
Statistik