2018/08/22 by Georg Berschneider, Berschneider, Georg, Björn Böttcher +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60E15 #60G15 #62H10 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Statistical Methods and Inference #Statistics Theory (math.ST) #math.PR #math.ST #msc:60E15 #msc:60G15 #msc:62H10 #stat.TH
paper · pdf · doi:10.48550/arxiv.1808.07280
improved presentation of the results of the previous version (v1)
openalex publication_date 2018/08/22 · openalex created_date 2018/08/31 · arxiv created 2019/03/19 · arxiv updated 2019/03/20 · openalex updated_date 2026/07/28
The paper contains results in three areas: First we present a general estimate for tail probabilities of Gaussian quadratic forms with known expectation and variance. Thereafter we analyze the distribution of norms of complex Gaussian random fields (with possibly dependent real and complex part) and derive representation results, which allow to find efficient estimators for the moments of the associated Gaussian quadratic form. Finally, we apply these results to sample distance multivariance, which is the test statistic corresponding to distance multivariance -- a recently introduced multivariate dependence measure. The results yield new tests for independence of multiple random vectors. These are less conservative than the classical tests based on a general quadratic form estimate and they are (much) faster than tests based on a resampling approach. As a special case this also improves independence tests based on distance covariance, i.e., tests for independence of two random vectors.