Data Driven Smooth Tests for Bivariate Normality

Based upon the idea of construction of data driven smooth tests for composite hypotheses presented in Inglotet al.(1997) and Kallenberg and Ledwina (1997), two versions of data driven smooth test for bivariate normality are proposed. Asymptotic null distributions are derived, and consistency of the newly introduced tests against every bivariate alternative with marginals having finite variances is proved. Included results of power simulations show that one of the proposed tests performs very well in comparison with other commonly used tests for bivariate normality.