Asymptotic Distribution of the Hermite Normality Test
نویسندگان
چکیده
This paper presents some asymptotical results of the Hermite Normality test previously introduced. We show that the Hermite statistic S H is distributed under the null hypothesis as a quadratic form of normal variates and under the nonnull hypothesis as normal. The special case of tests with two polynomials is studied in details. Finally, we give some considerations for the choice of a best Hermite test when prior knowledge is available and especially we determine the test asymptotically the most powerful for a xed alternative distribution (the uniform distribution). Those results are supported by simulations.
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