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ON THE WEISS TEST OF
LARGE SAMPLE TESTS FOR NORMALITY
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1_Pn alternative distributions analog assume assumptions asymptotic distribution theory asymptotic power asymptotic purposes asymptotically normally chapter chi-square chi-square distribution completes the proof contiguous alternatives converges stochastically converges to zero covariance matrix critical region defined denote the quantity distribution function disturbance functions easily shown eigenvalues empirical estimates expression Hence Hermite polynomials Hn(x implies increasing subset Kn+1 Kolmogorov-Smirnov test l+o(D l+o(l large-sample log 1/p log(l/p mean vector non-trivial power normal random variables normally distributed null hypothesis number of order obtain order statistics proof of lemma sample quantiles sample spacings satisfy scale-location parameter family selected subset sequence of alternatives Sg(n Shapiro-Francia test smaller order terms Stephens stochastically to zero subset of order tail Taylor series tends to infinity test statistic tests based tests for normality Tests of Fit variance W-test Weiss Wet and Venter Wilk-Shapiro test