For testing P = P0 in the model of densities (14.35) with Tj the normalized Legendre polynomials,
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For testing P = P0 in the model of densities (14.35) with Tj the normalized Legendre polynomials, show that Neyman’s smooth test is consistent in power against any distribution P as long as the first k moments of P are not all identical to the first k moments of P0.
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Related Book For 
Testing Statistical Hypotheses
ISBN: 9781441931788
3rd Edition
Authors: Erich L. Lehmann, Joseph P. Romano
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