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Abstract:
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In the implementation of some well-known inference methods, such as the partial least squares regression and supervised principal component analysis, one has to determine the number of orthogonal components selected into the final model. Inspired by Lockhart et al. [Ann. Stat. 42, 413-446], we develop a significant test to tackle this problem without conducting the cross validation. Our testing procedure is coupled with a simple test statistic whose tail probability under the null hypothesis can even be derived exactly when the number of candidate components is small.
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