A DECISION PROCEDURE FOR DETERMINING THE NUMBER OF COMPONENTS IN PRINCIPAL COMPONENT ANALYSIS

In principal component analysis, a lot of heuristic rules are proposed to determine the number of components. All of those approaches lack consideration of protection in terms of the probability of CD (correct decision). Under some regularity conditions, this paper proposes a natural selection rule to achieve the goal. The sample size and critical value, which are needed to select the potential number of components, are computed with the protection of the probability of CD to a specified value P*. Besides, a simulation study is carried out to study the property of the proposed rule when the underlying distribution follows a multivariate elliptical t-distribution. The results show that the proposed rule is insensitive to the variations of multivariate t-distribution.