Module ncomp 

Automatic selection of the number of principal components (ncomp).

Provides methods for choosing how many FPC scores to retain in FPCA-based monitoring: cumulative variance, elbow detection, or a fixed count.

For functional linear regression, the optimal ncomp grows as O(n^{1/5}) (Hall & Horowitz, 2007, Theorem 1, p. 73). In practice, retaining 95% cumulative variance (Jackson, 1991, Chapter 4) is a widely used default that adapts to the eigenvalue decay rate.

References

• Cattell, R.B. (1966). The scree test for the number of factors. Multivariate Behavioral Research, 1(2), 245–276. p. 252.
• Hall, P. & Horowitz, J.L. (2007). Methodology and convergence rates for functional linear regression. Annals of Statistics, 35(1), 70–91. Theorem 1, p. 73.
• Jackson, J.E. (1991). A User’s Guide to Principal Components. Wiley, Chapter 4.
• Kaiser, H.F. (1960). The application of electronic computers to factor analysis. Educational and Psychological Measurement, 20, 141–151. pp. 145–146.

Enums

NcompMethod

Method for selecting the number of principal components.

Functions

select_ncomp

Select the number of principal components from an eigenvalue spectrum.