Update fpc #2
Open
Update fpc #2
Conversation
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Before updating, eigenequation verified is given by integral(C_n(s, t) * FPC_j(t) dt) = FPC_j(s) * lambda_j, but being C_n(s, t) = X'X. Since the kernel of the autocovariance operator is usual given by C_n(s, t) = (1/n) * X'X, a new factor 1/sqrt(n) is incorporated inside of the SVD procedure Now, integral(C_n(s, t) * FPC_j(t) dt) = FPC_j(s) * lambda_j, but being C_n(s, t) = (1/n) * X'X. This change does not affect the estimation and testing results since it is just a scale factor, which is compensated by the component-wise coefficients
|
Pending to merge until there are proper unit tests in the package. |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
Before updating, eigenequation verified is given by integral(C_n(s, t) * FPC_j(t) dt) = FPC_j(s) * lambda_j, but being C_n(s, t) = X'X. Since the kernel of the autocovariance operator is usual given by C_n(s, t) = (1/n) * X'X, a new factor 1/sqrt(n) is incorporated inside of the SVD procedure
Now, integral(C_n(s, t) * FPC_j(t) dt) = FPC_j(s) * lambda_j, but being C_n(s, t) = (1/n) * X'X.
This change does not affect the estimation and testing results since it is just a scale factor, which is compensated by the component-wise coefficients