English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

A test based on tapering is proposed for use in testing a global linearhypothesis under a functional linear model. The test statistic is constructedas a weighted sum of squared linear combinations of Fourier coefficients, atapered quadratic form, in which higher Fourier frequencies are down-weightedso as to emphasize the smooth attributes of the model. A formula is$Q_n^{OPT}=n\sum_{j=1}^{p_n}j^{-1/2}\|\boldsymbol{Y}_{n,j}\|^2$. Down-weightingby $j^{-1/2}$ is selected to achieve adaptive optimality among tests based ontapering with respect to its ``rates of testing,'' an asymptotic framework formeasuring a test's retention of power in high dimensions under smoothnessconstraints. Existing tests based on truncation or thresholding are known tohave superior asymptotic power in comparison with any test based on tapering;however, it is shown here that high-order effects can be substantial, and thata test based on $Q_n^{OPT}$ exhibits better (non-asymptotic) power against thesort of alternatives that would typically be of concern in functional dataanalysis applications. The proposed test is developed for use in practice, anddemonstrated in an example application.

A powerful test based on tapering for use in functional data analysis