3 problems

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Asymptotic equivalence of zero-order spline principal components and the Brownian covariance operator
The working model uses principal components derived from the design matrix of zero-order splines. Asymptotic equivalence conjecture. These principal components are conjectured to b…
Conjectureopenprincipal-components spline-regression stochastic-processesarXiv posted 2 days ago
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Conjecture on stationary-process approximation for higher-order dynamic principal components
Let $\widehat{f}_t$ denote the first dynamic principal component (DPC) of order $k$ constructed from a stationary vector process $\mathbf{z}_t$ . For the first DPC of order $k$ , the…
Conjectureopenprincipal-components stationary-processes time-seriesarXiv posted 2 days ago
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Conjectured optimal eigenfunction rate for functional data
Optimal eigenfunction rate conjecture. The optimal rate for the $l_2$ risk of the eigenfunctions is of order
Conjectureopenfunctional-data nonparametric-statistics principal-componentsarXiv posted 2 days ago

Asymptotic equivalence of zero-order spline principal components and the Brownian covariance operator