
Spatiotemporal Covariance Estimation by Shifted Partial Tracing
We consider the problem of covariance estimation for replicated spaceti...
read it

Asymptotically Efficient Estimation of Smooth Functionals of Covariance Operators
Let X be a centered Gaussian random variable in a separable Hilbert spac...
read it

LowRank Covariance Function Estimation for Multidimensional Functional Data
Multidimensional function data arise from many fields nowadays. The cova...
read it

Quantifying deviations from separability in spacetime functional processes
The estimation of covariance operators of spatiotemporal data is in man...
read it

Testing Separability of Functional Time Series
We derive and study a significance test for determining if a panel of fu...
read it

On the Multiplicative Decomposition of Heterogeneity in Continuous Assemblages
A system's heterogeneity (equivalently, diversity) amounts to the effect...
read it

Some Insights About the Small Ball Probability Factorization for Hilbert Random Elements
Asymptotic factorizations for the smallball probability (SmBP) of a Hil...
read it
Principal Separable Component Analysis via the Partial Inner Product
The nonparametric estimation of covariance lies at the heart of functional data analysis, whether for curve or surfacevalued data. The case of a twodimensional domain poses both statistical and computational challenges, which are typically alleviated by assuming separability. However, separability is often questionable, sometimes even demonstrably inadequate. We propose a framework for the analysis of covariance operators of random surfaces that generalises separability, while retaining its major advantages. Our approach is based on the additive decomposition of the covariance into a series of separable components. The decomposition is valid for any covariance over a twodimensional domain. Leveraging the key notion of the partial inner product, we generalise the power iteration method to general Hilbert spaces and show how the aforementioned decomposition can be efficiently constructed in practice. Truncation of the decomposition and retention of the principal separable components automatically induces a nonparametric estimator of the covariance, whose parsimony is dictated by the truncation level. The resulting estimator can be calculated, stored and manipulated with little computational overhead relative to separability. The framework and estimation method are genuinely nonparametric, since the considered decomposition holds for any covariance. Consistency and rates of convergence are derived under mild regularity assumptions, illustrating the tradeoff between bias and variance regulated by the truncation level. The merits and practical performance of the proposed methodology are demonstrated in a comprehensive simulation study.
READ FULL TEXT
Comments
There are no comments yet.