Incomplete observations in high-dimensional or functional spaces can be tested by averaging standard tests over finite-dimensional projections, provided missingness is independent of the data and every coordinate subset has a chance of being fully observed.
Escobar, Bernadette Klotz, Beatriz E
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A unified approach for testing in Hilbert spaces on incomplete data
Incomplete observations in high-dimensional or functional spaces can be tested by averaging standard tests over finite-dimensional projections, provided missingness is independent of the data and every coordinate subset has a chance of being fully observed.