Testing: Variations On A Theme (Solo And Choir)
summary
Sixty years of work on testing is condensed into concrete claims: nonparametric vs semi‑parametric tools, rank/median procedures and Wilcoxon‑style tests show rank/median tests more robust than mean‑based tests; local contiguous alternatives reveal that omnidirectional tests lose asymptotic efficiency (power can be essentially zero against any specific direction); m‑out‑of‑n resampling and extrapolation provide a fix so m-out-of-n bootstrap restores valid null distributions; final proposals temper infinite families of score tests into a sum that regains power against targeted alternatives.
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chapters (10)
- 0:00Introduction
- 7:11Non-parametric statistics
- 14:49PhD thesis on Hotelling's T²
- 27:06Variance dependence in linear models
- 35:34Goodness-of-fit for kernel regression
- 41:26Bootstrap hypothesis testing
- 48:28Correlation tests with Taylor properties
- 53:11Semi-parametric hypothesis tests
- 57:32Testing in big data
- 1:00:14Common themes in Peter's work