Finite-Sample Calibration and Power Benchmarks in Two-Sample Random-Integration Tests
Abstract
In high-dimensional two-group studies, a supplied variable set can be used directly or to learn a projection. We study how much attainable power these choices retain at fixed observation and calibration budgets. For complete unbiased random-integration statistics under Gaussian common shape, a fixed-spectrum comparison orders direction-wise power and gives an explicit criterion balancing an oracle advantage against learning loss. Joint regeneration controls level for a specified learner with unknown diagonal shape. A paired construction permits observation reuse and finite-reference calibration of fitted scores and menus. In the paired diagonal experiment, an invariant sparse likelihood-ratio benchmark provides an attainable efficiency target. Finite-amplitude bounds connect a classical bounded quadratic to this target; conditioning on the coordinate maximum yields informative complementary bounds at moderate and strong signals. Both comparisons include finite reference budgets, and null-only simulations certify local comparisons with specified fitted rules. Equal-budget experiments and a leukemia application compare aggregation, projection and fitted quadratic scores. For correlated paired data, classical sign randomization supplies a separate calibration under central symmetry. The efficiency guarantees apply to the stated experiments and signal classes; general small-budget shape efficiency and adaptation to unknown signal allocation remain open.
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BibTeX
@misc{wang2026finitesample,
title = {{Finite-Sample Calibration and Power Benchmarks in Two-Sample Random-Integration Tests}},
author = {Pengfei Wang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00865},
eprint = {2611.00865},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00865},
}
RIS
TY - UNPB
TI - Finite-Sample Calibration and Power Benchmarks in Two-Sample Random-Integration Tests
AU - Pengfei Wang
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00865
UR - https://arxiv.org/abs/2611.00865
AB - In high-dimensional two-group studies, a supplied variable set can be used directly or to learn a projection. We study how much attainable power these choices retain at fixed observation and calibration budgets. For complete unbiased random-integration statistics under Gaussian common shape, a fixed-spectrum comparison orders direction-wise power and gives an explicit criterion balancing an oracle advantage against learning loss. Joint regeneration controls level for a specified learner with unknown diagonal shape. A paired construction permits observation reuse and finite-reference calibration of fitted scores and menus. In the paired diagonal experiment, an invariant sparse likelihood-ratio benchmark provides an attainable efficiency target. Finite-amplitude bounds connect a classical bounded quadratic to this target; conditioning on the coordinate maximum yields informative complementary bounds at moderate and strong signals. Both comparisons include finite reference budgets, and null-only simulations certify local comparisons with specified fitted rules. Equal-budget experiments and a leukemia application compare aggregation, projection and fitted quadratic scores. For correlated paired data, classical sign randomization supplies a separate calibration under central symmetry. The efficiency guarantees apply to the stated experiments and signal classes; general small-budget shape efficiency and adaptation to unknown signal allocation remain open.
ER -