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Composite Tests under Corrupted Data.

Michel Broniatowski1, Jana Jurečková2,3, Ashok Kumar Moses4

  • 1Laboratoire de Probabilités, Statistique et Modélisation, Sorbonne Université, 75005 Paris, France.

Entropy (Basel, Switzerland)
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Summary
This summary is machine-generated.

This study introduces new statistical tests for corrupted data, addressing measurement errors. The proposed methods aggregate likelihood ratios and divergence-based statistics for improved hypothesis testing performance.

Keywords:
Chernoff Stein lemmaNeyman Pearson testcomposite hypothesescorrupted datadivergence based testingleast-favorable hypotheses

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Area of Science:

  • Statistical inference
  • Hypothesis testing
  • Measurement error theory

Background:

  • Mismeasured observations (X_i = Z_i + δV_i) are common in data analysis.
  • Standard tests assume accurate data, failing under measurement error.
  • Hypothesis testing requires distinguishing between densities f_0 and g_0 for underlying variables (Z_i).

Purpose of the Study:

  • To develop robust test procedures for statistical hypotheses with corrupted data.
  • To introduce a novel aggregation method for likelihood ratio tests under measurement error.
  • To propose and evaluate alternative divergence-based aggregated tests.

Main Methods:

  • Aggregation of likelihood ratios across a range of measurement error parameters (δ).
  • Definition of least-favorable hypotheses for aggregated tests.
  • Analysis of Kullback-Leibler divergence for aggregated test families.
  • Development and simulation of divergence-based aggregated tests.

Main Results:

  • Finite-sample lower bounds for test power were derived analytically and through simulation.
  • The proposed aggregated likelihood ratio test provides a framework for hypothesis testing with corrupted data.
  • Aggregated divergence-based tests demonstrated potentially superior performance compared to aggregated likelihood ratio tests.

Conclusions:

  • Aggregated likelihood ratio tests offer a method to handle corrupted data in hypothesis testing.
  • Divergence-based aggregated tests can outperform likelihood ratio approaches in certain scenarios.
  • The study provides valuable tools for statistical analysis when data quality is compromised by measurement errors.