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Likelihood Ratio Testing under Measurement Errors.

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Summary
This summary is machine-generated.

This study addresses statistical hypothesis testing with measurement errors. Ignoring these errors alters type I error rates, but a novel minimax test, using pseudo-capacities, offers robust performance against misspecified hypotheses.

Keywords:
2-alternating capacitiesmeasurement errorsmisspecified hypothesis and alternativerobust testingtwo-sample test

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Area of Science:

  • Statistics
  • Hypothesis Testing
  • Measurement Error Analysis

Background:

  • Likelihood ratio tests are fundamental in statistical inference.
  • Measurement errors in observed data can significantly distort hypothesis testing outcomes.
  • Ignoring measurement errors can lead to deviations in type I error rates from nominal values.

Purpose of the Study:

  • To analyze the impact of measurement errors on the likelihood ratio test.
  • To develop a robust statistical test for situations with unobservable measurement errors.
  • To derive a minimax test for misspecified hypotheses in the presence of measurement errors.

Main Methods:

  • Investigated the properties of the likelihood ratio test when observations are subject to additive measurement errors (Z_i = X_i + δV_i).
  • Derived a minimax test by leveraging the concept of pseudo-capacities.
  • Employed numerical experiments to evaluate the performance of the proposed test.

Main Results:

  • The standard likelihood ratio test, when ignoring measurement errors, maintains its power property but with altered type I error rates.
  • A novel minimax test was successfully derived for families of misspecified hypotheses and alternatives.
  • Numerical experiments demonstrated the practical applicability and effectiveness of the developed test.

Conclusions:

  • Measurement errors necessitate adjustments in standard hypothesis testing procedures.
  • The proposed minimax test offers a robust solution for statistical inference under measurement error conditions.
  • The study highlights the utility of pseudo-capacities in constructing reliable statistical tests.