May 30, 2024AxiomsOpen Access

A Discrete Cramér–Von Mises Statistic Related to Hahn Polynomials with Application to Goodness-of-Fit Testing for Hypergeometric Distributions

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A discrete Cramér–von Mises statistic achieves local asymptotic Bahadur optimality for goodness-of-fit testing, establishing an exact discrete analogue to classical Gaussian processes.
Theoretical derivation gives the Karhunen–Loève expansion for discrete weighted Brownian bridges, using fundamental properties of Hahn polynomials on hypergeometric distributions.
The framework resolves known computational limits in discrete goodness-of-fit testing, enabling theoretical extensions across classical orthogonal polynomials and their q-analogues.

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Implication

Theoretical analysis demonstrates local asymptotic Bahadur optimality for discrete Cramér–von Mises statistics, suggesting wider applicability to classical orthogonal polynomials.

Cite This Study

Jean‐Renaud Pycke (2024) studied this question.

synapsesocial.com/papers/68e67ba3b6db643587605a2e https://doi.org/10.3390/axioms13060369

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Implication

Theoretical analysis demonstrates local asymptotic Bahadur optimality for discrete Cramér–von Mises statistics, suggesting wider applicability to classical orthogonal polynomials.

A Discrete Cramér–Von Mises Statistic Related to Hahn Polynomials with Application to Goodness-of-Fit Testing for Hypergeometric Distributions

Key Points

Discussion

Implication

Cite This Study

A Discrete Cramér–Von Mises Statistic Related to Hahn Polynomials with Application to Goodness-of-Fit Testing for Hypergeometric Distributions

Key Points

Discussion

Implication

Cite This Study

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