Asymptotic properties of some goodness-of-fit tests based on the \(L_ 1\)-norm

DOI10.1007/BF00057739zbMath0695.62021MaRDI QIDQ910121

Sigeo Aki, Nobuhisa Kashiwagi

Publication date: 1989

Published in: Annals of the Institute of Statistical Mathematics (Search for Journal in Brave)

zbMATH Keywords

symmetryGaussian processmartingalegoodness-of-fit testsdensity functionempirical processasymptotic tail probabilitystandard Wiener process\(L_ 1\)-normapproximate Bahadur efficiencytable of some percentage points

Mathematics Subject Classification ID

Nonparametric hypothesis testing (62G10) Asymptotic distribution theory in statistics (62E20) Non-Markovian processes: hypothesis testing (62M07) Markov processes: hypothesis testing (62M02)

Related Items

On nonparametric tests for symmetry in \(R^ m\) ⋮ A rule of thumb for testing symmetry about an unknown median against a long right tail

Cites Work

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• Martingale Approach in the Theory of Goodness-of-Fit Tests
• An explicit formula for the c.d.f. of the \(L_ 1 \)norm of the Brownian bridge
• On nonparametric tests for symmetry
• Some test statistics based on the martingale term of the empirical distribution function
• On the integral of the absolute value of the pinned Wiener process
• The integral of the absolute value of the pinned Wiener process - calculation of its probability density by numerical integration
• A Cramer Von-Mises Type Statistic for Testing Symmetry
• Stochastic Comparison of Tests
• A Test for Symmetry Using the Sample Distribution Function
• On the Average of a Certain Wiener Functional and a Related Limit Theorem in Calculus of Probability