Goodness of fit testing using a specific density estimate

Albers, Casper J. and Schaafsma, Willem (2008). Goodness of fit testing using a specific density estimate. Statistics & Decisions, 26(1) pp. 3–23.

DOI: https://doi.org/10.1524/stnd.2008.0909

Abstract

To test the hypothesis H₀: f=? that an unknown density f is equal to a specified one, ?, an estimate f^ of f is compared with ?. The total variation distance || f^-?||₁ is used as test statistic. The density estimate f^ considered is a peculiar one. A table of critical values is provided, this table is applicable for arbitrary ?. Relations with other methods, Neyman´s smooth tests in particular, are discussed and power comparisons are performed. In certain situations, our test is recommendable. An example from practice is provided.

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