Goodness Of Fit Testing Using A Specific Density Estimate

To test the hypothesis H0 : f = ψ that an unknown density f is equal to a specified one, ψ, an estimate f̂ of f is compared with ψ. The total variation distance ||f̂ − ψ||1 is used as test statistic. The density estimate f̂ considered is a peculiar one. A table of critical values is provided, this table is applicable for arbitrary ψ. 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.