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 f^ of f is compared with ψ. The total variation distance ∥ f^-ψ∥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 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