Goodness of fit testing using a specific density estimate

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