The minimum distance method of testing

Billingsley, P.: Convergence of Probability Measures. New York 1968.

Birch, M.W.: A new proof of the Fisher-Pearson theorem. Ann. Math. Statist.35, 1964, 817–824.

Blackman, J.: On the approximation of a distribution function by an empirical distribution. Ann. Math. Statist.26, 1955, 256–267.

Bolthausen, E.: Convergence in distribution of minimum distance estimators. Metrika24, 1977. 215–227.

Chernoff, H.: On the distribution of the likelihood ratio. Ann. Math. Statist.25, 1954, 573–578.

Chernoff, H., andE.L. Lehmann: The use of maximum likelihood estimates inX 2 tests for good-ness-of-fit. Ann. Math. Statist.25, 1954, 579–586.

Chibisov, D.M.: An investigation of the asymptotic power of the tests of fit. Theor. Prob. Appl.10, 1965, 421–437.

Cramér, H.: Mathematical Methods of Statistics. Princeton 1964.

Csörgő, M., andM.D. Burke: Weak approximations of the empirical process when parameters are estimated. Lect. Notes in Math.566, 1976, 1–16.

Csörgő, M. J. Komlós, P. Major, P. Révész andG. Tusnády: On the empirical process when parameters are estimated. Trans. Seventh Prague Conference 1974. Prague 1977, 87–97.

Darling, D.A.: The Cramér/Smirnov test in the parametric case. Ann. Math. Statist.26, 1955, 1–20.

Dudley, R.M.: Weak convergence of probabilities on non-separable metric spaces and empirical measures on Euclidean spaces. Ill. J. Math.10, 1966, 109–126.

—: Measures on non-separable metric spaces. Ill. J. Math.11, 1967, 449–453.

—: Distances of probability measures and random variables. Ann. Math. Statist.39, 1968, 1563–1572.

—: Sample functions of the Gaussian process. Ann. Probability1, 1973, 66–103.

—: Central limit theorems for empirical measures. Ann. Probability,6, 1978, 899–929.

Durbin, J.: Weak convergence of the sample distribution function when parameters are estimated. Ann. Statistics1, 1973, 279–290.

—: Kolmogorov-Smirnov tests when parameters are estimated. Lect. Notes in Math.566, 1976. 33–44.

Eggleston, H.G.: Convexity. Cambridge 1977.

Elker, J.D., D. Pollard andW. Stute: Glivenko-Cantelli theorems for classes of convex sets. Adv. Appl. Prob., 1979 (to appear).

Kac, M., J. Kiefer andJ. Wolfowitz: On tests of normality and other tests of goodness of fit based on distance methods. Ann. Math. Statist.26, 1955, 189–211.

Le Cam, L.: On the assumptions used to prove asymptotic normality of maximum likelihood estimates. Ann. Math. Statist.41, 1970, 802–828.

Neuhaus, G.: Asymptotic properties of the Cramér-von Mises statistic when parameters are estimated. Proc. Prague Symp. on Asymp. Stat Ed by Hájek. 1973, 257–297.

—: Weak convergence under continguous alternatives of the empirical process when parameters are estimated: theD k approach. Lect. Notes in Math.566, 1976a, 68–82.

—: Asymptotic power properties of the Cramér-von Mises test under contiguous alternatives. J. Multiv. Analysis6, 1967b, 95–110.

Neuhaus, G.: Asymptotic theory of goodness of fit tests when parameters are present: a survey. Lecture at tenth European mtg of Statisticians. Leuven 1977.

Pollard, D.: Weak convergence on non-separable metric spaces. J. Austral. Math. Soc. (Series A)28, 1979a, 197–204.

Pollard, D.: General chi-square goodness-of-fit tests with data-dependent cells. Z. Wahrscheinlichkeitstheorie verw. geb, 1979b, (to appear).

Pyke, R.: Applications of almost surely convergent constructions of weakly convergent processes. Lect. Notes in Math.89, 1969, 187–200.

Pyke, R.: Asymptotic results for rank statistics. Nonparametric Techniques in Statistical Inference. Ed. by Puri. Cambridge 1970, 21–37.

Rockafellar, R.T.: Convex Analysis. Princeton 1972.

Strassen, V.: The existence of probability measures with given marginals. Ann. Math. Statist.36, 1965, 423–439.

Watson, G.S.: Some recent results in chi-square goodness-of-fit tests. Biometrics15, 1959, 440–468.

Wichura, M.J.: On the construction of almost uniformly convergent random variables with given weakly convergent image laws. Ann. Math. Statist.41, 1970, 284–291.

Witting, H., andG. Nölle: Angewandte Mathematische Statistik. Stuttgart 1970.

Wolfowitz, J.: The minumum distance method. Ann. Math. Statist.28, 1957, 75–88.