Sign regularity of a generalized Cauchy kernel with applications

Journal of Statistical Planning and Inference

Volumn 52, Issue 2, 1996, Pages 131-142

  Dette, Holger ^a   Munk, Axel ^a  

^a RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

Chebyshev systems; Generalized Cauchy kernel; Interval hypotheses; Pearson type distribution; Scaled F distribution; Sign regularity; Total positivity; UMP tests

Indexed keywords

EID: 0030585644     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/0378-3758(95)00108-5     Document Type: Article

References (28)

1. Achieser, N.J. (1956). Theory of Approximation. Dover, New York.
2. Bar-Lev, S.K. and B. Reiser (1982). An exponential subfamily which admits UMPU-tests based on a single test statistic. Ann. Statist. 10, 979-989.
3. Barndorff-Nielsen, O. (1978). Information and Exponential Families in Statistical Theory. Wiley, New York.
4. Bristol D.R. and M.M. Desu (1990). Comparison of two exponential distributions. Biometrical J. 32, 267-76.
5. Brown, L.D., I.M. Johnstone and K.B. MacGibbon (1981). Variation diminishing transformations: a direct approach to total positivity and its statistical applications. J. Amer. Statist. Assoc. 76, 824-832.
6. Gautschi, W. (1993). Gauss type quadrature rules for rational functions. In: H. Braess and G. Hämmerlin, Eds., Numerical Integration IV, Proceedings of the conference at the Mathematical Research Institute, Oberwolfach, Nov. 8-14, 1992, p. 111-130, Birkhäuser Verlag, Basel.
7. Hodges, J.L. and E.L. Lehmann (1954-1955). Testing the approximative validity of statistical hypotheses. J. Roy. Statist. Soc. Ser. B 16, 261-268.
8. Hsu, P.L. (1938). Contributions to the theory of Student's t-test as applied to the problem of two samples. In: J. Neyman and E.S. Pearson, Eds., Statistical Research Memoirs II. London: University of London, London.
9. Johnson, N.L. and S. Kotz (1970). Distributions in Statistics. Continuous Univariate Distributions-I. Wiley, New York.
10. Kallenberg, W.C.M. et al. (1984). Testing Statistical Hypotheses: Worked Solutions. CWI Syllabus 3.
11. Karlin, S. (1955). Decision theory for Polya-type distributions. Case of two actions I. Proc. 3rd Berkeley Symp. on Mathematical Statistics and Probability, Vol. 1, Berkeley Univ. Calif. Press, Berkeley, CA 115-29.
12. Karlin, S. (1957). Polya-type distributions II. Ann. Math. Statist. 28, 281-308.
13. Karlin, S. (1968). Total Positivity. Stanford University Press, Stanford, CA.
14. Karlin, S. (1976). On a class of best nonlinear approximation problems and extended monosplines. In: S. Karlin, C.A. Micchelli, A. Pinkus and IJ. Schoenberg, Eds., Studies in Spline Functions and Approximation Theory. Academic Press, New York.
15. Karlin, S. and W.J. Studden (1966a). Tchebycheff Systems: with Applications in Analysis and Statistics. Interscience, New York.
16. Karlin, S. and W.J. Studden (1966b). Optimal experimental designs. Ann. Math. Statist. 37, 783-815.
17. Karlin, S. and Y. Rinott (1981). Total positivity properties of absolute value multinormal variables with applications to confidence interval estimates and related probabilistic inequalities. Ann. Statist. 9, 1035 -1049.
18. Lehmann, E.L. (1986). Testing Statistical Hypotheses. 2nd ed. Wiley, New York.
19. Metzler, C.M. (1974). Bioavailability. A problem in equivalence. Biometrics 30, 309-317.
20. Moser, B.K. and G.R. Stevens (1992). Homogenity of variance in the two-sample means test. Amer. Statist. 1, 19-21.
21. Pickands, J. (1975). Statistical inference using extreme order statistics. Ann. Statist. 3, 119-131.
22. Posten, H.O., H.C. Yeh and D.B. Owen (1982). Robustness of the two sample t-test under violations of the homogenity of variance assumptions. Comm. Statist. Theory Methods. 11, 109-126.
23. Richter-Dyn, N. (1971). Properties of minimal integration rules II. SIAM J. Numer. Anal. 8, 497-508.
24. Rinott, Y. (1973). Multivariate Majorization and rearrangement inequalities with some applications to probability and statistics, Israel J. Math. 15, 60-77.
25. Staudte, R.G. and S.J. Sheather (1990). Robust Estimation and Testing. Wiley, New York.
26. Studden, W.J. (1968). Optimal designs on Chebyshev points. Ann. Math. Statist. 39, 1435-1447.
27. Studden, W.J. and J.Y. Tsay (1976). Remez's procedure for finding optimal designs. Ann. Statist. 4, 1271-1279.
28. VanAssche, W. and I. Vanherwegen (1993). Quadrature formulas based on rational interpolation. Math. Comp. 61, 765-783.