Maximum Likelihood and Minimum x 2 Estimates of the Logistic Function

• The Mayo Foundation is a part of the Graduate School of the Univereity of Minnesota. 1 Unless otherwise specified, the x' referred to is the classic x' of Pearson. Appendix Note 1 should be read for the definition of the minimum x' estimate. • It is worth noting that in deriving the x' estimate, we needed only to be able to write the expectation PN, but to derive the maximum likelihood estimate, we needed to asaume that the ob... rved :II ie

[1]  K. Pearson On the Criterion that a Given System of Deviations from the Probable in the Case of a Correlated System of Variables is Such that it Can be Reasonably Supposed to have Arisen from Random Sampling , 1900 .

[2]  R. Fisher,et al.  On the Mathematical Foundations of Theoretical Statistics , 1922 .

[3]  Rory A. Fisher,et al.  Theory of Statistical Estimation , 1925, Mathematical Proceedings of the Cambridge Philosophical Society.

[4]  C. I. Bliss THE CALCULATION OF THE DOSAGE-MORTALITY CURVE , 1935 .

[5]  R. Fisher,et al.  The Logic of Inductive Inference , 1935 .

[6]  R. Fisher PROFESSOR KARL PEARSON AND THE METHOD OF MOMENTS , 1937 .

[7]  Joseph Berkson,et al.  Some Difficulties of Interpretation Encountered in the Application of the Chi-Square Test , 1938 .

[8]  R. A. Fisher,et al.  Statistical Tables for Biological, Agricultural and Medical Research , 1956 .

[9]  Tables of Natural Logarithms. , 1942 .

[10]  E B Wilson,et al.  The Determination of L.D.50 and Its Sampling Error in Bio-Assay. , 1943, Proceedings of the National Academy of Sciences of the United States of America.

[11]  J. Berkson Application of the Logistic Function to Bio-Assay , 1944 .

[12]  M. Kendall,et al.  The advanced theory of statistics , 1945 .

[13]  Joseph Berkson,et al.  Approximation of Chi-Square by “Probits” and by “Logits” , 1946 .

[14]  D. Blackwell Conditional Expectation and Unbiased Sequential Estimation , 1947 .

[15]  W. R. Thompson,et al.  USE OF MOVING AVERAGES AND INTERPOLATION TO ESTIMATE MEDIAN-EFFECTIVE DOSE: I. Fundamental Formulas, Estimation of Error, and Relation to Other Methods. , 1947, Bacteriological reviews.

[16]  J. Berkson Minimum X2 maximum likelihood solution in terms of a linear transform, with particular reference to bio-assay. , 1949, Journal of the American Statistical Association.

[17]  On the Relative Efficiencies of Ban Estimates , 1950 .

[18]  Calyampudi R. Rao,et al.  Advanced Statistical Methods in Biometric Research. , 1953 .

[19]  J. Berkson A Statistically Precise and Relatively Simple Method of Estimating the Bio-Assay with Quantal Response, Based on the Logistic Function , 1953 .

[20]  William F. Taylor,et al.  Distance Functions and Regular Best Asymptotically Normal Estimates , 1953 .

[21]  Rory A. Fisher,et al.  256: The Analysis of Variance with Various Binomial Transformations. , 1954 .