Simple Estimation for Categorical Data
This chapter summarizes several simple procedures often used in the analysis of categorical data. These include maximum likelihood estimation of parameters of binomial, multinomial, and Poisson distributions and also unbiased estimation with unequal selection probabilities. The Lagrange multiplier method is introduced, and maximum likelihood estimation in general parametric models is considered. In addition to the usual formula for the standard error of an estimated probability, the δ-method is used to derive asymptotic standard errors for estimates of more complex quantities, which are routinely reported in surveys. Standard errors of estimates of fractions based on stratified samples are compared to standard errors obtained from simple random samples.
- 11.Bertsekas, D.P.: Constrained Optimization and Lagrange Multiplier Methods. Academic Press, New York (1982)Google Scholar
- 38.Hansen, M.H., Hurwitz, W.N. Madow, W.G.: Sample Survey Methods and Theory, Volumes I and II. Wiley, New York (1993)Google Scholar
- 41.Kish, L.: Survey Sampling. Wiley, New York (1995)Google Scholar
- 54.Lohr, S.L.: Sampling: Design and Analysis. Brooks/Cole, Boston (2009)Google Scholar