Abstract
In this dissertation, procedures are presented for developing estimators which incorporate information from incomplete or fragmentary data to estimate unknown parameters in a multivariate distribution. Detailed treatment is given to the case in which the observation vectors are assumed to follow the multivariate normal distribution. Distinction is made between the following two cases: (i) those in which information on the individual parameters and general linear combinations of the parent population parameters are available, and (ii) those in which only observations on marginal of the parent distribution are available. The multinomial analogue is also considered with particular attention given to the case in which, in addition to vectors providing estimates of the parent distribution parameter vector, information on some of its marginal is available. The development in each situation consisted of (i) generalizing the sequential estimator of Hocking and Smith (1968), (ii) developing and simplifying the likelihood equations, and (iii) establishing the relationship between the two resulting estimators.
Oxspring, Harry Hollis (1971). Optimal estimation of multivariate parameters from fragmentary data. Doctoral dissertation, Texas A&M University. Texas A&M University. Libraries. Available electronically from
https : / /hdl .handle .net /1969 .1 /DISSERTATIONS -179306.