STATISTICAL ESTIMATION IN MULTIVARIATE NORMAL DISTRIBUTION WITH A BLOCK OF MISSING OBSERVATIONS

Author

Yi Liu

Graduation Semester and Year

2017

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Chien-Pai Han

Abstract

Missing observations occur quite often in data analysis. We study a random sample from a multivariate normal distribution with a block of missing observations, here the observations missing is not at random. We use maximum likelihood method to obtain the estimators from such a sample. The properties of the estimators are derived. The prediction problem is considered when the response variable has missing values. The variances of the mean estimators of the response variable under with and without extra information are compared. We prove that the variance of the mean estimator of the response variable using all data is smaller than that we do not consider extra information, when the correlation between response variable and predictors meets some conditions. We derive three kinds of prediction interval for the future observation. An example of a college admission data is used to obtain the estimators for the bivariate and multivariate situations.

Keywords

Maximum likelihood estimators, Missing observations, Properties of MLE, Prediction interval, Variance comparison

Disciplines

Mathematics | Physical Sciences and Mathematics

License

This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.

Comments

Degree granted by The University of Texas at Arlington

Recommended Citation

Liu, Yi, "STATISTICAL ESTIMATION IN MULTIVARIATE NORMAL DISTRIBUTION WITH A BLOCK OF MISSING OBSERVATIONS" (2017). Mathematics Dissertations. 191.
https://mavmatrix.uta.edu/math_dissertations/191