Far East Journal of Theoretical Statistics
Volume 38, Issue 2, Pages 101 - 120
(February 2012)
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MISSING PLOT TECHNIQUE BY EM ALGORITHM
Angshuman Sarkar
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Abstract: Analysis of data in the presence of missing or unobserved response is a major issue in many applied statistics problems. Almost all the statistical softwares available in the market ignore the missing values for solving different estimation related problems. This method leads to inefficient and biased estimators of the parameters involved. In this work, we have considered two basic designs, namely Completely Randomized Design and Randomized Block Design, which are mostly applied in many agricultural or biological experiments for assessing different treatments’ performance. The usual analysis procedure of these designs in the presence of missing data involves estimation of missing values by solving a system of linear equations. So, when the number of missing observations is large or even moderately large, then it is hard to maintain the consistency of this system of linear equations which leads to the failure of the existing procedure of analysis. In this work, we have proposed an analysis procedure of the above mentioned designs in presence of missing observations using the Expectation Maximization (EM) algorithm. The proposed procedure does not require the estimation of missing values. Thus, the consistency related issues do not arise. Moreover, as the proposed analysis procedure is based on the Maximum Likelihood Estimation, so it can take into account different missing algorithms, namely Missing at Random or Non-ignorable Missing Data. The performance of the procedure has been judged in terms of the power of the involved tests. Some examples are also given for illustration. |
Keywords and phrases: completely randomized design, maximum likelihood estimate, missing data, randomized block design. |
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