A comparison of ordinary least squares estimators in a simple linear regression under two-stage sampling

• Main Authors: Abulo, Maria Cristina P., Pentoja, Chiara Yasmin M.
• Format: text
• Language: English
• Published: Animo Repository 2001
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/17154
• Institution: De La Salle University

In a simple linear regression model under two stage sampling, the generalized least squares (GLS) estimator is the best linear unbiased (BLU) estimator after taking into account the intracluster correlation. However, due to the unavailability of computer packages that generates this kind of procedure, the ordinary least squares (OLS) remains unbiased but would have a loss of efficiency when a positive intracluster correlation is present within the sampling units. This paper illustrates the effect of positive intracluster correlation in the estimation of variance when OLSE is used in place of GLSE. The performance of OLS and GLS were compared using the same data samples in both methods. Out of the results in the five trials with sample sizes of 30, inferences were made in several statistical measurements. Results manifested that estimates of OLS and GLS method are both unbiased. However, results showed that the OLS estimate of error variance is smaller than that of the GLS, which contradicts the idea that under two stage sampling, GLS is the BLU. The OLS estimate of error variance could be unbiased in this particular case.