A new generalized regression estimator and variance estimation for unequal probability sampling without replacement for missing data

Review of how the generalized regression estimators contribute to estimating the financial and economic data with missing observations under unequal probability sampling

“…the agricultural industry such as total yield, total profit, and total income can be applied using the GREG estimator to find out these values in advance for planning for effective decision making which can develop economic wealth for the whole nation. Handling missingness appropriately can benefit the reliability of the data that is utilized for planning in Thailand and other countries around the world (Lawson and Siripanich, 2022).…”

“…Unfortunately, the works we mentioned above are considered under a strong assumption when the nonresponse mechanism is MCAR where the response probability is constant only. The novel GREG estimators for population mean and total under a more flexible situation where nonresponse occurs under missing at random or MAR, which is a more practical situation, were proposed based on the previous works when the auxiliary variable is known to improve the efficiency of the estimators (Lawson and Siripanich (2022). In their study, they assumed that, C 1 : r n → 0 as n → ∞, where fr n g is a sequence of positive real numbers and…”

“…The GREG estimator was applied to estimate the total monthly household income from five communities in Bang Sue district, Bangkok, Thailand (Lawson and Siripanich, 2022). The results were based on a sample of size 195 households that was drawn using UPWOR with Midzuno's (1952) scheme out of 1,181 households which consists of 30% nonresponse in the monthly income.…”

“…Shao and Steel, 1999;Haziza and Rao, 2006;Haziza, 2010). Under this reverse method, the population total estimators and the GREG estimators along with their variance estimators were investigated within the MCAR and MAR nonresponse mechanisms and under different assumptions for the response probabilities and the sampling fractions (Lawson, 2017;Lawson and Ponkaew, 2019;Lawson and Siripanich, 2022;Ponkaew and Lawson, 2023).…”

New Generalized Regression Estimators Using a Ratio Method and Its Variance Estimation for Unequal Probability Sampling without Replacement in the Presence of Nonresponse

“…Lawson and Ponkaew [6] studied the scenario of having a small sampling fraction in which the response probabilities were uniform. Recently, Lawson and Panich [9] proposed a new GREG estimator that was made by adjusting Lawson and Ponkaew's estimator [6] using different nonresponse mechanisms when the response probability was non-uniform and the sampling fraction was large and could not be omitted.…”