Statistical properties of three estimators in the context of the rotating panel design of the National Forest and Soil Inventory of Mexico

Abstract

From a re-measurement perspective, the sampling design of the National Forests and Soil Inventory (INFyS) consists of rotating panels or panelized samples, from which only the 20 % of the total sample is collected each year over a five-year period. To explore the most suitable statistical methods for the rotating panelized design, an evaluation of three sampling estimators was conducted: generalized least squares (MCG), replicated sampling (MRE) and the univariate composite estimator (ECU). The specific forest parameter examined in this study was the average basal area observed across two measurement cycles: 2004 - 2007 and 2009 - 2012. The data used in this analysis, drawn from the INFyS, represented an artificial population, combining the data acquired in the states of Durango, Quintana Roo, Hidalgo, Jalisco, Estado de Mexico, Chihuahua and Michoacán and spanning 7,597 panelized conglomerates. The performance of the proposed estimators was evaluated for each measurement cycle, involving the generation of 100 random samples, each with sizes of 1,000 and 1,500. Results show that, despite a slight bias, the MCG estimator exhibited lower variance compared to the MRE. In each sample, the ECU estimator displayed a relative estimation bias that struck a balance between the MCG and MRE, while maintaining lower variance than the MRE. Under these conditions, the ECU estimator can be regarded as a minimum variance quasi-unbiased estimator. The adoption of the ECU estimator has the potential to reduce costs and sampling efforts across re-measurement cycles without compromising statistical precision.