Ratio in Ratio Type Exponential Strategy for the Estimation of Population Mean

This paper is an attempt to develop an estimator for finite population mean. Motivated by Kiregyera (1984), a ratio in ratio type exponential strategy is developed for estimation of population mean in double sampling for stratification. To compare with relevant considered estimators, expressions for bias and mean squared error of the developed estimator have been derived. The developed estimator has been compared with usual unbiased estimator, Ige and Tripathi (1987), ratio estimator and ratio type exponential estimator given by Tailor et al (2014) theoretically as well as empirically.

Variance estimation for mean growth from successive double sampling for stratification

Double sampling for stratification (2SS) is a sampling design that is widely used for forest inventories. We present the mathematical derivation of two appropriate variance estimators for mean growth from repeated 2SS with updated stratification on each measurement occasion. Both estimators account for substratification based on the transition of sampling units among the strata due to the updated allocation. For the first estimator, sizes of the substrata were estimated from the second-phase sample (sample plots), whereas the respective sizes in the second variance estimator relied on the larger first-phase sample. The estimators were empirically compared with a modified version of Cochran’s well-known 2SS variance estimator that ignores substratification. This was done by performing bootstrap resampling on data from two German forest districts. The major findings were as follows: (i) accounting for substratification, as implemented in both new estimators, has substantial impact in terms of significantly smaller variance estimates and bias compared with the estimator without substratification, and (ii) the second estimator with substrata sizes being estimated from the first-phase sample shows a smaller bias than the first estimator.

Estimating volume growth from successive double sampling for stratification

Volume growth is a key indicator in forest management and planning and, accordingly, an integral part of the estimation procedure of forest resources from sample based inventories. Growth estimation from successive double sampling for stratification (2SS) is somewhat challenging and has not been sufficiently addressed in the pertinent literature. Applying 2SS on successive occasions, with updated stratification on each occasion, may lead to fluctuation of sampling units among the strata and to a certain number of sample plots that have to be discarded or that have to be newly established on the second occasion, to obtain the required per-strata sampling proportions, which are stipulated in advance. After presenting a notation to implement growth estimation into 2SS standard formulas, the question of strata shifts and the occurrence of discarded and of new sample plots in the context of growth estimation is addressed. Although growth, unlike net change, can only be estimated from direct observations on remeasured sample plots, it was shown that ignoring discarded or new plots might lead to severely biased estimators. Modified estimators for mean growth and variances are provided and their application is illustrated using data from a repeated survey in a central German forest district.