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UBC Theses and Dissertations

Resampling-based variance estimators in ratio estimation with application to weigh scaling Ladak, Al-Karim Madatally


Weigh scaling is a method of estimating the total volume of timber harvested from a given region. The implementation of statistical sampling techniques in weigh scaling is described, along with related issues. A review of ratio estimators, along with variance estimators of the classical ratio estimator is conducted. The estimation of the variance of the estimated total volume is considered using jackknife- and bootstrap-based variance estimators. Weighted versions of the jackknife and bootstrap variance estimators are derived using influence functions and Fisher Information matrices. Empirical studies of analytic and resampling-based variance estimators are conducted, with particular emphasis on small sample properties and on robustness with respect to both the homoscedastic variance and zero-intercept population characteristics. With a squared error loss function, the resampling-based variance estimators are shown to perform very well at all sample sizes in finite populations with normally distributed errors. These estimators are found to have small negative biases for small sample sizes and to be robust with respect to heteroscedasticity.

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