## LSU Historical Dissertations and Theses

1995

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Renewable Natural Resources

Quang V. Cao

#### Abstract

All statistical procedures are based on a set of assumptions, such as normality, independence and linearity. In practical applications, these assumptions can rarely be satisfied completely. Deviation from classical parametric assumptions may result in loss of efficiency or even lead to misleading conclusions. Robust statistics that have been extensively studied in the past two decades provide alternatives to deal with such problems. This research was designed to investigate the applicability of robust estimation of population means and robust linear regression in forestry. Five robust estimators, Huber's minimax estimator, Hampel's three parameter redescending estimator, Andrew's wave estimator, Tukey's biweight estimator, and sample median were examined for their performance in estimating population means. Simulations on four families of distributions, beta, gamma, lognormal, and Weibull, suggested that the five robust estimators have a bias problem in estimating means of skewed populations. Analyses of simulated data revealed that magnitudes of robust estimator bias were closely related to a proposed robust sample skewness measure, Skew$\sb{\alpha}$. Regression models were developed to predict bias of the five robust estimators from Skew$\sb{\alpha}$. The predicted bias was then used in constructing a bias corrected robust estimator from each of the five estimators. The modified estimators were evaluated against corresponding original estimators and the sample mean on simulated data from four families of distributions and also on a forestry data set. The bias-corrected robust estimators were better than the original estimators in terms of bias and mean square error. Two robust linear regression procedures, least median of squares and least trimmed squares, were used to fit two individual tree volume equations on nine data sets and two yield models on one data set. The two robust regressions were evaluated against ordinary least squares based on prediction capabilities. For most of the data sets the robust procedures and least squares method produced similar prediction error values. For data sets that contained extreme outliers, the two robust procedures yielded smaller prediction error values than least-squares estimation.

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