# IJPAM: Volume 83, No. 3 (2013)

CONFIDENCE INTERVAL ESTIMATION FOR AN EMPIRICAL
MODEL QUANTIFYING THE EFFECT OF SOIL MOISTURE
AND PLANT DEVELOPMENT ON SOYBEAN (GLYCINE MAX
(L.) MERR.) LEAF CONDUCTANCE

Jessica L. Matthews1, Ralph C. Smith2, Edwin L. Fiscus3
1Cooperative Institute for Climate and Satellites NC (CICS-NC)
North Carolina State University, and
NOAA's National Climatic Data Center (NCDC)
151 Patton Avenue, Asheville, NC 28801, USA
2Department of Mathematics and
Center for Research in Scientific Computation
North Carolina State University
Raleigh, NC 27695, USA
3United States Department of Agriculture-Agricultural
Research Service (USDA-ARS)
Plant Science Research Unit and
Department of Crop Science
North Carolina State University
Raleigh, NC 27695, USA

Abstract. In this work, we address uncertainty analysis for a model, presented in a separate paper, quantifying the effect of soil moisture and plant age on soybean (Glycine max (L.) Merr.) leaf conductance. To achieve this we present several methods for confidence interval estimation. Estimation of confidence intervals for model parameters and predictions is investigated using asymptotic theory, Monte Carlo methods, and bootstrap methods. A computationally feasible solution for estimating confidence intervals for model parameters via asymptotic theory is unattainable. Confidence intervals for model predictions under water-stressed environmental conditions when using asymptotic theory and Monte Carlo methods are artificially large due to underlying false assumptions of normality. For this model, where the residuals exhibit heteroscedasticity, the confidence intervals estimated by the wild bootstrap method appear the most realistic of the methods investigated. Of the three methods presented for estimating 95% confidence intervals for model predictions, it is our opinion that the bootstrap method is the most reliable.

AMS Subject Classification: 62F25, 62F40, 90C31, 92C80

Key Words and Phrases: uncertainty analysis, asymptotic theory, delta method, Monte Carlo, bootstrap

DOI: 10.12732/ijpam.v83i3.6 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 83
Issue: 3