NONPARAMETRIC-ESTIMATION OF RATE-EQUATIONS FOR NUTRIENT-UPTAKE

• 成果类型: Article
• 署名作者: MEIER, K; NYCHKA, D
• 署名单位: North Carolina State University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.2307/2290342
• 发表日期: 1993
• 页码: 602-614
• 关键词: smoothing noisy data; numerical differentiation; spline functions; response curves; kernel-method; regression; derivatives; GROWTH

摘要

Knowledge of the rate of a biological process is important for characterizing the system and is necessary for gaining a deeper understanding of the process. Consider measurements, Y, made over time on a system following the model Y = f(t) + e, where f is a smooth, unknown function and e is measurement error. Although most statistical methodology has focused on estimating f(t) or f'(t), in some applications what is of real biological interest is the relationship between f and f'. One example is the study of nitrogen absorption by plant roots through a solution depletion experiment. In this case f(t) is the nitrate concentration of the solution surrounding the roots at time t and -f'(t) is the absorption mte of nitrate by plant roots at time t. One is interest in the rate of nitrate absorption as a function of concentration; that is, one is interested in PHI, where PHI(f) = -f'. Knowledge of PHI is important in quantifying the ability of a particular plant species to absorb nitrogen and in comparing the absorption ability of different crop varieties. A parametric model for PHI is usually not available, and thus a nonparametric estimate of PHI is particularly appropriate. This article proposes using spline-based curve estimates with the smoothing parameter chosen by cross-validation and suggests a method for obtaining confidence bands using a form of the parametric bootstrap. These methods are used to analyze a series of solution depletion experiments and are also examined by a simulation study designed to mimic the main features of such data. Although the true f is a monotonic function, simulation results indicate that for our specific application, constraining the estimate of f to be monotonic does not reduce the average squared error of the rate curve estimate, PHI. Although using a cross-validated estimate of the smoothing parameter tends to inflate the average squared error of the rate estimated an analysis of a set of solution depletion experiments is still possible. Using the proposed methods, we are able to detect a difference in mte curves obtained under different experimental conditions. This is established by applying an analysis of variance (ANOVA)-like test to the estimated rate curves, where the critical value is determined by a parametric version of the bootstrap, and by examining confidence bands for the difference of two rate cures. This finding is important, because it suggests that the shape of PHI may not be constant under the experimental conditions examined.