Nonlinear Varying-Coefficient Models with Applications to a Photosynthesis Study


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Kurum E., Li R., Wang Y., Sentuerk D.

JOURNAL OF AGRICULTURAL BIOLOGICAL AND ENVIRONMENTAL STATISTICS, cilt.19, ss.57-81, 2014 (SCI İndekslerine Giren Dergi)

  • Cilt numarası: 19 Konu: 1
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1007/s13253-013-0157-7
  • Dergi Adı: JOURNAL OF AGRICULTURAL BIOLOGICAL AND ENVIRONMENTAL STATISTICS
  • Sayfa Sayısı: ss.57-81

Özet

Motivated by a study on factors affecting the level of photosynthetic activity in a natural ecosystem, we propose nonlinear varying-coefficient models, in which the relationship between the predictors and the response variable is allowed to be nonlinear. One-step local linear estimators are developed for the nonlinear varying-coefficient models and their asymptotic normality is established leading to point-wise asymptotic confidence bands for the coefficient functions. Two-step local linear estimators are also proposed for cases where the varying-coefficient functions admit different degrees of smoothness; bootstrap confidence intervals are utilized for inference based on the two-step estimators. We further propose a generalized F-test to study whether the coefficient functions vary over a covariate. We illustrate the proposed methodology via an application to an ecology data set and study the finite sample performance by Monte Carlo simulation studies.

Motivated by a study on factors affecting the level of photosynthetic activity in a natural ecosystem, we propose nonlinear varying-coefficient models, in which the relationship between the predictors and the response variable is allowed to be nonlinear. One-step local linear estimators are developed for the nonlinear varying-coefficient models and their asymptotic normality is established leading to point-wise asymptotic confidence bands for the coefficient functions. Two-step local linear estimators are also proposed for cases where the varying-coefficient functions admit different degrees of smoothness; bootstrap confidence intervals are utilized for inference based on the two-step estimators. We further propose a generalized F-test to study whether the coefficient functions vary over a covariate. We illustrate the proposed methodology via an application to an ecology data set and study the finite sample performance by Monte Carlo simulation studies.