Random Weighting Approach In Nonlinear and Hierarchical Regression Models
Nonlinear regression models with random and fixed effects are commonly used to analyze repeated measures data. Such data, consisting of repeated measurements taken on several individuals, typically arise in biological and biomedical applications amongst many other applications. The standard two-stage estimation (STS) method is intuitive and simple to implement in such circumstance, but the main difficulty is that not much is available on the sampling distribution of the resulting parameters estimates. In this work, we develop re-sampled versions of the least squares estimators (LSE) of the parameters in nonlinear regression as well as hierarchical nonlinear regression models. The approach we take for re-sampling is based on a general random weighting technique, however implemented in the more complex context of the hierarchical regression models which are not restricted to the typical normality assumption of the random components. We obtain the asymptotic properties on consistency and distribution of the resample (or recycled) LSE in the nonlinear regression as well as in the hierarchical regression models using the so-called Standard Two Stage (STS) estimation procedure. In particularly, we have proved the recycled LSE and STS estimates have an asymptotic normal distribution. Additionally, we conducted extensive simulation studies to evaluate and demonstrate the finite-sample properties of the recycled LSE in nonlinear regression, the STS estimates as well as recycled STS estimates in the hierarchical nonlinear regression models. Furthermore, we illustrated the application of the proposed estimation procedures with two real-data examples.
Boukai, Purdue University.
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