β Scribed by Naveen K. Bansal; G.G. Hamedani; Hao Zhang
No coin nor oath required. For personal study only.
We consider a non-linear regression model when the index variable is multidimensional. Su cient conditions on the non-linear function are given under which the least-squares estimators are strongly consistent and asymptotically normally distributed. These su cient conditions are satisΓΏed by harmonic type functions, which are also of interest in the one dimensional index case where Wu's (Asymptotic theory of non-linear least-squares estimation, Ann. Statist. 9 (1981) 501-513) and Jennrich's (Asymptotic properties of non-linear least-squares estimators, Ann. Math. Statist. 40 (1969) 633-643) su cient conditions are not applicable.
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In this paper we present an estimating equation approach to statistical inference for non-linear random effects regression models for correlated data. With this approach, the distribution of the observations and the random effects need not be specified; only their expectation and covariance structur