Abstract
A finite series approximation technique is introduced. We first applythis approximation technique to a semiparametric single-index model toconstruct a nonlinear least squares (LS) estimator for an unknown parameterand then discuss the confidence region for this parameter based on theasymptotic distribution of the nonlinear LS estimator. Meanwhile, acomputational algorithm and a small sample study for this nonlinear LSestimator are developed. Additionally, we apply the finite seriesapproximation technique to a partially nonlinear model and obtain some newresults.
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Gao, J., Liang, H. Statistical Inference in Single-Index and Partially Nonlinear Models. Annals of the Institute of Statistical Mathematics 49, 493–517 (1997). https://doi.org/10.1023/A:1003118812392
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DOI: https://doi.org/10.1023/A:1003118812392