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In this article, we consider the problem of estimation of the single-index varying-coefficient model when covariates are not fully observed. By using the bias-correction and inverse selection probability methods, a weighted estimating equations estimator for the index parameters with missing covariates is constructed, and its asymptotic properties has been established. The local linear estimator for the coefficient functions is proved to converge at an optimal rate. Numerical studies based on simulation and application suggest that the proposed estimation procedure is powerful and easy to implement.

Single-index varying-coefficient models with missing covariates at random