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In this article, we consider the semiparametric regression modelwhereare known fixed design points,  β  is an unknown parameter to be estimated,andare unknown functions defined on a compact set. Assume that the random errorsare zero mean widely orthant dependent (WOD, for short) random variables. Under some suitable conditions, we investigate the complete consistency for the least squares estimators (LSE, for short) and the weighted least squares estimators (WLSE, for short) of  β  andIn addition, a numerical simulation is given to study the numerical performance based on finite samples.

Complete consistency for the weighted least squares estimators in semiparametric regression models