In this paper, we develop a novel spline-kernel estimation method for a single index binary response model with cross-sectional dependence. We address the challenge of modeling interdependencies between cross-sectional units in a binary response framework, where the observations may exhibit correlations due to omitted factors or network effects. To estimate the coefficients, we apply spline-based smoothing techniques coupled with kernel functions, ensuring non-parametric flexibility and robustness. Bootstrap inference is used to assess the statistical properties of the estimators, providing valid confidence intervals for the model parameters. Our approach is tested through both simulation studies.
Tao et al. (Sun,) studied this question.