Welsh, A. H.2026-01-012026-01-010167-7152https://hdl.handle.net/1885/733799707The sparsity function is important in nonparametric inference based on order statistics. In this paper, we consider kernel estimation of the sparsity function. We establish an invariance principle for the kernel estimator and then construct a simple adaptive estimator which we show is asymptotically efficient in the mean squared error sense.Support for this research was provided in part by National Science Foundation Grant No.6enefficient estimationkernelmean squared errororder statisticssparsity functionweak convergence198810.1016/0167-7152(88)90103-438249031035