The problem of recovering an analytic function in the class of bandlimited functions is studied. Estimation techniques derived from the Whittaker-Shannon cardinal expansion are introduced and their statistical properties are established This includes consistency and rate of convergence in the mean square error sense as well as asymptotic normality The estimators are of the kernel convolution type with the non-integrable kernel function sin (t)/πt. Both an ordinary kernel type regression estimate and a version based on binned data are considered.