Monotonicity Constraints in the Estimation of Distributions with Smoothing Splines

A non-parametric method of distribution estimation for univariate data is presented. The idea is to adapt the smoothing spline procedure used in regression to the estimation of distributions via a scatterplot smoothing of theempirical distribution function. An explicit formula for the estimator is obtained by minimizing a penalized weighted sum of squares. The issue of monotonicity of the resulting function is discussed in detail and the estimator's large sample properties are studied.


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