type="main" xml:id="sjos12045-abs-0001" <title type="main">ABSTRACT</title>Small area estimation has long been a popular and important research topic due to its growing demand in public and private sectors. We consider here the basic area level model, popularly known as the Fay–Herriot model. Although much of current...

We study the class of penalized spline estimators, which enjoy similarities to both regression splines, without penalty and with fewer knots than data points, and smoothing splines, with knots equal to the data points and a penalty controlling the roughness of the fit. Depending on the number of...

A number of criteria exist to select the penalty in penalized spline regression, but the selection of the number of spline basis functions has received much less attention in the literature. We propose a likelihood-based criterion to select the number of basis functions in penalized spline...