type="main" xml:id="sjos12016-abs-0001" <title type="main">ABSTRACT</title> <p>We give a formal definition of a representative sample, but roughly speaking, it is a scaled-down version of the population, capturing its characteristics. New methods for selecting representative probability samples in the presence of auxiliary...</p>

type="main" xml:id="sjos12042-abs-0001" <title type="main">ABSTRACT</title> <p>We derive two types of Akaike information criterion (AIC)-like model-selection formulae for the semiparametric pseudo-maximum likelihood procedure. We first adapt the arguments leading to the original AIC formula, related to empirical estimation...</p>

type="main" xml:id="sjos12048-abs-0001" <title type="main">ABSTRACT</title> <p>For fixed size sampling designs with high entropy, it is well known that the variance of the Horvitz–Thompson estimator can be approximated by the Hájek formula. The interest of this asymptotic variance approximation is that it only involves...</p>

type="main" xml:id="sjos12064-abs-0001" <title type="main">ABSTRACT</title> <p>The Quermass-interaction model allows to generalize the classical germ-grain Boolean model in adding a morphological interaction between the grains. It enables to model random structures with specific morphologies, which are unlikely to be...</p>