Minimax strategies in survey sampling

The risk of a sampling strategy is a function on the parameter space, which is the set of all vectors composed of possible values of the variable of interest. It seems natural to ask for a minimax strategy, minimizing the maximal risk. So far answers have been provided for completely symmetric parameter spaces. Results available for more general spaces refer to sample size 1 or to large sample sizes allowing for asymptotic approximation. In the present paper we consider arbitrary sample sizes, derive a lower bound for the maximal risk under very weak conditions and obtain minimax strategies for a large class of parameter spaces. Our results do not apply to parameter spaces with strong deviations from symmetry. For such spaces a minimax strategy will prescribe to consider only a small number of samples and takes a non-random and purposive character

Survey sampling : a linear game

A linear game consists of two subsets of a vector space with a scalar product. The idea is that players 1 and 2 select, independently, elements of the first and second set, respectively. Then, player 2 has to pay to player 1 the value of the scalar product of the selected elements. We will discuss survey sampling within the framework of linear games with the statistician in the role of player 2. The vector space to be considered is the set of all symmetric matrices of order N x N with a scalar product identical with the usual mean squared error. The subset from which the statistician's selection is to be made is neither convex nor compact. Standard results of the theory of linear games have to be modified appropriately. The existence of minimax strategies will be established. At the same time we hope to improve our understanding of random selection and of the duality between the fixed population approach and model based approaches to the theory of survey sampling

Asymptotic minimaxity of the ratio strategy

SIGLEAvailable from Bibliothek des Instituts fuer Weltwirtschaft, ZBW, Duesternbrook Weg 120, D-24105 Kiel / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman