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Microchip arrays have become one of the most rapidly growing techniques for monitoring gene expression at the genomic level and thereby gaining valuable insight about various important biological mechanisms. Examples of such mechanisms are: identifying disease-causing genes, genes involved in the regulation of some aspect of the cell cycle, etc. In this article, we discuss the problem of estimating gene expression based on a proper statistical model. More precisely, we show how the model introduced by Li and Wong can be used in its full bivariate generality to provide a new measure of gene expression from high-density oligonucleotide arrays. We also present a second gene expression index based on a new way of reducing the model into a simpler univariate model. In both cases, the gene expression indices are shown to be unbiased and to have lower variance than the established ones. Moreover, we present a bootstrap method aiming at providing non-parametric confidence intervals for the expression index.