In previous research (ThÈriault et al., 2005 & 2007), we developed a novel approach for assessing centrality and accessibility to urban amenities distinguishing among city centre, labour market and other types of services, like schools, shopping centres, groceries and health facilities. Complementary indices for each type of amenity derived from suitable opportunity sets (based on willingness to travel thresholds) are integrated within a hedonic model of housing markets. Results are highly significant and permit in-depth comparison (and ordering) of the marginal value of accessibility (by car, bus and walking) to several types of amenity within an integrated hedonic framework, while controlling for multicollinearity related to urban form and transportation networks, using principal component analysis. However, there is remaining significant spatial autocorrelation among the model residuals. Thus, spatial drift is eventually harming the robustness of estimates of the coefficients and of their standard errors. The purpose of this paper is to explore ways to get rid of this spatial autocorrelation or, at least, to handle the spatial drift which could be present in the perception of accessibility (and its valuation) among buyers. Building on a comprehensive hedonic model using thousands of single-family house transactions made during the 1993-2004 period in the Quebec Metropolitan Area, this paper compares the efficiency of OLS (ordinary least square), SAR (spatial autoregression) and Quantile regression techniques for handling spatial autocorrelation in the hedonic model and, eventually, for identifying factors behind the spatial drift that could influence buyerís valuation of urban centrality and accessibility to amenities. Moreover, assessment of the marginal effects of market segmentation on the valuation of accessibility to specific amenities (e.g. schools versus labour market, schools versus shopping centres) provides bases for discussing spatial drift estimations in-line with urban economic theory.