Since the seminal work by Clark (1951), a number of researches on urban population density have been appeared in several journals. In 1989 McDonald conducted a survey on the econometric study of urban population density functions. In the review he recommended the estimation technique pointed by Frankena (1978) and the use of Box−Cox transformation for choosing an optimal functional form. He also addressed to the model and estimation of beyond the distance−density functions such as varying parameter model. This paper begins in the second section with a choice of functional form. Sections 3 and 4 review the
estimation model of suburbanization and the identification of the CBD including multi−center case. Recently more complicated population distributions are found in the real urban areas. Thus, more sophisticated models are needed to explain the real population distribution. In section 5 three estimation models ; cubic−spline,
switching regression, and varying coefficient models are reviewed and in the varying coefficient model we propose theoretical foundations for the estimation of varying parameter model. In section 6 we describe data
problems concerning population density estimation and estimation bias when we use census tract data. Finally, section 7 states a possible direction of the further research.