By H.M. Amman, D.A. Kendrick, J. Rust
Vol. 1 / Hans M. Amman, David A. Kendrick, and John Rust -- Vol. 2 / L. Tesfatsion and K.L. Judd
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And, the trial and error procedure connected with such transformation selections does not guarantee success. This empirical example links the issue of data transformations to that of homogeneity assumptions, and in part demonstrates that spatial statistical results tend to be highly sensitive to deviations from the homogeneity assumption, a feature uncharacteristic of many classical statistics. Suppose the process at work is normally distributed. Consider a set of independent and identically distributed (iid) white noise random variables , '" (jl(l, (j~I), which are indistinguishable from n iid ~i '" N(jl~, random variates.
Such a synthesis could be attained through the use of· generalized canonical correlation analysis.
Two points concerning the boundedness of a geographic region merit attention now, namely homogeneity assumptions, and the use of a torus mapping to emulate an unbounded surface. The homogeneity assumption underlies much of the empirical research that has been conducted on spatial autocorrelation. Clearly if a drift exists in the spatial pa~tern under study, the constant mean assumption can be replaced with a trend surface specification. Moreover, /11 is replaced by Xp, where X is an n-by-p matrix of powers of the absolute co-ordinates for the areal units in question, except that Xl == 1, an n-by-l vector of unity values.