Abstract
Some fundamental issues on statistical inferences relating to varying-coefficient regression models are addressed and studied. An exact testing procedure is proposed for checking the goodness of fit of a varying-coefficient model fited by the locally weighted regression technique versus an ordinary linear regression model. Also, an appropriate statistic for testing variation of model parameters over the locations where the observations are collected is constructed and a formal testing approach which is essential to exploring spatial non-stationarity in geography science is suggested.
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