April 03, 2012

Relative Distributions and Smooth Tests (Advanced Data Analysis from an Elementary Point of View)

Applying the right CDF to a continuous random variable makes it uniformly distributed. How do we test whether some variable is uniform? The smooth test idea, based on series expansions for the log density. Asymptotic theory of the smooth test. Choosing the basis functions for the test and its order. Smooth tests for non-uniform distributions through the transformation. Dealing with estimated parameters. Some examples. Non-parametric density estimation on [0,1]. Checking conditional distributions and calibration with smooth tests. The relative distribution idea: comparing whole distributions by seeing where one set of samples falls in another distribution. Relative density and its estimation. Illustrations of relative densities. Decomposing shifts in relative distributions.

Reading: Notes, chapter 17

Optional reading: Bera and Ghosh, "Neyman's Smooth Test and Its Applications in Econometrics"; Handcock and Morris, "Relative Distribution Methods"

Advanced Data Analysis from an Elementary Point of View

Posted at April 03, 2012 09:00 | permanent link

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