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Operational Algebra And Regression T-Tests, Peter C.B. Phillips

Cowles Foundation Discussion Papers

Data reduction involves a physical transition from sample data to econometric estimator and test statistic. This transition induces a mapping on the probability law of the sample, whose image is the distribution of the statistic of interest. At a general level, the mapping can often be captured by means of an operational algebra. Some methods than employ nonlinear functions of differential operators are suggested which can perform this task. The methods are related to pseudodifferential operator techniques that are used in abstract mathematics to solve systems of partial differential equations. They also generalize the fractional calculus methods developed by the …