Some nonparametric tests for constancy of regression relationships over time

dc.contributor.authorRoller, William Fredericken
dc.description.abstractLet Y₁, Y₂... be a sequence of random variables obeying the law Y<sub>i</sub> = β’<sub>i</sub> + ε<sub>i</sub>, where β₁, β₂, ... is a sequence of unknown k-dimensional regression vectors; x₁, x₂, ... is a sequence of known k-dimensional regressor vectors; and ε₁ , ε₂, ... is a sequence of independent and identically distributed random variables. Assume that β₁ = ... = β<sub>m</sub> = β, m ≥ k, and that β̂₀ is an asymptotically normal estimate of β based on Y₁ , ..., Y<sub>m</sub>. This study develops nonparametric procedures for testing H₀: = β = β<sub>m+1</sub> = β<sub>m+2</sub> = …. The proposed tests involve sequences of truncated sequential tests. That is, a function of the residuals Y<sub>m+1</sub> - β̂’₀ x<sub>m+1</sub>, …, Y<sub>m+N</sub> - β̂’₀ x<sub>m+N</sub> is examined for a shift in the model. If no shift is indicated all m+N observations are pooled and a new estimate of β, β̂₁, is formed. The next N residuals are then examined for a shift. The procedure continues until a.shift is indicated. Brownian motion results are used to obtain approximate critical values when the function of the residuals is: the cumulative sum of the signs of the residuals; the sequential Wilcoxon scores; the ordinary cumulative sums of residuals. Exact results are obtained for the cumulative sum of signs procedure when testing for a shift in median. Asymptotic relative efficiency results are also obtained.en
dc.description.degreePh. D.en
dc.format.extentiv, 205 leavesen
dc.publisherVirginia Polytechnic Institute and State Universityen
dc.relation.isformatofOCLC# 9386809en
dc.rightsIn Copyrighten
dc.subject.lccLD5655.V856 1977.R64en
dc.subject.lcshNonparametric statisticsen
dc.titleSome nonparametric tests for constancy of regression relationships over timeen
dc.type.dcmitypeTexten Polytechnic Institute and State Universityen D.en
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