Let 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. / Ph. D.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/71281 |
| Date | January 1977 |
| Creators | Roller, William Frederick |
| Contributors | Statistics |
| Publisher | Virginia Polytechnic Institute and State University |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation, Text |
| Format | iv, 205 leaves, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 9386809 |
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