Abstract
Robust recursive estimation provides considerable computational advantage over iterative robust regression estimation, especially for large and ordered (e.g., with time) data sets. The robust recursive estimates are less sensitive than recursive least squares to the outliers and structural shifts, and produce residuals which are more effective in constructing tests for detecting a shift. In this paper we consider a problem of detecting a shift in regression when it is masked by outliers, and summarize results of a simulation study comparing several tests and estimates of the change point.
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References
Beckman, R.J. and R.D. Cook (1979), “Testing for two-phase regression,” Technometrics, 21, 65–69.
Brown, R.I., J. Durbin, and J.M. Evans (1975), “Techniques for testing the constancy of regression relationships over time,” JRSS, B37, 149–192.
Chow, G. (1960), “Tests of the equality between two sets of coefficients in two linear regressions,” Econometrica, 28, 561–605.
Dufour, J-M. (1982), “Recursive stability analysis of linear regression relationships,” Journal of Econometrics, 19, 31–76.
Hannan, E.J. (1977), “ARMAX and state space systems and recursive calculations, in M.D. Intrilligator, ed. Frontiers of Quantitative Economics-111A, Amsterdam: North-Holland, 321–336.
Harvey, A.C. and G.D.A. Phillips (1979), “Maximum likelihood estimation of regression models with autoregressive — moving average disturbances,” Biometrika, 66, 1, 49–58.
Hinkley, D. (1970), “Inference about the Change-Point in a Sequence of Random variables,” Biometrika, 57, 1–17.
Huber, P. (1981), Robust Statistics, J. Wiley and Sons, New York.
Jazwinski, A.H. (1970), Stochastic Processes and Filtering Theory, Academic Press, New York.
Krasker, W. and R.E. Welsch (1982), “Efficient bounded-influence regression estimation,” JASA, 77, 595–604.
Kuh, E., A. Samarov and M. Shell (1986), RECUR: A program for robust recursive estimation, stability testing, and forecasting, Technical Report No. 62, CCREMS, MIT., Cambridge, MA.
Ljung, L. and T. Soderstrom (1983), Theory and practice of recursive identification, MIT Press, Cambridge, MA.
Martin, R.D., C.J. Masreliez (1975), “Robust estimation via stochastic approximation,” IEEE Trans. on Information Theory, IT-21, 3, 263–271.
Phillips, G.D.A. and A.C. Harvey (1974), “A simple test for serial correlation in regression analysis,” JASA, 69, 935–939.
Polyak, B. and Ja. Tsypkin (1979), “Adaptive estimation,” Automation and Remote Control3, 71–84.
Quandt, R.E. (1958), “The estimation of the parameters of a linear regression system obeying two separate regimes,” JASA, 53, 873–880.
Ronchetti, E. (1982), “Robust testing in linear models: the infinitesimal approach,” Ph.D dissertation, ETH, Zurich, 1982.
Schrader, R.M. and T.P. Hettmansperger (1980), “Robust analysis of variance based upon a likelihood ratio criterion, Biometrica, 67, 93–101.
Schweder, T. (1976), “Some ‘optimal’ methods to detect structural shift or outliers in regression,” JASA, 71, 491–501.
Sen, P. (1982), “Invariance principles for recursive residuals,” Annals of Mathematical Statistics, 10, 1, 307–312.
West, M. (1981), “Robust sequential approximate Bayesian estimation,” JRSS, B, 43, 2, 157–166.
Young, P. (1974), “Recursive approaches to time series analysis,” Bull Inst. Math. App 10, 209–224.
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© 1986 Physica-Verlag, Heidelberg for IASC (International Association for Statistical Computing)
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Kuh, E., Samarov, A. (1986). Robust Recursive Estimation and Detection of Shifts in Regression. In: De Antoni, F., Lauro, N., Rizzi, A. (eds) COMPSTAT. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-46890-2_32
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DOI: https://doi.org/10.1007/978-3-642-46890-2_32
Publisher Name: Physica-Verlag HD
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