## Retrospective Theses and Dissertations

Dissertation

1992

#### Degree Name

Doctor of Philosophy

Statistics

Wayne A. Fuller

#### Abstract

We consider the simple measurement error regression model y[subscript] t = [beta][subscript]0 + [beta][subscript]1x[subscript] t + q[subscript] t, (Y[subscript] t,X[subscript] t) = (y[subscript] t,x[subscript] t) + (w[subscript] t,u[subscript] t), where [beta] = ([beta][subscript]0, [beta][subscript]1) is the parameter of interest, (Y[subscript] t, X[subscript] t), t = 1, 2, ..., n, are the observations, (y[subscript] t, x[subscript] t) are the true vectors, (w[subscript] t, u[subscript] t) are measurement errors, and q[subscript] t is the equation error. We assume that the measurement errors a[subscript] t = (w[subscript] t, u[subscript] t), t = 1, 2, ..., n, are independent of (q[subscript] j, x[subscript] j) for all t and j and that q[subscript] j is independent of x[subscript] t for all t and j. It is also assumed that the covariance matrix of a[subscript] t is known;Extreme observations have an adverse effect on the usual estimators of the parameters. A class of estimators of [beta] is constructed in which the effect of extreme observations is reduced. Our estimation procedure is based on the robust regression of Y on X and the robust regression of X on Y. The asymptotic joint distribution of the robust estimators of the regression coefficients and error mean squares is obtained when the observations are sampled from a bivariate normal distribution. The robust estimator of [beta] is a smooth function of the estimated regression coefficients and the estimated error mean squares from the two robust regressions. We show that for normal distributions, under certain regularity conditions, our estimator is consistent and normally distributed in the limit. The robust estimation procedure is developed to be robust against a single outlier and then extended to be robust against multiple outliers. A Monte Carlo study is presented to show that our estimator is insensitive to outliers and that the efficiency loss is modest when there is no outlier in the sample.

#### DOI

https://doi.org/10.31274/rtd-180813-11622

#### Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/

#### Copyright Owner

Joseph H.R. Croos

en

AAI9234801

application/pdf

145 pages

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