REGRESSION QUANTILES' A simple minimization problem yielding the ordinary sample quantiles in the location model is shown to generalize naturally to the linear model generating a new class of statistics we term "regression quantiles." The estimator which minimizes the sum of absolute residuals is an important special case. Some equivariance properties and the joint asymptotic distribution of regression quantiles are established. These results permit a natural generalization to the linear model of certain well-known robust estimators of location. Estimators are suggested, which have comparable efficiency to least squares for Gaussian linear models while substantially out-performing the least-squares estimator over a wide class of non-Gaussian error distributions.
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. The Econometric Society is collaborating with JSTOR to digitize, preserve and extend access to Econometrica.A new class of tests for heteroscedasticity in linear models based on the regression quantile statistics of Koenker and Bassett [17] is introduced. In contrast to classical methods based on least-squares residuals, the new tests are robust to departures from Gaussian hypotheses on the underlying error process of the model. 'The authors wish to thank Robert Hogg and Colin Mallows for helpful comments on a previous draft. We are also deeply indebted to an anonymous referee whose "rough calculations" on an example stimulated an extensive revision of Sections 3 and 4. Complete responsibility for remaining errors and malapropisms rests with the authors. 2An exposition of least squares theory from this point of view may be found in a valuable monograph by Goldberger [14].
Abstract. Recent developments in the theory of choice under uncertainty and risk yield a pessimistic decision theory that replaces the classical expected utility criterion with a Choquet expectation that accentuates the likelihood of the least favorable outcomes. A parallel theory has recently emerged in the literature on risk assessment. It is shown that pessimistic portfolio optimization based on the Choquet approach may be formulated as an exercise in quantile regression.
The regression quantile statistics of Koenker and Bassett (1978) are employed to construct an estimate of the error quantile function in linear models with iid errors. Some finite sample properties and the asymptotic behavior of the proposed estimator are derived. Comparisons with procedures based on residuals are made. The stackloss data of Brownlee (1965) is reanalyzed to illustrate the technique.
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