Skip to main content Accessibility help

Asymptotics for Least Absolute Deviation Regression Estimators

  • David Pollard (a1)


The LAD estimator of the vector parameter in a linear regression is defined by minimizing the sum of the absolute values of the residuals. This paper provides a direct proof of asymptotic normality for the LAD estimator. The main theorem assumes deterministic carriers. The extension to random carriers includes the case of autoregressions whose error terms have finite second moments. For a first-order autoregression with Cauchy errors the LAD estimator is shown to converge at a 1/n rate.



Hide All
1.Amemiya, T.Two stage least absolute deviations estimators. Econometrica 50 (1982): 689711.
2.Amemiya, T.Advanced Econometrics. Cambridge, MA: Harvard University Press, 1985.
3.An, H.-Z. & Chen, Z.-G.. On convergence of LAD estimates in autoregression with infinite variance. Journal of Multivariale Analysis 12 (1982): 335345.
4.Andersen, P.K. & Gill, R.. Cox's regression model for counting processes: a large sample study. Annals of Statistics 10 (1982): 11001120.
5.Bassett, G. & Koenker, R.. Asymptotic theory of least absolute error regression. Journal of the American Statistical Association 73 (1978): 618622.
6.Bickel, P.J.One-step Huber estimates in the linear model. J. American Statistical Association 70 (1975): 428433.
7.Bloomfield, P. & Steiger, W.L.. Least Absolute Deviations: Theory, Applications, and Algorithms. Boston: Birkhauser, 1983.
8.Davis, R.A., Knight, K. & Liu, J.. M-estimation for autoregressions with infinite variance. Preprint (1990).
9.Heiler, S. & Willers, R.. Asymptotic normality of R-estimates in the linear model. Statistics 19 (1988): 173184.
10.Jureckov´, J.Asymptotic relations of M-estimates and R-estimates in linear regression model. Annals of Statistics 5 (1977): 464472.
11.Knight, K. A proof of asymptotic normality of LAD and L-estimates in linear regression. Preprint, University of Toronto (1989a).
12.Knight, K.Limit theory for autoregressive-parameter estimates in an infinite-variance random walk. Canadian Journal of Statistics 17 (1989b): 261278.
13.Pakes, A. & Pollard, D.. Simulation and the asymptotics of optimization estimators. Econometrica 57 (1989): 10271058.
14.Pollard, D.A central limit theorem for k-means clustering. Annals of Probability 10 (1982): 919926.
15.Pollard, D.Convergence of Stochastic Processes. New York: Springer-Verlag, 1984.
16.Pollard, D.New ways to prove central limit theorems. Econometric Theory. 1 (1985): 295314.
17.Pollard, D.Asymptotics via empirical processes. Statistical Science 4 (1989): 341366.
18.Pollard, D. Empirical processes: theory and applications. NSF-CBMS Regional Conference Series in Probability and Statistics, Vol.2. Hayward, CA: Institute of Mathematical Statistics, 1990.
19.Rockafellar, R.T.Convex Analysis. Princeton, NJ: Princeton University Press, 1970.
20.Ruppert, D. & Carroll, R.J.. Trimmed least squares estimation in the linear model. J. American Statistical Association 75 (1980): 828838.
21.Sanz, G.n r-consistency of certain optimal estimators, 0 <r<½ . Preprint, Universidad de Zaragoza, 1988.
22.Van de Geer, S. Asymptotic normality of minimum L 1-norm estimators in linear regression. Preprint, University of Bristol, 1988.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
  • URL: /core/journals/econometric-theory
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed