zbMATH — the first resource for mathematics

Asymptotic behavior of regression quantiles in non-stationary, dependent cases. (English) Zbl 0737.62078
The author derives a Bahadur representation of regression quantiles for error processes which are highly non-stationary. The conditions for dependence are based on an unpublished decomposition of K. C. Chanda, M. L. Puri and F. H. Ruymgaart which covers linear processes, and, hence, includes ARMA processes as well.

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62J05 Linear regression; mixed models
62G35 Nonparametric robustness
Full Text: DOI
[1] Bassett, G.W; Koenker, R.W, An empirical quantile function for linear models with i.i.d. errors, J. amer. statist. assoc., 77, 407-415, (1982) · Zbl 0493.62047
[2] Babu, G.J, Strong representations for LAD estimators in linear models, Probab. theory related fields, 83, 547-588, (1989) · Zbl 0665.62033
[3] Carroll, R.J; Ruppert, D, ()
[4] Chanda, K.C; Puri, M.L; Ruymgaart, F.H, Asymptotic normality of L-statistics based on decomposable time series, (1989), Preprint · Zbl 0778.62080
[5] Gastwirth, J.L; Rubin, H, The behavior of robust estimators on dependent data, Ann. statist., 3, 1070-1100, (1975) · Zbl 0359.62042
[6] Gutenbrunner, C; Jurečková, J, Regression rank scores and regression quantiles, Ann. statist., (1990), to appear · Zbl 0759.62015
[7] Heinrich, L, Nonuniform estimates, moderate and large deviations in the central limit theorem for m-dependent random variables, Math. nachr., 121, 107-121, (1985) · Zbl 0572.60031
[8] Jurečková, J, Asymptotic relations of M-estimates and R-estimates in linear regression model, Ann. statist., 5, 464-472, (1977) · Zbl 0365.62034
[9] Koenker, R.W; Bassett, G.W, Regression quantiles, Econometrica, 46, 33-50, (1978) · Zbl 0373.62038
[10] Koenker, R.W; Bassett, G.W, Robust tests for heteroscedasticity based on regression quantiles, Econometrica, 50, 43-61, (1981) · Zbl 0482.62023
[11] Koenker, R.W; d’Orey, Computing regression quantiles, Appl. statist., 36, 383-393, (1987)
[12] Koenker, R.W; Portnoy, S, L-estimation for the linear model, J. amer. statist. assoc., 82, 851-857, (1987) · Zbl 0658.62078
[13] Koul, H, Behavior of robust estimators in the regression model with dependent errors, Ann. statist., 5, 681-699, (1977) · Zbl 0358.62032
[14] Martin, R.D, Robust estimators for time series, (), 147-176
[15] Pollard, D, ()
[16] Portnoy, S, Tightness of the sequence of c.d.f. processes defined from regression fractiles, (), 231-246
[17] Portnoy, S, Using regression quantiles to identify outliers, (), 345-356
[18] Portnoy, S, Asymptotic number of regression quantile breakpoints, J. sci. statist. comput., (1988), submitted
[19] Portnoy, S, Regression quantile diagnostics for multiple outliers, (), to appear
[20] Portnoy, S, A regression quantile based statistic for testing nonstationarity of errors, (), to appear
[21] Portnoty, S; Koenker, R.W, Adaptive L-estimation of linear models, Ann. statist., 17, 362-381, (1989)
[22] Ruppert, D; Carroll, R.J, Trimmed least squares estimation in the linear model, J. amer. statist. assoc., 75, 828-838, (1980) · Zbl 0459.62055
[23] Welsh, A; Portnoy, S, Exactly what is being modelled by the systematic component in a heteroscedastic linear regression does matter, (1989), Submitted
[24] Portnoy, S, Robust estimation in dependent situations, Ann. statist., 5, 22-43, (1977) · Zbl 0355.62047
[25] Portnoy, S, Further remarks on robust estimation in dependent situations, Ann. statist., 7, 224-231, (1979) · Zbl 0399.62038
[26] Koenker, R, A comparison of asymptotic testing methods for L1 regression, (), 287-295
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.