Nonparametric estimates of the nuisance parameter in the lad tests

References

• Adichie , J.N. 1978 . Rank tests of subhypotheses in general linear regression . Ann. Statist , 6
   Google Scholar
• Babu , G.J. 1989 . Strong represenution for LAD estimators in linear models . Prob. Theory and Related Fields , 83
   Google Scholar
• Bai , Z.D. , Chen , X.R. , Wu , Y. and Zhao , L.C. 1987 . “ Asymptotic normality of minimum L-norm estimates in linear models ” . In Center for Multivariate analysis , University of Pittsburgh . Technical Report 87-35
   Google Scholar
• Bai , Z.D. , Rao , C.R. and Yin , Y.Q. 1987 . “ Least absolute deviations analysis of variance ” . In Center for Multivariate Analysis , University of Pittsburgh . Technical Report 87-45
   Google Scholar
• Bassett , G. and Koenkar , R. 1978 . Asymptotic theory of least absolute error regression . JASA , 73
   Google Scholar
• Bloch , D.A. and Gastwirth , J.L. 1968 . On a simple estimate of the reciprocal of the density function . Ann. Math. Statist , 39
   Google Scholar
• Brillinger , D. , Fienberg , S. , Gani , J. , Hartigan , J. and Krickeberg , K. 1983 . Von Mises calculus for statistical Junctionals , Springer-verlag .
   Google Scholar
• Brown , B.M. 1983 . “ Invariant tests in bivariate models and the L1 criterion ” . In Statistical Data Analysis Based on the L ₁norm and Related Methods , Edited by: Dodge , Y. North-Holland .
   Google Scholar
• Chen , G.J. 1983 . Strong convergence rate of estimators of density function, its derivative function and mode . Chinese Sci , 7 Series A
   Google Scholar
• Chen , X.R. 1984 . Uniform convergence rate of kernel density estimators . Chinese Sci , 8 Series A
   Google Scholar
• Chen , X.R. 1981b . The convergence rate of NN density estimators . Chinese Sci , 12
   Google Scholar
• Devroye , L.P. 1981 . On the almost everywhere convergence of nonparametric regression function estimates . Ann. Statist , 9
   Google Scholar
• Devroye , L.P. and Wagner , T.J. 1977 . The strong uniform consistency of nearest neighbor density estimates . Ann. Statist , 5
   Google Scholar
• Devroye , L.P. and Wagner , T.J. 1980 . “ The strong uniform consistency of kernel density estimates ” . In Multivariate Analysis V , Edited by: Krishnaiab , P.R. North-Holland .
   Google Scholar
• Dupacova , J. 1987 . “ Asymptotic properties of restricted L 1 - estimates of regression ” . In Statistical Data Analysis Based on the L ₁-norm and Related Methods , Edited by: Dodge , Y. North-Holland .
   Google Scholar
• Gower , J.C. 1974 . The median center . App. Statist , 2
   Google Scholar
• Hall , P. and Sheather , S.J. 1988 . On the distribution of a studentized quantile . J. R. Statist. Soc. B , 2
   Google Scholar
• Hettmansperger , T.P. and McKean , J.W. 1983 . A geometric interpretation of inferences based on ranks in linear model . JASA , 78
   Google Scholar
• Hettmansperger . 1984 . Statistical Inference Based on Ranks , New York : Wiley .
   Google Scholar
• Koenkar , R. 1987 . “ A comparison of asymptotic testing methods for l 1-regression ” . In Statistical Data Analysis Based on the L ₁norm and Related Methods , Edited by: Dodge , Y. North-Holland .
   Google Scholar
• Koenkar , R. and Bassett , G. 1982 . Tests of hypotheses and l 1 estimation . Econometrika , 50
   PubMed Web of Science ®Google Scholar
• Liu , Z. 1986 . Strong consistency of The NN-kernel estimators of conditional density functions . Chinese J. App. Prob. &amb; Statist , 3
   Google Scholar
• Liu , Z.J. and Jin , C. 1984 . Strong convergence of a sequential estimator of probability density functions . J. China Utiv. of Sci. and Tech , 3
   Google Scholar
• Liu , Z.J. and Tu , D.S. 1987 . Kernel methods on conditional median estimation . Kexue Tongbao (Chinese Bulletin of Science) , 32
   Google Scholar
• Loftsgarden , D.G. and Quesenberry , C.P. 1965 . A nonparametric estimate of a multivariate density function . Ann. Math. Statist , 36
   Google Scholar
• McKean , J.W. and Hettmansperger , T.P. 1976 . Tests of hypotheses based on ranks in the general linear model . Communications in Statist. Theory and Methods , A5 ( 8 )
   Google Scholar
• McKean , J.W. and Schrader , R.M. 1984 . A comparison of methods for studentizing the sample median . Communication in Statistics B , 13 ( 8 )
   Google Scholar
• Moore , D.S. and Jackel , J.W. 1977 . Consistency properties of nearest neighbor density function estimates . Ann. Statist , 5 ( 8 )
   Google Scholar
• Parzen , E. 1962 . On estimation of a probability density function . Ann. Math. Statist , 33 ( 8 )
   Google Scholar
• Petrov , V.V. 1975 . Sums of independent random variable , Berlin : Springer-Verlag .
   Google Scholar
• Rao , C.R. 1989 . Methodology based on the L1norm in statistical inference . Sankhya A , 50
   Google Scholar
• Rao , C.R. 1973 . Linear Statistical Inference and Its Applications , New York : Wiley .
   Google Scholar
• Rosenblatt , M. 1956 . Remarks on some nonparametric estimates of a density function . Ann. Math. Statist , 27
   Google Scholar
• Schrader , R.M. and Hettmansperger , T.P. 1980 . Robust ANDUA based on a likelihood ratio criterion . Biometrika , 78
   Google Scholar
• Schrader , R.M. and McKean , J.W. 1987 . “ Small sample properties of least absolute errors analysis of variance ” . In Statistical Data Analysis Based on the L ₁ fnorm and Related Methods , Edited by: Dodge , Y. North-Holland .
   Google Scholar
• Sheather , S.J. and McKean , J.W. 1987 . A comparison of testing and confidence interval methods for the median . Statist. Probabil. Lett , 6
   Google Scholar
• Siddiqui , M.M. 1960 . Distribution of quantiles in samples from bivariate population . J. Res. Nat I. Bur. Stand. B , 64
   Google Scholar
• Tu , D.S. , Rao , C.R. and Liu , Z.J. 1990 . “ Strong representation for kernel estimates of conditional medians ” . In Center for Multivariate Analysis Penn State Technical Report 90-06
   Google Scholar
• Wald , A. and Wolfwitz , J. 1944 . Statistical test based on permutation of the observations . Ann. Math. Statist , 15
   Google Scholar
• Zhao , L.C. and Liu , Z.J. 1985 . Strong consistency of the kernel estimates of conditional density function . Acta Math. Sinica , 1 New Series
   Google Scholar