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1993-1995 | 22 | 4 | 515-529

Tytuł artykułu

Estimation of nuisance parameters for inference based on least absolute deviations

Treść / Zawartość

Języki publikacji

EN

Abstrakty

EN
Statistical inference procedures based on least absolute deviations involve estimates of a matrix which plays the role of a multivariate nuisance parameter. To estimate this matrix, we use kernel smoothing. We show consistency and obtain bounds on the rate of convergence.

Rocznik

Tom

22

Numer

4

Strony

515-529

Daty

wydano
1995
otrzymano
1994-04-06

Twórcy

  • Institute of Applied Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

Bibliografia

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  • L. Bobrowski (1986), Linear discrimination with symmetrical models, Pattern Recognition 19, 101-109.
  • Y. Dodge (ed.) (1987), Statistical Data Analysis Based on $L_1$-norm and Related Methods, North-Holland.
  • Y. Dodge (ed.) (1987), (ed.) (1992), $L_1$-Statistical Analysis and Related Methods, North-Holland.
  • D. J. Hand (1981), Discrimination and Classification, Wiley, New York.
  • J. Jurečková (1989), Consistency of M-estimators in a linear model, generated by non-monotone and discontinuous ψ-functions, Probab. Math. Statist. 10, 1-10.
  • J. Jurečková and P. K. Sen (1987), A second-order asymptotic distributional representation of M-estimators with discontinuous score functions, Ann. Probab. 15, 814-823.
  • J. Jurečková and P. K. Sen (1987) (1989), Uniform second order asymptotic linearity of M-statistics in linear models, Statist. Decisions 7, 263-276.
  • J. Kiefer (1967), On Bahadur's representation of sample quantiles, Ann. Math. Statist. 38, 1323-1342.
  • J. Kim and D. Pollard (1990), Cube root asymptotics, Ann. Statist. 18, 191-219.
  • R. Koenker (1987), A comparison of asymptotic testing methods for $l_1$-regression, in: Statistical Data Analysis Based on $L_1$-norm and Related Methods, Y. Dodge (ed.), North-Holland, 287-295.
  • R. Koenker and G. Basset (1978), Regression quantiles, Econometrica 46, 33-50.
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  • D. Pollard, (1991), Asymptotics for least absolute deviation regression estimators, Econom. Theory 7, 186-199.
  • C. R. Rao (1988), Methodology based on the $L_1$-norm in statistical inference, Sankhyā Ser. A 50, 289-313.
  • R. M. Schrader and J. W. McKean (1987), Small sample properties of Least Absolute Errors Analysis of Variance, in: Statistical Data Analysis Based on $L_1$-norm and Related Methods, Y. Dodge (ed.), North-Holland, 307-321.
  • L. Schwartz (1967), Analyse Mathématique, Hermann.
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