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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
Warianty tytułu
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
Opis fizyczny
Daty
wydano
1995
otrzymano
1994-04-06
Twórcy
  • Institute of Applied Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland
Bibliografia
  • G. J. Babu (1986), Efficient estimation of the reciprocal of the density quantile function at a point, Statist. Probab. Letters 4, 133-139.
  • P. Bloomfield and W. L. Steiger (1983), Least Absolute Deviations, Theory, Applications, Algorithms, Birkhäuser, Boston.
  • 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.
  • J. W. McKean and R. M. Schrader (1987), Least Absolute Errors Analysis of Variance, in: Statistical Data Analysis Based on $L_1$-norm and Related Methods, Y. Dodge (ed.), North-Holland, 297-305.
  • W. Niemiro (1987), Statistical properties of the method of minimization of perceptron criterion function in linear discriminant analysis, Prace IBIB PAN 23 (in Polish).
  • W. Niemiro, (1989), $L^1$-optimal statistical discrimination procedures and their asymptotic properties, Mat. Stos. 31, 57-89 (in Polish).
  • W. Niemiro, (1992), Asymptotics for M-estimators defined by convex minimization, Ann. Statist. 20, 1514-1533.
  • W. Niemiro, (1993), Least empirical risk procedures in statistical inference, Applicationes Math. 22, 55-67.
  • D. Pollard (1984), Convergence of Stochastic Processes, Springer.
  • D. Pollard, (1989), Asymptotics via empirical processes, Statist. Sci. 4, 341-366.
  • 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.
  • P. J. Szabłowski (1990), Elliptically contoured random variables and their application to the extension of Kalman filter, Comput. Math. Appl. 19, 61-72.
  • A. H. Welsh (1987), Kernel estimates of the sparsity function, in: Statistical Data Analysis Based on $L_1$-norm and Related Methods, Y. Dodge (ed.), North-Holland, 369-377.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv22z4p515bwm
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