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## Applicationes Mathematicae

1993-1995 | 22 | 4 | 515-529
Tytuł artykułu

### Estimation of nuisance parameters for inference based on least absolute deviations

Autorzy
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.
Słowa kluczowe
EN
Czasopismo
Rocznik
Tom
Numer
Strony
515-529
Opis fizyczny
Daty
wydano
1995
otrzymano
1994-04-06
Twórcy
autor
• 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.
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Bibliografia
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