Estimation of nuisance parameters for inference based on least absolute deviations

• Autorzy: Wojciech Niemiro
• 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

least absolute deviations   kernel density/regression estimation  

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1993-1995
• Tom: 22
• Numer: 4
• Strony: 515-529

Daty

wydano

1995

otrzymano

1994-04-06

Twórcy

autor

Wojciech Niemiro

• 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.