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.
@article{bwmeta1.element.bwnjournal-article-zmv22z4p515bwm, author = {Wojciech Niemiro}, title = {Estimation of nuisance parameters for inference based on least absolute deviations}, journal = {Applicationes Mathematicae}, volume = {23}, year = {1995}, pages = {515-529}, zbl = {0820.62035}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv22z4p515bwm} }
Niemiro, Wojciech. Estimation of nuisance parameters for inference based on least absolute deviations. Applicationes Mathematicae, Tome 23 (1995) pp. 515-529. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv22z4p515bwm/
[000] G. J. Babu (1986), Efficient estimation of the reciprocal of the density quantile function at a point, Statist. Probab. Letters 4, 133-139. | Zbl 0597.62022
[001] P. Bloomfield and W. L. Steiger (1983), Least Absolute Deviations, Theory, Applications, Algorithms, Birkhäuser, Boston. | Zbl 0536.62049
[002] L. Bobrowski (1986), Linear discrimination with symmetrical models, Pattern Recognition 19, 101-109. | Zbl 0622.62064
[003] Y. Dodge (ed.) (1987), Statistical Data Analysis Based on -norm and Related Methods, North-Holland.
[004] Y. Dodge (ed.) (1987), (ed.) (1992), -Statistical Analysis and Related Methods, North-Holland.
[005] D. J. Hand (1981), Discrimination and Classification, Wiley, New York. | Zbl 0587.62119
[006] 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. | Zbl 0679.62020
[007] 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. | Zbl 0635.62017
[008] J. Jurečková and P. K. Sen (1987) (1989), Uniform second order asymptotic linearity of M-statistics in linear models, Statist. Decisions 7, 263-276. | Zbl 0676.62056
[009] J. Kiefer (1967), On Bahadur's representation of sample quantiles, Ann. Math. Statist. 38, 1323-1342. | Zbl 0158.37005
[010] J. Kim and D. Pollard (1990), Cube root asymptotics, Ann. Statist. 18, 191-219. | Zbl 0703.62063
[011] R. Koenker (1987), A comparison of asymptotic testing methods for -regression, in: Statistical Data Analysis Based on -norm and Related Methods, Y. Dodge (ed.), North-Holland, 287-295.
[012] R. Koenker and G. Basset (1978), Regression quantiles, Econometrica 46, 33-50. | Zbl 0373.62038
[013] J. W. McKean and R. M. Schrader (1987), Least Absolute Errors Analysis of Variance, in: Statistical Data Analysis Based on -norm and Related Methods, Y. Dodge (ed.), North-Holland, 297-305.
[014] W. Niemiro (1987), Statistical properties of the method of minimization of perceptron criterion function in linear discriminant analysis, Prace IBIB PAN 23 (in Polish).
[015] W. Niemiro, (1989), -optimal statistical discrimination procedures and their asymptotic properties, Mat. Stos. 31, 57-89 (in Polish). | Zbl 0698.62060
[016] W. Niemiro, (1992), Asymptotics for M-estimators defined by convex minimization, Ann. Statist. 20, 1514-1533. | Zbl 0786.62040
[017] W. Niemiro, (1993), Least empirical risk procedures in statistical inference, Applicationes Math. 22, 55-67. | Zbl 0797.62021
[018] D. Pollard (1984), Convergence of Stochastic Processes, Springer. | Zbl 0544.60045
[019] D. Pollard, (1989), Asymptotics via empirical processes, Statist. Sci. 4, 341-366. | Zbl 0955.60517
[020] D. Pollard, (1991), Asymptotics for least absolute deviation regression estimators, Econom. Theory 7, 186-199.
[021] C. R. Rao (1988), Methodology based on the -norm in statistical inference, Sankhyā Ser. A 50, 289-313. | Zbl 0677.62058
[022] R. M. Schrader and J. W. McKean (1987), Small sample properties of Least Absolute Errors Analysis of Variance, in: Statistical Data Analysis Based on -norm and Related Methods, Y. Dodge (ed.), North-Holland, 307-321.
[023] L. Schwartz (1967), Analyse Mathématique, Hermann. | Zbl 0171.01301
[024] P. J. Szabłowski (1990), Elliptically contoured random variables and their application to the extension of Kalman filter, Comput. Math. Appl. 19, 61-72. | Zbl 0698.60038
[025] A. H. Welsh (1987), Kernel estimates of the sparsity function, in: Statistical Data Analysis Based on -norm and Related Methods, Y. Dodge (ed.), North-Holland, 369-377.