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1993-1995 | 22 | 1 | 55-67
Tytuł artykułu

Least empirical risk procedures in statistical inference

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider the empirical risk function $Q_n(α)={1\over n} \sum_{i=1}^n \cdot f(α,Z_i)$ (for iid $Z_i$'s) under the assumption that f(α,z) is convex with respect to α. Asymptotics of the minimum of $Q_n(α)$ is investigated. Tests for linear hypotheses are derived. Our results generalize some of those concerning LAD estimators and related tests.
Rocznik
Tom
22
Numer
1
Strony
55-67
Opis fizyczny
Daty
wydano
1993
otrzymano
1992-9-24
Twórcy
  • Institute of Applied Mathematics, Department of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland
Bibliografia
  • K. Adamczyk (1993), Asymptotic properties of ANOVA test under general loss functions, Mat. Stos., to appear.
  • Z. D. Bai, C. R. Rao and Y. Q. Yin (1990), Least absolute deviations analysis of variance, Sankhyā A 52, 166-177.
  • Z. D. Bai, C. R. Rao and Y. H. Wu (1992), M-estimation of multivariate linear regression parameters under a convex discrepancy function, Statist. Sinica 2 (1), 237-254.
  • G. Basset and R. Koenker (1978), Asymptotic theory of least absolute error regression, J. Amer. Statist. Assoc. 73, 618-622.
  • P. Bloomfield and W. L. Steiger (1983), Least Absolute Deviations, Theory, Applications, Algorithms, Birkhäuser, Boston.
  • L. Bobrowski, H. Wasyluk and W. Niemiro (1987), Some technique of linear discrimination with application to analysis of thyroid diseases diagnosis, Biocybernetics Biomed. Engrg. 7, 23-32.
  • P. A. Devijver and J. Kittler (1982), Pattern Recognition: A Statistical Approach, Prentice-Hall, London.
  • J. K. Ghosh (1971), A new proof of the Bahadur representation of quantiles and an application, Ann. Math. Statist. 42, 1957-1961.
  • S. J. Haberman (1989), Concavity and estimation, Ann. Statist. 17, 1631-1661.
  • J. B. S. Haldane (1948), Note on the median of a multivariate distribution, Biometrika 25, 414-415.
  • D. J. Hand (1981), Discrimination and Classification, Wiley, New York.
  • 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.
  • P. Milasevic and G. R. Ducharme (1987), Uniqueness of the spatial median, Ann. Statist. 15, 1332-1333.
  • 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., to appear.
  • D. Pollard (1991), Asymptotics for least absolute deviation regression estimators, Econometric Theory 7, 186-199.
  • C. R. Rao (1988), Methodology based on the $L_1$-norm in statistical inference, Sankhyā A 50, 289-313.
  • R. T. Rockafellar (1970), Convex Analysis, Princeton University Press.
  • 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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv22i1p55bwm
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