$L_p $-Criteria for the Estimation of Location Parameters

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Previous article Next article $L_p $-Criteria for the Estimation of Location ParametersH. Ekblom and S. HenrikssonH. Ekblom and S. Henrikssonhttps://doi.org/10.1137/0117104PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] John R. Rice and , John S. White, Norms for smoothing and estimation, SIAM Rev., 6 (1964), 243–256 10.1137/1006061 MR0168069 (29:5334) 0121.34102 LinkISIGoogle Scholar[2] Harald Cramér, Mathematical Methods of Statistics, Princeton Mathematical Series, vol. 9, Princeton University Press, Princeton, N. J., 1946xvi+575 MR0016588 (8,39f) 0063.01014 Google Scholar[3] John R. Rice, The approximation of functions. Vol. I: Linear theory, Addison-Wesley Publishing Co., Reading, Mass.-London, 1964xi+203 MR0166520 (29:3795) 0114.27001 Google Scholar[4] Tore Dalenius, The mode—a negelcted statistical parameter, J. Roy. Statist. Soc. Ser. A, 128 (1965), 110–117 MR0185720 (32:3182) CrossrefISIGoogle Scholar[5] Ulf Grenander, Some direct estimates of the mode, Ann. Math. Statist, 36 (1965), 131–138 MR0170409 (30:647) 0131.17702 CrossrefISIGoogle Scholar[6] G. H. Hardy, , J. E. Littlewood and , G. Pólya, Inequalities, Cambridge University Press, Cambridge, 1934 0010.10703 Google Scholar[7] Edwin F. Beckenbach and , Richard Bellman, Inequalities, Second revised printing. Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge, Band 30, Springer-Verlag, New York, Inc., 1965xi+198 MR0192009 (33:236) 0128.27401 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Multicollinearity in regression: an efficiency comparison between Lp-norm and least squares estimatorsQuality & Quantity, Vol. 52, No. 4 | 12 September 2017 Cross Ref The First Problem of Algebraic RegressionLinear and Nonlinear Models | 21 December 2011 Cross Ref The Fifth Problem of Probabilistic RegressionLinear and Nonlinear Models | 21 December 2011 Cross Ref The Nonlinear Problem of the 3d Datum Transformation and the Procrustes AlgorithmLinear and Nonlinear Models | 21 December 2011 Cross Ref The Sixth Problem of Generalized Algebraic RegressionLinear and Nonlinear Models | 21 December 2011 Cross Ref Special Problems of Algebraic Regression and Stochastic EstimationLinear and Nonlinear Models | 21 December 2011 Cross Ref Algebraic Solutions of Systems of EquationsLinear and Nonlinear Models | 21 December 2011 Cross Ref The First Problem of Probabilistic Regression: The Bias ProblemLinear and Nonlinear Models | 21 December 2011 Cross Ref The Second Problem of Algebraic RegressionLinear and Nonlinear Models | 21 December 2011 Cross Ref The Second Problem of Probabilistic RegressionLinear and Nonlinear Models | 21 December 2011 Cross Ref The Third Problem of Algebraic RegressionLinear and Nonlinear Models | 21 December 2011 Cross Ref The Third Problem of Probabilistic RegressionLinear and Nonlinear Models | 21 December 2011 Cross Ref The Fourth Problem of Probabilistic RegressionLinear and Nonlinear Models | 21 December 2011 Cross Ref The Fifth Problem of Algebraic Regression: The System of Conditional Equations: Homogeneous and Inhomogeneous Equations: $$\{\mathbf{By} = \mathbf{Bi}\ \mathbf{versus} -\mathbf{c} + \mathbf{By} = \mathbf{Bi}\}$$Linear and Nonlinear Models | 21 December 2011 Cross Ref Image denoising and deblurring: non-convex regularization, inverse diffusion and shock filterScience China Information Sciences, Vol. 54, No. 6 | 19 April 2011 Cross Ref Tomographic observation of shallow-water inhomogeneities in the case of probing by a focused high-frequency acoustic field. 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