113
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

On Exact Computation of Some Statistics Based on Projection Pursuit in a General Regression Context

Pages 948-956 | Received 24 Aug 2010, Accepted 02 Feb 2011, Published online: 22 Mar 2011

References

  • Boyd , S. , Vandenberghe , L. ( 2004 ). Convex Optimization . Cambridge : Cambridge University Press . http://www.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf
  • Friedman , J. H. ( 1987 ). Exploratory projection pursuit . Journal of the American Statistical Association 82 : 249 – 266 .
  • Hallin , M. , Paindaveine , D. , Šiman , M. ( 2010a ). Multivariate quantiles and multiple-output regression quantiles: from L 1 optimization to halfspace depth . Annals of Statistics 38 : 635 – 669 .
  • Hallin , M. , Lu , Z. , Paindaveine , D. , Šiman , M. ( 2010b ). Local bilinear multiple-output quantile regression and regression depth . [Manuscript in preparation.]
  • Hlubinka , D. , Kotík , L. , Vencálek , O. ( 2010 ). Weighted halfspace depth . Kybernetika 46 : 125 – 148 .
  • Huber , P. J. ( 1985 ). Projection pursuit . Annals of Statistics 13 : 435 – 475 .
  • Jurečková , J. , Sen , P. K. ( 1996 ). Robust Statistical Procedures: Asymptotics and Interrelations . New York : Wiley .
  • Kim , T.-H. , White , H. ( 2004 ). On more robust estimation of skewness and kurtosis . Finance Research Letters 1 : 56 – 73 .
  • Koenker , R. , Basset , G. J. ( 1978 ). Regression quantiles . Econometrica 46 : 33 – 50 .
  • Koenker , R. ( 2005 ). Quantile Regression . New York : Cambridge University Press .
  • Kong , L. , Mizera , I. ( 2008 ). Quantile tomography: Using quantiles with multivariate data . Eprint arXiv : 0805.0056 .
  • Liu , R. Y. , Singh , K. , Teng , J. H. ( 2004 ). Linear fitting by simplicial intercept depth (SID): reflection invariance and robustness . Statistica Sinica 14 : 431 – 448 .
  • Malkovich , J. F. , Afifi , A. A. ( 1973 ). On tests of multivariate normality . Journal of the American Statistical Association 68 : 176 – 179 .
  • Paindaveine , D. , Šiman , M. ( 2011a ). On directional multiple-output quantile regression . Journal of Multivariate Analysis 102 : 193 – 392 .
  • Paindaveine , D. , Šiman , M. ( 2011b ). Computing multiple-output regression quantile regions . Computational Statistics & Data Analysis in press .
  • Paindaveine , D. , Šiman , M. ( 2011c ). Computing multiple-output regression quantile regions from projection quantiles . Computational Statistics in press .
  • Rousseeuw , P. J. , Hubert , M. ( 1999 ). Regression depth . Journal of the American Statistical Association 94 : 388 – 402 .
  • Rousseeuw , P. J. , Ruts , I. ( 1999 ). The depth function of a population distribution . Metrika 49 : 213 – 244 .
  • White , H. , Kim , T.-H. , Manganelli , S. ( 2010 ). Modeling autoregressive conditional skewness and kurtosis with multi-quantile CAViaR . In: Volatility and Time Series Econometrics . New York : Oxford University Press , pp. 231 – 257 .
  • Zuo , Y. ( 2003 ). Projection-based depth functions and associated medians . Annals of Statistics 31 : 1460 – 1490 .
  • Zuo , Y. ( 2004 ). Projection-based affine equivariant multivariate location estimators with the best possible finite sample breakdown point . Statistica Sinica 14 : 1199 – 1208 .
  • Zuo , Y. ( 2011 ). Exact computation of the bivariate projection depth and Stahel–Donoho estimator . Computational Statistics & Data Analysis 55 : 1173 – 1179 .
  • Zuo , Y. , Cui , H. (2004). Statistical depth functions and some applications. Advances in Mathematics 33:1–25.
  • Zuo , Y. , Serfling , R. ( 2000a ). On the performance of some robust nonparametric location measures relative to a general notion of multivariate symmetry . Journal of Statistical Planning and Inference 84 : 55 – 79 .
  • Zuo , Y. , Serfling , R. ( 2000b ). General notions of statistical depth functions . Annals of Statistics 28 : 461 – 482 .
  • Zuo , Y. , Ye , X. ( 2009 ). ExPD2D: Exact Computation of Bivariate Projection Depth based on Fortran Code. R package version 1.0.1, http://cran.r-project.org/package=ExPD2D

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.