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Moving to Higher Dimensions

In: Multivariate Statistics

Author

Listed:
  • Wolfgang Karl Härdle

    (Humboldt-Universität zu Berlin, C.A.S.E. Centre f. Appl. Stat. & Econ. School of Business and Economics)

  • Zdeněk Hlávka

    (Charles University in Prague, Faculty of Mathematics and Physics Department of Statistics)

Abstract

The basic tool used for investigating dependencies between the ith and jth components of a random vector X is the covariance $$\displaystyle{ \sigma _{X_{i}X_{j}} =\mathop{ \mathrm{\mathsf{Cov}}}\nolimits (X_{i},X_{j}) =\mathop{ \mathrm{\mathsf{E}}}\nolimits (X_{i}X_{j}) - (\mathop{\mathrm{\mathsf{E}}}\nolimits X_{i})(\mathop{\mathrm{\mathsf{E}}}\nolimits X_{j}). }$$ From a data set, the covariance between the ith and jth columns can be estimated as $$\displaystyle{ s_{X_{i}X_{j}} = \frac{1} {n}\sum _{k=1}^{n}(x_{ ik} -\bar{ x}_{i})(x_{jk} -\bar{ x}_{j}). }$$

Suggested Citation

  • Wolfgang Karl Härdle & Zdeněk Hlávka, 2015. "Moving to Higher Dimensions," Springer Books, in: Multivariate Statistics, edition 2, chapter 0, pages 27-42, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-36005-3_3
    DOI: 10.1007/978-3-642-36005-3_3
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