Moving to Higher Dimensions

Wolfgang Karl Härdle and Zdeněk Hlávka
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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

Chapter Chapter 3 in Multivariate Statistics, 2015, pp 27-42 from Springer

Abstract: 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 $$\displaystyle{ s_{X_{i}X_{j}} = \frac{1} {n}\sum _{k=1}^{n}(x_{ ik} -\bar{ x}_{i})(x_{jk} -\bar{ x}_{j}). }$$

Keywords: Null Hypothesis; Regression Line; Marketing Strategy; Variance Matrix; Empirical Covariance (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-36005-3_3

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DOI: 10.1007/978-3-642-36005-3_3

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