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Gauss inequalities on ordered linear spaces

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  • Jensen, D.R.

Abstract

Markov inequalities on ordered linear spaces are tightened through the [alpha]-unimodality of the corresponding measures. Modality indices are studied for various induced measures, including the singular values of a random matrix and the periodogram of a time series. These tools support a detailed study of linear inference and the ordering of random matrices, to include fixed and random designs and probability bounds on their comparative efficiencies. Other applications include probability bounds on quadratic forms and of order statistics on on periodograms in the analysis of time series, and on run-length distributions in multivariate statistical process control. Connections to other topics in applied probability and statistics are noted.

Suggested Citation

  • Jensen, D.R., 2006. "Gauss inequalities on ordered linear spaces," Journal of Multivariate Analysis, Elsevier, vol. 97(4), pages 985-998, April.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:4:p:985-998
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    References listed on IDEAS

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    1. Holger Dette & Ingrid Spreckelsen, 2003. "A Note on a Specification Test for Time Series Models Based on Spectral Density Estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(3), pages 481-491, September.
    2. Perlman, Michael D., 1974. "Jensen's inequality for a convex vector-valued function on an infinite-dimensional space," Journal of Multivariate Analysis, Elsevier, vol. 4(1), pages 52-65, March.
    3. Efstathios Paparoditis, 2000. "Spectral Density Based Goodness‐of‐Fit Tests for Time Series Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(1), pages 143-176, March.
    4. Jensen, D. R. & Foutz, R. V., 1981. "Markov inequalities on partially ordered spaces," Journal of Multivariate Analysis, Elsevier, vol. 11(2), pages 250-259, June.
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