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Is a subspace containing a splitting subspace a splitting subspace?

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  • Triacca, Umberto

Abstract

If V, A and B are three closed subspaces of we say that V is a splitting subspace for A,B if and only if A and B are conditionally orthogonal given V. If V is a splitting subspace for A,B, we shall say that V splits A,B. Rozanov [Rozanov, Y.A., 1979. Stochastic Markovian Fields. In: Developments in Statistics, vol. 2. Academic Press, New York, p. 205] observes that A[perpendicular]BV does not imply that the closed subspace W[superset of or equal to]V splits A,B. However, no example is provided. In this note we provide one.

Suggested Citation

  • Triacca, Umberto, 2008. "Is a subspace containing a splitting subspace a splitting subspace?," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2997-2999, December.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:17:p:2997-2999
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    1. Khon, R., 1981. "A characterization of Granger-Sims exogeneity," Economics Letters, Elsevier, vol. 8(2), pages 129-133.
    2. Lutkepohl, Helmut, 1982. "Non-causality due to omitted variables," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 367-378, August.
    3. Granger, C. W. J., 1980. "Testing for causality : A personal viewpoint," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 329-352, May.
    4. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
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