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Determining the form of the mean of a stochastic process


  • Spruill, Carl


Let [mu] be the mean function of an observable stochastic process whose sample paths fall in some Banach space with a basis and assume [mu] is also in this space. A procedure like Cover's (Ann. Statist.1, 862-871, 1973) is given which has the property that if the last nonzero coordinate of [mu] is the mth then with probability one this is discovered after at most a finite number of erros. If [mu] has an infinite number of nonzero coordinates, then with probability one this is discovered after at most a finite number of errors except for a set of [mu] of prior probability zero.

Suggested Citation

  • Spruill, Carl, 1977. "Determining the form of the mean of a stochastic process," Journal of Multivariate Analysis, Elsevier, vol. 7(2), pages 278-285, June.
  • Handle: RePEc:eee:jmvana:v:7:y:1977:i:2:p:278-285

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    References listed on IDEAS

    1. Robinson, P M, 1987. "Asymptotically Efficient Estimation in the Presence of Heteroskedasticity of Unknown Form," Econometrica, Econometric Society, vol. 55(4), pages 875-891, July.
    2. Pollard, David, 1985. "New Ways to Prove Central Limit Theorems," Econometric Theory, Cambridge University Press, vol. 1(03), pages 295-313, December.
    3. Andrews, Donald W. K., 1988. "Chi-square diagnostic tests for econometric models : Introduction and applications," Journal of Econometrics, Elsevier, vol. 37(1), pages 135-156, January.
    4. Andrews, Donald W K, 1988. "Chi-Square Diagnostic Tests for Econometric Models: Theory," Econometrica, Econometric Society, vol. 56(6), pages 1419-1453, November.
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