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Testing Hypotheses on Spectrum Parameters of a Gaussian Time Series

  • K. Dzhaparidze
Chapter
  • 477 Downloads
Part of the Springer Series in Statistics book series (SSS)

Abstract

Following the general ideas of LeCam [80–82] (cf. also [110]) we shall consider a sequence of experiments
$${E_n} = \{ {X_n},{\mathfrak{A}_n},{P_{n,}}_\theta ,\theta \in \theta \} ,\,n = 1,2,...,$$
where the family of distributions Pnθ, θ ∈ θ for some choice of random vector Δn,θ = Δn, θ(x), xXn, and the nonrandom matrices Γθ satisfy the conditions (D1)–(D4) for τn = \(\mathop n\limits^\_ \) of asymptotic differentiability as well as the condition (D5) which assures the asymptotic normality of the vector Δn,θ (cf. the Introduction, page 21 and Section 1 of Chapter III). Assume for definiteness that the set θ ∈ Rp of possible values of the vector-valued parameter θ contains the origin and consider the problem of testing the hypothesis H0 that the parameter θ takes on the value 0. A test for this hypothesis is given by a sequence of test functions Φn = Φn(x) defined on the sample space xXn. Any measurable function taking on values 0 ⩽ Φn ⩽ 1 may serve as a test function which determines the probability Φn(x) that hypothesis H0 will be rejected when x is observed.

Keywords

Random Vector Critical Region Consistent Estimator Spectrum Parameter Noncentrality Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1986

Authors and Affiliations

  • K. Dzhaparidze
    • 1
  1. 1.Mathematisch CentrumAmsterdamThe Netherlands

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