On Darling–Robbins type confidence sequences and sequential tests with power one for parameters of an autoregressive process
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Cites background or methods from "On Darling–Robbins type confidence ..."
...The proof of the first one is quite trivial while the second follows as a consequence of Basu & Mukhopadhyay (1998, 1999)....
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...Step 2 demands special attention and requires some novel techniques, as in Basu & Mukhopadhyay (1998, 1999), modified accordingly to suit the present problem....
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...This difficulty may be overcome by considering the series of HR and EHV for a given plant as a time series (the data are usually collected for each day) and extending the idea of providing confidence interval for the autoregressive parameters as has been done by Basu & Mukhopadhyay (1998, 1999)....
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...…Z∗t−1Z ∗′ t−1 )−1 ( n∑ t=1 Z∗t−1εt ) (A6) Write Mn = ∑nt=1 Z∗t−1Z∗′t−1 and (0) = E ( n∑ t=1 Z∗t−1Z ∗′ t−1 ) (A7) It is well known that, as n → ∞ (Mn/n) a.s.−→ (0), and 1 σ 2 (α̂ − α)′Mn(α̂ − α)χ2p (A8) Following Basu & Mukhopadhyay (1998, 1999), a fixed width SCI for l′α, l : l′l = 1, may be given…...
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References
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