Locally most powerful sequential tests of a simple hypothesis vs. one-sided alternatives

Novikov, Andrey; Novikov, Petr

doi:10.1016/j.jspi.2009.09.004

Cited by 10 publications

(29 citation statements)

References 11 publications

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“…The proof is based on the simple lemma below which is essentially a reformulation of Lemma A.2 in [29]. For any random variable v with E|v| < ∞ let us define:…”

Section: A1 Proof Of Theoremmentioning

confidence: 99%

Characterizations of Optimal Policies in a General Stopping Problem and Stability Estimating

Gordienko¹,

Novikov²

2014

Prob. Eng. Inf. Sci.

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We consider an optimal stopping problem for a general discrete-time process X 1 , X 2 , . . . , Xn, . . . on a common measurable space. Stopping at time n (n = 1, 2, . . . ) yields a reward Rn(X 1 , . . . , Xn) ≥ 0, while if we do not stop, we pay cn(X 1 , . . . , Xn) ≥ 0 and keep observing the process. The problem is to characterize all the optimal stopping times τ , i.e., such that maximize the mean net gain:cn(X 1 , . . . , Xn)).We propose a new simple approach to stopping problems which allows to obtain not only sufficient, but also necessary conditions of optimality in some natural classes of (randomized) stopping rules.In the particular case of Markov sequence X 1 , X 2 , . . . we estimate the stability of the optimal stopping problem under perturbations of transition probabilities.

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“…The proof is based on the simple lemma below which is essentially a reformulation of Lemma A.2 in [29]. For any random variable v with E|v| < ∞ let us define:…”

Section: A1 Proof Of Theoremmentioning

confidence: 99%

Characterizations of Optimal Policies in a General Stopping Problem and Stability Estimating

Gordienko¹,

Novikov²

2014

Prob. Eng. Inf. Sci.

Self Cite

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show abstract

“…the test (τ, δ) is locally most powerful in a wider, than in [18], class of sequential tests (in [18], the class of tests (τ ′ , δ ′ ) such that β θ 0 (τ ′ , δ ′ ) = α and E θ 0 τ ′ ≤ E θ 0 τ is considered). For the discrete-time processes of general form, the same extension of the class of tests is adopted in [16]. We conjecture that, under the conditions of [18], this extension can be obtained in many cases, as easily as above, from the corresponding generalization of (27) to the continuous-time case.…”

mentioning

confidence: 91%

“…Let now β 0 = 0. From (16) and (23) it follows that ∆ h β/h → 0, as h → 0, i.e.β 0 = 0. Hence, (24) is also holds.…”

mentioning

confidence: 94%

“…We follow [16] in definitions and notation related to sequential hypothesis testing problems (see also [22], [5], [4], [19], [3], [15], among many others).…”

mentioning

confidence: 99%

“…, N − 1. P r o o f. It is sufficient to express the elements of the optimal stopping rule from Corollary 4.1 [16] (V N n and R N n ) through the corresponding functions v N n and r N n . Let us show that for all N = 1, 2, .…”

mentioning

confidence: 99%

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