Adjustments for a class of tests under nonstandard conditions

Akashi, Fumiya; Taniguchi, Masanobu; Monti, Anna Clara; Amano, Tomoyuki

doi:10.5705/ss.202016.0093

Cited by 2 publications

(4 citation statements)

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“…Monti and Taniguchi (2018) developed the third‐order asymptotic theory for tests when the parameter is on the boundary of parameter space. Here, assuming that the parameter

θ

is scalar, and the parameter space is

false[θ_{0}, b false)

, where

θ_{0}

is the true value and

b

is a finite constant, we impose that the likelihood function

L_{n} false(θ false)

is five times differentiable with respect to

θ

from the right‐hand side of

θ_{0}

.…”

Section: Whittle Likelihood Approachmentioning

confidence: 99%

“…Let

W_{1} = g^{prefix- 1 false/ 2} Z_{1} false(θ false)

for

θ = θ_{0}

. From (5.2) of Monti and Taniguchi (2018, p. 1455) it follows that

P_{n, θ_{0}} false(W_{1} > 0 false) = \frac{1}{2} prefix- \frac{1}{6 \sqrt{2 π}} \frac{K}{\sqrt{n}} + o ((), \frac{1}{\sqrt{n}}) .

Then from Proposition 1, conditioning on

W_{1} > 0

, it is not difficult to see that the second‐order term of

E^{θ_{0}} false[\sqrt{n} false({\overset{θ}{true}}_{B} prefix- θ_{0} false) false]

equals

true \frac{1}{\sqrt{n}} true[prefix- true \frac{K}{6 \sqrt{2 π}} prefix- true \frac{J}{g^{2}} prefix- true \frac{K}{2 g^{2}} + \frac{1}{2 ξ g} ξ^{'} true],

which leads to the minimax prior

ξ

satisfying

true \frac{1}{ξ} ξ^{'} = \frac{K g}{3 \sqrt{2 π}} + \frac{2 J}{g} + \frac{K}{g},

…”

Section: Whittle Likelihood Approachmentioning

confidence: 99%

“…Self and Liang (1987) studied asymptotic properties of MLE and likelihood ratio tests under non‐standard conditions with the parameter on the boundary of parameter space. Monti and Taniguchi (2018) extensively developed the third‐order asymptotic theory for a class of tests under this condition, while Phillips (1991) and Sims and Uhlig (1991) considered the non‐regular issue in the cases of a unit root and near unit root. We also discussed the minimax problem in the case where the parameter is on the boundary of the space.…”

Section: Introductionmentioning

confidence: 99%

“…Let W 1 = g −1∕2 Z 1 (𝜃) for 𝜃 = 𝜃 0 . From (5.2) of Monti andTaniguchi (2018, p. 1455) it follows that…”

mentioning

confidence: 99%

See 3 more Smart Citations

Higher‐order asymptotics of minimax estimators for time series

Liu

Taniguchi

2022

Journal Time Series Analysis

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We consider the minimax estimation of time series in view of higher-order asymptotic theory. Under the framework of Bayesian inference, we focus on the Bayes estimator and the Bayesian Whittle estimator for parameter estimation. It is shown that these estimators are minimax with respect to the Bayes risk of higher-order bias appeared in their asymptotic expansion. The minimax problem in the boundary issue with parameter on the boundary of parameter space is also discussed. Our theoretical discovery is justified by simulation studies even when the sample size is small.

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“…Monti and Taniguchi (2018) developed the third‐order asymptotic theory for tests when the parameter is on the boundary of parameter space. Here, assuming that the parameter