- 著者
- Yutaka Kano
- 出版者
- THE JAPAN STATISTICAL SOCIETY
- 雑誌
- JOURNAL OF THE JAPAN STATISTICAL SOCIETY (ISSN:18822754)
- 巻号頁・発行日
- vol.26, no.1, pp.101-117, 1996 (Released:2009-01-22)
- 参考文献数
- 43
- 被引用文献数
- 1 1
Takeuchi [37], Takeuchi and Akahira [38] and Pfanzagl [27] among others proved that any first-order efficient estimators are second-order efficient. Many other authors e. g., Ghosh [15], have conjectured that any third-order efficient estimators are also fourth-order efficient. Based on the concentration probability of estimators about a true parameter, this paper gives a positive answer to the conjecture in a curved exponential family with multi-structural parameters. It is seen that choice of bias-correction factors is critical.
- 著者
- Ekkehart Schlicht
- 出版者
- THE JAPAN STATISTICAL SOCIETY
- 雑誌
- JOURNAL OF THE JAPAN STATISTICAL SOCIETY (ISSN:18822754)
- 巻号頁・発行日
- vol.35, no.1, pp.99-119, 2005 (Released:2006-01-19)
- 参考文献数
- 10
- 被引用文献数
- 34 40
This note gives a statistical description of the Hodrick-Prescott Filter (1997), originally proposed by Leser (1961). A maximum-likelihood estimator is derived and a related moments estimator is proposed that has a straightforward intuitive interpretation and coincides with the maximum-likelihood estimator for long time series. The method is illustrated by an application and several simulations. The statistical treatment in the state-space tradition implies some scepticism regarding the interpretation in terms of low-frequency filtering.
- 著者
- Ngai Hang Yury A. Kutoyants
- 出版者
- 日本統計学会
- 雑誌
- JOURNAL OF THE JAPAN STATISTICAL SOCIETY (ISSN:18822754)
- 巻号頁・発行日
- vol.40, no.2, pp.277-303, 2010-03-22 (Released:2011-09-22)
- 参考文献数
- 36
- 被引用文献数
- 2 3
In this article, several important problems of threshold estimation in a Bayesian framework for nonlinear time series models are discussed. The paper starts with the issue of calculating the maximum likelihood and the Bayesian estimators for threshold autoregressive models. It turns out that the asymptotic efficiency of the Bayesian estimators in this type of singular estimation problems is superior than the maximum likelihood estimators. To illustrate the properties of these estimators and to explain the proposed method, the paper begins with the study of a linear threshold autoregressive model with i.i.d. Gaussian noise. The paper then extends the idea to other nonlinear and non-Gaussian models and illustrates the paradigm of limiting likelihood ratio, which is applicable to a much wider class of nonlinear models. The article also investigates the robustness issue and the possibility of restricting the observation window by narrow bands, which allows one to obtain asymptotically efficient estimators. Finally, the paper indicates how these results can be generalized from a TAR(1) model to a higher-order TAR(p) model with multiple thresholds. The paper concludes with a discussion of other related problems and illustrates the methodology by numerical simulations.