Sequential Point Estimation of a Function of the Exponential Scale Parameter
DOI:
https://doi.org/10.17713/ajs.v33i3.442Abstract
We consider sequential point estimation of a function of the scale parameter of an exponential distribution subject to the loss function given as a sum of the squared error and a linear cost. For a fully sequential sampling scheme, we present a sufficient condition to get a second order approximation to the risk of the sequential procedure as the cost per observation tends to zero. In estimating the mean, our result coincides with that of Woodroofe (1977). Further, in estimating the hazard rate for example, it is shown thatour sequential procedure attains the minimum risk associated with the best fixed sample size procedure up to the order term.
References
Ali, M., and Isogai, E. (2003). Sequential point estimation of the powers of an exponential scale parameter. Scientiae Mathematicae Japonicae, 58, 39-53.
Aras, G., and Woodroofe, M. (1993). Asymptotic expansions for the moments of a randomly stopped average. The Annals of Statistics, 21, 503-519.
Chow, Y. S., Hsiung, C. A., and Lai, T. L. (1979). Extended renewal theory and moment convergence in anscombe’s theorem. The Annals of Probability, 7, 304-318.
Chow, Y. S., and Teicher, H. (1988). Probability theory (second ed.). New York: Springer-Verlag.
Mukhopadhyay, N., Padmanabhan, A. R., and Solanky, T. K. S. (1997). On estimating the reliability after sequentially estimating the mean: the exponential case. Metrika, 45, 235-252.
Takada, Y. (1986). Non-existence of fixed sample size procedures for scale families. Sequential Analysis, 5, 93-100.
Takada, Y. (1997). Fixed-width confidence intervals for a function of normal parameters. Sequential Analysis, 16, 107-117.
Uno, C., and Isogai, E. (2002). Sequential point estimation of the powers of a normal scale parameter. Metrika, 55, 215-232.
Woodroofe, M. (1977). Second order approximations for sequential point and interval estimation. The Annals of Statistics, 5, 984-995.
Downloads
Published
How to Cite
Issue
Section
License
The Austrian Journal of Statistics publish open access articles under the terms of the Creative Commons Attribution (CC BY) License.
The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed.
Copyright on any research article published by the Austrian Journal of Statistics is retained by the author(s). Authors grant the Austrian Journal of Statistics a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified.
Manuscripts should be unpublished and not be under consideration for publication elsewhere. By submitting an article, the author(s) certify that the article is their original work, that they have the right to submit the article for publication, and that they can grant the above license.
