Sequential Point Estimation of a Function of the Exponential Scale Parameter

Authors

  • Chikara Uno Akita University, Japan
  • Eiichi Isogai Niigata University, Japan
  • Daisy Lou Lim Niigata University, Japan

DOI:

https://doi.org/10.17713/ajs.v33i3.442

Abstract

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 that
our 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

2016-04-03

How to Cite

Uno, C., Isogai, E., & Lim, D. L. (2016). Sequential Point Estimation of a Function of the Exponential Scale Parameter. Austrian Journal of Statistics, 33(3), 281–291. https://doi.org/10.17713/ajs.v33i3.442

Issue

Section

Articles