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 thatour sequential procedure attains the minimum risk associated with the best fixed sample size procedure up to the order term.
Highlights
Let X1, X2, . . . be independent and identically distributed random variables according to an exponential distribution having the probability density function fσ(x)
We consider the estimation of a function of the scale parameter
Suppose that θ(x) is a positive-valued and three times continuously differentiable function on x > 0 and that θ (x) = 0 for x > 0, where θ stands for the first derivative of θ
Summary
We consider the estimation of a function of the scale parameter. We can not use the best fixed sample size procedure n0. There is no fixed sample size procedure that will attain the minimum risk Rn0 (see Takada, 1986).
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