Sequential Point Estimation of the Difference of Two Normal Means

On sequential procedures for the point estimation of the mean of a normal population

“…R e m a r k 2. F o r s = 2 , t = l , we obtain co( C) = C + o( C) as C---0, for all m _> 3, which is the result obtained by Ghosh and Mukhopadhyay (1980). Moreover, the result lim co(C)= 0, for all m _ 3, obtained by C~0 Nagao and Takada (1980) also follows immediately.…”

“…They also proved that for all m _> 3, lim q ( C ) = 1 and lim o9(C) = 0. A stronger bound for C~0 C~0 og(C) is available in Ghosh and Mukhopadhyay (1980). In the next two sections, we shall derive second-order approximations for ~o(C), E ( N ) and E ( N 2) for all s and t. In the remaining part of this note, we shall denote by k any generic constant independent of C, [y] will be used for the integral part of y, and I ( S ) will stand for the indicator function defined on the set S.…”

On Behrens–Fisher problem for continuous time Gaussian processes

“…Our study is inspired in a sequence of papers by Ghosh and Mukhopadhyay [2], Mukhopadhyay and Abid [3], Mukhopadhyay and Liberman [4], Mukhopadhyay and Duggan [5]. These papers consider the problem in the discrete time case providing confidence regions, with given confidence level and diameter, for the difference between the means of two multidimensional normal distributions with nuisance parameters in their covariances.…”

“…The one-dimensional case is considered in [2], which also deals with the multidimensional case assuming that both covariance matrices have the same form σ 2 H . This is extended in [3] to the case of different covariances matrices, σ 2 1 H / = σ 2 2 H and σ 2 1 H 1 / = σ 2 2 H 2 successively.…”

Sequential Estimation of the Ratio of Scale Parameters in the Exponential Two-sample Problem

“…For instance, Ghosh and Mukhopadhyay (1980) and Mukhopadhyay and Chattopadhyay (1991) considered the normal and the exponential cases, respectively and gave second order approximations to the risks as c → 0. Mukhopadhyay and Purkayastha (1994) and Uno and Isogai (2000) treated the same problem in the case of unspecified distributions.…”