For squared error plus linear cost, the problems of sequential minimum risk point estimation of t... more For squared error plus linear cost, the problems of sequential minimum risk point estimation of the difference of means of two independent populations are addressed. Under a very general set up, a second-order theory is first developed for the associated regret function assuming appropriate conditions. A few interesting examples are provided including distribution-free situations, mixture normal distributions and two-parameter negative exponential distributions.
In situations where the experimental or sampling units in a study can be more easily ranked than ... more In situations where the experimental or sampling units in a study can be more easily ranked than quantified, Mclntyre (1952) proposed that the mean of η units based on a ranked set sample (RSS) be used to estimate the population mean, and observed that it provides an unbiased estimator with a smaller variance compared to a simple random sample of the same size n. Mclntyre's concept of RSS is essentially nonparametric in nature in that the underlying population distribution is assumed to be completely unknown. In this paper we further explore the concept of RSS when the population is partially known. To be specific, we address the problems of estimation of a normal mean and a normal variance, and an exponential mean. It turns out that for all the three problems the use of RSS and its suitable modifications results in much improved estimators compared to the use of a simple random sample.
In [15], a circularly symmetric directional distribution was obtained by showing that in the clas... more In [15], a circularly symmetric directional distribution was obtained by showing that in the class of circularly symmetric distributions on the circle it is the only distribution for which the sample circular median is a maximum likelihood estimate of the location Parameter. We demonstrate asymptotic efficiency of such a sample circular median as an estimate of the location parameter of this model, with asymptotic efficiency being described within the Hajek-LeCam framework. Accordingly, a suitable notion of local asymptotic normality for distributions on the circle is introduced and a convolution theorem characterizing the limit laws of regulär estimates is proved in the process.
For squared error plus linear cost, the problems of sequential minimum risk point estimation of t... more For squared error plus linear cost, the problems of sequential minimum risk point estimation of the difference of means of two independent populations are addressed. Under a very general set up, a second-order theory is first developed for the associated regret function assuming appropriate conditions. A few interesting examples are provided including distribution-free situations, mixture normal distributions and two-parameter negative exponential distributions.
In situations where the experimental or sampling units in a study can be more easily ranked than ... more In situations where the experimental or sampling units in a study can be more easily ranked than quantified, Mclntyre (1952) proposed that the mean of η units based on a ranked set sample (RSS) be used to estimate the population mean, and observed that it provides an unbiased estimator with a smaller variance compared to a simple random sample of the same size n. Mclntyre's concept of RSS is essentially nonparametric in nature in that the underlying population distribution is assumed to be completely unknown. In this paper we further explore the concept of RSS when the population is partially known. To be specific, we address the problems of estimation of a normal mean and a normal variance, and an exponential mean. It turns out that for all the three problems the use of RSS and its suitable modifications results in much improved estimators compared to the use of a simple random sample.
In [15], a circularly symmetric directional distribution was obtained by showing that in the clas... more In [15], a circularly symmetric directional distribution was obtained by showing that in the class of circularly symmetric distributions on the circle it is the only distribution for which the sample circular median is a maximum likelihood estimate of the location Parameter. We demonstrate asymptotic efficiency of such a sample circular median as an estimate of the location parameter of this model, with asymptotic efficiency being described within the Hajek-LeCam framework. Accordingly, a suitable notion of local asymptotic normality for distributions on the circle is introduced and a convolution theorem characterizing the limit laws of regulär estimates is proved in the process.
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