Sankhya: The Indian Journal of Statistics

2002, Volume 64, Series A, Pt. 2, 268--281



V.P. GODAMBE, University of Waterloo, Canada

SUMMARY. Statistical investigation of any scientific question such as the effect of a treatment on a disease or the effect of traffic intensity on pollution starts generally with an assumption of a probabilistic parametric model. The estimation of these parameters from the data is supposed to suggest an answer to the question under investigation. Now underlying the model just mentioned is the concept of a `hypothetical population' of results (observations) obtained from a large number of independent repetitions of a chance experiment. However in many situations, `implicit' with the `hypothetical population' there is an `actual' population of individuals such as humans, households, towns. This actual population is called a `survey population', for the ultimate `data' is obtained by observations on the individuals sampled from this population. Yet in many statistical investigations (biostatistics, ecology), a general tendency is to ignore, for simplicity of analysis, the underlying survey population. Much is lost by so doing. For taking into account `explicitly' the survey sampling aspect of the data collection can often enhance the efficiency of estimation. This would be demonstrated in connection with weighted distributions as they arise in some common ecological setting. (The problem within a biostatistical setting was discussed previously by Godambe \& Vijayan, 1996). This note, though self contained, is based on and is a continuation of the paper by Godambe and Rajarshi (1989). Here we further emphasize the contribution to the efficiency of estimation in situations where along with the hypothetical population model a corresponding survey population framework is available.

AMS (1991) subject classification}. Primary 62G05; secondary 62P10.

Key words and phrases: Estimating function, hypothetical population, maximum likelihood estimation; survey population, weighted distribution.

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