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Abstract:
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One-dimensional indices are prerequisites of any total order. Such uni-dimensional indicators are utilized by economists, psychologists and almost anyone who is faced with multiply measured complex units(individuals, companies, etc.). I will present a scalar-valued statistic based on the p-dimensional measurements whose values partition the population into sectors within which the joint distribution of the measurements is a p-dimensional uniform. In other words, this is a single-index exhausting all the information in the p-variates that could be used for unit ordering. Any p-dimensional random variable, may be reduced to a one-dimensional pivotal sufficient summary. Examples of spherically symmetric distributions and their estimation will be discussed along with limitations of such drastic reductions.
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