Statistical inference based on complex survey designs using rank information and order statistics

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In many experiments, an important factor in implementing a statistically sound sampling design is the cost of taking measurements from sampling units. Sometimes researchers have access to some auxiliary information, or results of earlier surveys, expert-opinion knowledge, or inexpensive and useful measurements from the population that can be used to easily rank sampling units prior to taking final measurements on them. For example, consider the problem of estimation of bone mineral density in a human population. Subjects for such a study are plentiful, but measurement of bone mineral density via dual x-ray absorptiometry on the selected subjects is expensive. Thus, it is important to minimize the number of measurements required for such a study without reducing the amount of reliable information obtained about the bone mineral density makeup of the population. One successful strategy is to use expert-opinion knowledge on a large number of sampling units to identify more representative samples from the population from which the expensive bone mineral density measurement should be collected via dual x-ray absorptiometry. Rank-based sampling  designs provide a collection of techniques to obtain and analyze these expensive measurements with the help of inexpensive information.  These designs have found applications in fisheries, agricultural, environmental and ecological studies such as radiation (soil contamination and disease clusters) or pollution (water contamination and root disease of crops)  as well as in medical research, machine learning and image processing.***This research proposal focuses on developing new methodologies for parametric and nonparametric inference based on complex survey designs using rank information and order statistics in finite and infinite populations. The mathematical analysis will provide insight into the process of inference from rank-based data and suggest  new methodologies for efficient inference with such samples. The main objective is to answer broad research problems involving rank-based data from both the Bayesian and frequentist perspectives. I will also study the optimization opportunities that take into account quality of rankers, number of rankers, sample size and number of ranking classes.*** The research developments coming from this proposal will have many important applications. For example, the results could be of interest to Statistics Canada when designing surveys based on rank information; to Health Canada for water quality studies and environmental risk monitoring;  as well as to Fisheries and Oceans Canada for developing better methods for monitoring fisheries-related activities. The proposal would not only complement and extend the existing theory on rank-based sampling designs, but also has the potential to address methodological problems in other settings where observations involve censored and/or length-biased data. ******* **