Likelihood Inference in small-area estimation by combining time-series and cross-sectional data

Farhad Shokoohi: Likelihood Inference in small-area estimation by combining time-series and cross-sectional data. Shahid Beheshti University, 2012.

Abstract

Recently and for the past decades, small-area estimation (SAE) methods have gain a lot of attention in many fields such as medical, economical, social and agricultural sciences. These methods have many applications in providing reliable statistics demanded for areas with small or no sample. There are many different models in order to deal with available data in small area context. The main problems with these methods lie in complexity of calculating the estimators. In some methods, such as likelihood estimation, there are high dimensional integrals which often leads to meaningless solutions. Also in most of these methods, there are no exact estimations for “MSE” and “MSPE” and usually the approximation using Taylor expansion is used for their estimators. More importantly the analytic proof of identifiability of the model and estimability of parameters is very hard and mostly impossible. In addition to tradi- tional methods which are useful in working with most of introduced models in small area context, Bayesian methods are used to handle count or proportional response variables. On the other hand, we know that Bayesian inference depends on the choice of prior. In this thesis, the fundamental problems with current methods are discussed and the new method of data cloning approach is reviewed. In order to cope with the problems, a new methodology is introduced which helps analyzing the models in SAE context such as Rao-Yu model and then the models with count and proportional data are generalized. Also, the nonparametric model introduced by Opsomer et all. (2008) is generalized in order to account for time series data. For application of the new introduced methodology the Asthma rate of Manitoba province in Canada, the Acid rate in North-Eastern lakes of USA and the unemployment rate in Iran are analyzed.

    BibTeX (Download)

    @phdthesis{Shokoohi2012Thesis,
    title = {Likelihood Inference in small-area estimation by combining time-series and cross-sectional data},
    author = {Farhad Shokoohi},
    year  = {2012},
    date = {2012-09-04},
    school = {Shahid Beheshti University},
    abstract = {Recently and for the past decades, small-area estimation (SAE) methods have gain a lot of attention in many fields such as medical, economical, social and agricultural sciences. These methods have many applications in providing reliable statistics demanded for areas with small or no sample. There are many different models in order to deal with available data in small area context. The main problems with these methods lie in complexity of calculating the estimators. In some methods, such as likelihood estimation, there are high dimensional integrals which often leads to meaningless solutions. Also in most of these methods, there are no exact estimations for “MSE” and “MSPE” and usually the approximation using Taylor expansion is used for their estimators. More importantly the analytic proof of identifiability of the model and estimability of parameters is very hard and mostly impossible. In addition to tradi- tional methods which are useful in working with most of introduced models in small area context, Bayesian methods are used to handle count or proportional response variables. On the other hand, we know that Bayesian inference depends on the choice of prior. In this thesis, the fundamental problems with current methods are discussed and the new method of data cloning approach is reviewed. In order to cope with the problems, a new methodology is introduced which helps analyzing the models in SAE context such as Rao-Yu model and then the models with count and proportional data are generalized. Also, the nonparametric model introduced by Opsomer et all. (2008) is generalized in order to account for time series data. For application of the new introduced methodology the Asthma rate of Manitoba province in Canada, the Acid rate in North-Eastern lakes of USA and the unemployment rate in Iran are analyzed. },
    keywords = {Asthma, Bayesian computation, Data cloning, Hierarchical model, Likelihood based estimation, Prediction interval, Random effects, Small-area estimation, Time series},
    pubstate = {published},
    tppubtype = {phdthesis}
    }