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© Centre for Modeling & Simulation, Savitribai Phule Pune University
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State-space models in time series have a rich history of applications and methodological developments (see the books by Shumway and Stoffer (2000) and Fahrmeir and Tutz (2001)). A state space model consists of an unobservable stochastic process of states and an observable stochastic process depending on the states. The model is specified by a family of conditional probability mass/density functions which usually involve unknown parameters called the hyper-parameters of the model. Problems of interests in such models are estimation of the states the hyper-parameters, apart from the problem of identification of an appropriate model for an observed data sequence. For the Gaussian case, the Kalman filter and smoother are used to estimate the states and write the likelihood of the observed process to obtain a maximum likelihood (ML) estimator of the hyper-parameters. However in the non Gaussian case, most of the existing methods to compute the ML or suitable estimators are too cumbersome. We are interested in the Imputation Maximization (IM) algorithms which involve simulating the states given the observations and the current iterate value of the parameter and then maximizing the likelihood based on the `complete data', i.e., based on the observation and the states. Studying the performance of various estimators analytically so far has not been possible for most of the algorithms. Using simulations we propose to compare the IM algorithms with the other algorithms in terms of the computer efficiency, convergence and performance of the resulting estimators. We also plan to use computer intensive resampling and bootstrap methods to obtain the variance/precision and sampling distributions of the estimators. The models considered would be suitable for applications to financial data and reliability/life data.
M. Sc. in Statistics with minimum 55% or equivalent grade. Knowledge of elementary stochastic processes and probability theory. Knowledge of computer programming in Fortran or C.
The one-year project will result in an M. Phil. dissertation. If the candidate wishes to do further research, he/she can apply for financial support to other funding agencies. For example, the candidate can appear for the UGC/CSIR examination during the year.