Sampling theory and inferences

Measurement errors in sample surveys

variance model using preliminary tests of significance

Dynamic programming

Taxation of land

Company ka Samapak

Replacement models

We consider a mean-variance portfolio optimization problem, namely, a problem of minimizing the variance of the final wealth that results from trading over a fixed finite horizon in a continuous-time complete market in the presence of convex portfolio constraints, taking into account the cost imposed by margin requirements on trades and subject to the further constraint that the expected final wealth equal a specified target value. Market parameters are chosen to be random processes adapted to the information filtration available to the investor and asset prices are modeled by Itô processes. To solve this problem we use an approach based on conjugate duality: we start by synthesizing a dual optimization problem, establish a set of optimality relations that describe an optimal solution in terms of solutions of the dual problem, thus giving necessary and sufficient conditions for the given optimization problem and its dual to each have a solution. Finally, we prove existence of a solution of the dual problem, and for a particular class of dual solutions, establish existence of an optimal portfolio and also describe it explicitly. The method elegantly and rather straightforwardly constructs a dual problem and its solution, as well as provides intuition for construction of the actual optimal portfolio.

This thesis considers modelling and applications of random graph processes. A brief review on contemporary random graph models and a general Birth-Death model with relevant maximum likelihood inference procedure are provided in chapter one. The main result in this thesis is the construction of an epidemic model by embedding a competing hazard model within a stochastic graph process (chapter 2). This model includes both individual characteristics and the population connectivity pattern in analyzing the infection propagation. The dynamic outdegrees and indegrees, estimated by the model, provide insight into important epidemiological concepts such as the reproductive number. A dynamic reproductive number based on the disease graph process is developed and applied in several simulated and actual epidemic outbreaks. In addition, graph-based statistical measures are proposed to quantify the effect of individual characteristics on the disease propagation. The epidemic model is applied to two real outbreaks: the 2001 foot-and-mouth epidemic in the United Kingdom (chapter 3) and the 1861 measles outbreak in Hagelloch, Germany (chapter 4). Both applications provide valuable insight into the behaviour of infectious disease propagation with di erent connectivity patterns and human interventions.

This thesis proposes some inferential methods for use with multiple imputation for missing data and statistical disclosure limitation, and describes an application of multiple imputation to protect data confidentiality. A third component concerns model selection in random effects models.The use of multiple imputation to generate partially synthetic public release files for confidential datasets has the potential to limit unauthorized disclosure while allowing valid inferences to be made. When confidential datasets contain missing values, it is natural to use multiple imputation to handle the missing data simultaneously with the generation of synthetic data. This is done in a two-stage process so that the variability may be estimated properly. The combining rules for data multiply imputed in this fashion differ from those developed for multiple imputation in a single stage. Combining rules for scalar estimands have been derived previously; here hypothesis tests for multivariate components are derived. Longitudinal business data are widely desired by researchers, but difficult to make available to the public because of confidentiality constraints. An application of partially synthetic data to the U. S. Census Longitudinal Business Database is described. This is a large complex economic census for which nearly the entire database must be imputed in order for it to be considered for public release. The methods used are described and analytical results for synthetic data generated for a subgroup are described. Modifications to the multiple imputation combining rules for population data are also developed.Model selection is an area in which few methods have been developed for use with multiply-imputed data. Careful consideration is given to how Bayesian model selection can be conducted with multiply-imputed data. The usual assumption of correspondence between the imputation and analyst models is not amenable to model selection procedures. Hence, the model selection procedure developed incorporates the imputation model and assumes that the imputation model is known to the analyst.Lastly, a model selection problem outside the multiple imputation context is addressed. A fully Bayesian approach for selecting fixed and random effects in linear and logistic models is developed utilizing a parameter expanded stochastic search Gibbs sampling algorithm to estimate the exact model-averaged posterior distribution. This approach automatically identifies subsets of predictors having nonzero fixed coefficients or nonzero random effects variance, while allowing uncertainty in the model selection process. / Dissertation