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Grouped and right-censored (GRC) count data are widely adopted to study some sensitive topics or to collect information from less cognitive respondents in many research fields, such as psychology, sociology, and criminology. However, theoretical analysis of GRC counts is involved due to the co-existence of grouping schemes and right-censoring schemes. Recently, a modified Poisson regression model has been proposed to analyze GRC count data under the framework of maximum likelihood estimation. In this paper, I study the asymptotic properties of the maximum likelihood estimators of GRC counts that can cover the modified Poisson estimator. Existing results on modified Poisson estimators for GRC counts are only applicable to stochastic regressors with strictly positive definite Fisher information matrices. Results in this paper are derived under a milder condition that the information matrix of observations is divergent, which can cover the results for the stochastic case in the almost sure sense. Real data simulations are provided to investigate drug use in America. [ABSTRACT FROM AUTHOR]

Stochastic approximation methods for rewards of American type options are studied. Pay-off functions are non random possibly discontinuous functions or random càdlàg functions. General conditions of convergence for binomial, trinomial, and skeleton reward approximations are formulated. Underlying log-price processes are assumed to be random walks. These processes are approximated by log-price processes given by random walks with discrete distributions of jumps. Backward recurrence algorithms for computing of reward functions for approximating log-price processes are given. These approximation algorithms and their rates of convergence are numerically tested for log-price processes represented by Gaussian and compound Gaussian random walks. Comparison of the above approximation methods is made. [ABSTRACT FROM PUBLISHER]