Some problems of' statistical inference for discrete-valued time series are investigated in this study. New statistical theories and methods are developed which may aid us in gaining more insight into the understanding of discrete-valued time series data. The first part is concerned with the measurement of the serial dependence of binary time series. In early studies the classical autocorrelation function was used, which, however, may not be an effective and informative means of revealing the dependence feature of a binary time series. Recently, the autopersistence function has been proposed as an alternative to the autocorrelation function for binary time series. The theoretical autopersistence functions and their sample analogues, the autopersistence graphs, are studied within a binary autoregressive model. Some properties of the autopcrsistencc functions and the asymptotic properties of the autopersistence graphs are discussed, justifying that the antopersistence graphs can be used to assess the dependence feature. Besides binary time series, intcger-vall1ed time series arc perhaps the most commonly seen discrete-valued time series. A generalization of the Poisson autoregression model for non-negative integer-valued time series is proposed by imposing an additional threshold structure on the latent mean process of the Poisson autoregression. The geometric ergodicity of the threshold Poisson autoregression with perburbations in the latent mean process and the stochastic stability of the threshold Poisson autoregression are obtained. The maximum likelihood estimator for the parameters is discussed and the conditions for its consistency and asymptotic normally are given as well. Furthermore, there is an increasing need for models of integer-valued time series which can accommodate series with negative observations and dependence structure more complicated than that of an autoregression or a moving average. In this regard, an integer-valued autoregressive moving average process induced by the so-called signed thinning operator is proposed. The first-order model is studied in detail. The conditions for the existence of stationary solution and the existence of finite moments are discussed under general assumptions. Under some further assumptions about the signed thinning operators and the distribution of the innovation, a moment-based estimator for the parameters is proposed, whose consistency and asymptotic normality are also proved. The problem of conducting one-step-ahead forecast is also considered based on hidden Markov chain theory. Simulation studies arc conducted to demonstrate the validity of the theories and methods established above. Real data analysis such as the annual counts of major earthquakes data are also presented to show their potential usefulness in applications. / published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

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Background: The implementation of comprehensive smoking ban policies results in reduced population exposure to secondhand smoke, yielding health benefits such as improved respiratory function and decreased risk of cardiovascular events. However, smoking ban effects on respiratory and cerebrovascular mortality and effect differences by socioeconomic status (SES) are unknown. Methods: A literature review was conducted to understand the health benefits of smoking ban policies and to identify areas of research that needed to be addressed. Subsequently, an epidemiologic study employing an interrupted time-series approach was conducted with a national mortality dataset from the Republic of Ireland to determine effects following the implementation of the national workplace smoking ban. Irish census data were used to calculate frequencies of deprivation at the level of the local authority and principal component analysis was conducted to generate a composite SES index. To determine whether the smoking ban policy impacted inequalities, Poisson regression with interrupted time-series analysis was conducted to examine mortality rates, stratified by tertiles of discrete SES indicators and the composite index. Results: The review identified strong evidence for post-ban reductions in cardiovascular morbidity and mortality, and suggestive evidence of reductions in respiratory morbidity following smoking ban implementation. Few studies assessed ban effects by SES and findings were inconsistent; hence, insufficient evidence was available to determine smoking ban policy impacts on health inequalities. Epidemiologic analyses demonstrated that the national Irish smoking ban was associated with immediate reductions in early mortality for cardiovascular, cerebrovascular, and respiratory causes. Further analyses by discrete socioeconomic indicators and a composite index indicated that the national Irish smoking ban was associated with decreased inequalities in smoking-related mortality. Conclusions: Smoking ban policies are effective public health interventions for the prevention of cardiovascular, cerebrovascular, and respiratory mortality. Furthermore, findings indicate that smoking ban policies have the potential to reduce inequalities in mortality.

published_or_final_version / Applied Statistics / Master / Master of Social Sciences

published_or_final_version / Statistics / Master / Master of Philosophy

published_or_final_version / Statistics / Master / Master of Philosophy

published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

No description available.

No description available.