Estimation, Model Diagnosis, and Process Control Under the Normal Model

This chapter introduces statistical methods for copula-based Markov models under the normal margin. First, the data structures and the idea of statistical process control are reviewed. The copula-based Markov models and essential assumptions are introduced as well. Next, we derive the likelihood functions under the first-order and the second-order Markov models and define the maximum likelihood estimators (MLEs). We then give the asymptotic properties of the MLEs. We propose goodness-of-fit methods to test the model assumptions based on a given dataset. In addition, a copula model selection method is discussed. We introduce an R package Copula.Markov to implement the statistical methods of this chapter. Finally, we analyze three real datasets for illustration.

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