View Proposal

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Proposer

Wai Meng Kwok

Title

Investigating the Expectation-Maximization algorithm with applications to insurance claim counts

Goal

To investigate the expectation-maximization algorithm and its efficiencies in solving maximum likelihood problems. Once methods are soundly developed, we seek to implement our algorithms on insurance claim counts.

Description

Mixture models – including zero-inflated models – that allow for a combination of probability distributions are widely used in practical applications, but challenges arise in default maximum likelihood estimations of the model parameters due to the inconvenient functional forms of the resulting log-likelihood. To this end, Expectation-Maximization (EM) algorithms are an attractive alternative that simplifies estimation by introducing latent variables and iteratively optimizing a different quantity involving these latent variables to achieve maximum likelihood. This research aims to investigate theoretical properties of the general EM algorithm and how it ensures that the iterative process, through optimizing a different quantity, corresponds to the desired, original likelihood optimization. Subsequently, the concept will be applied on zero-inflated models whose components are from the exponential family of distributions, such as Poisson and/or Negative Binomial. The distributional parameters of these components may also be alternatively parameterized, for example, through a regression model. Specific EM algorithms detailing the probability distributions and expressions to be optimized can then be established for each of these zero-inflated models. These may eventually be applied to modelling insurance counts, which are often zero-inflated.

Resources

1. Dempster, Arthur P., Nan M. Laird, and Donald B. Rubin. "Maximum likelihood from incomplete data via the EM algorithm." Journal of the royal statistical society: series B (methodological) 39.1 (1977): 1-22. 2. Lambert, Diane. "Zero-inflated Poisson regression, with an application to defects in manufacturing." Technometrics 34.1 (1992): 1-14. 3. Lee, Simon CK. "Addressing imbalanced insurance data through zero-inflated Poisson regression with boosting." ASTIN Bulletin: The Journal of the IAA 51.1 (2021): 27-55. 4. Noll, Alexander, Robert Salzmann, and Mario V. Wuthrich. "Case study: French motor third-party liability claims." Available at SSRN 3164764 (2020).

Background

Url

Difficulty Level

Moderate

Ethical Approval

None

Number Of Students

1

Supervisor

Wai Meng Kwok

Keywords

expectation-maximisation, maximum likelihood, mixture models, optimization

Degrees

Bachelor of Science in Statistical Data Science