Parametric mixture models are commonly used in applied work, especially empirical economics, where these models are often employed to learn for example about the proportions of various types in a given population. This paper examines the inference question on the proportions (mixing probability) in a simple mixture model in the presence of nuisance parameters when sample size is large. It is we...

The aim of this paper is to provide simple nonparametric methods to estimate finite-mixture models from data with repeated measurements. Three measurements suffice for the mixtures to be fully identified and so our approach can be used even with very short panel data. We provide distribution theory for estimators of the number of mixture components, the mixing proportions, as well as of the mix...

Finite mixture models have a long history in statistics, having been used to model pupulation heterogeneity, generalize distributional assumptions, and lately, for providing a convenient yet formal framework for clustering and classification. This paper provides a detailed review into mixture models and model-based clustering. Recent trends in the area, as well as open problems are also discussed.

The analysis of finite mixture models for exponential repeated data is considered. The mixture components correspond to different possible states of the statistical units. Dependency and variability of repeated data are taken into account through random effects. For each component, an exponential mixed model is thus defined. When considering parameter estimation in this mixture of exponential m...

How to forecast next year’s portfolio-wide credit default rate based on last year’s default observations and the current score distribution? A classical approach to this problem consists of fitting a mixture of the conditional score distributions observed last year to the current score distribution. This is a special (simple) case of a finite mixture model where the mixture components are fixed...

Imputation is a widely used method for handling missing data. It consists in the replacement of missing values with plausible ones. Parametric and nonparametric techniques are generally adopted for modelling incomplete data. Both of them have advantages and drawbacks. Parametric techniques are parsimonious but depend on the model assumed, while nonparametric techniques are more flexible but req...