We propose a minimum distance estimator for the higher-order comoments of a multivariate distribution exhibiting a lower dimensional latent factor structure. We derive the influence function of the proposed estimator and prove its consistency and asymptotic normality. The simulation study confirms the large gains in accuracy compared to the traditional sample comoments. The empirical usefulness of the novel framework is shown in applications to portfolio allocation under non-Gaussian objective functions and to the extraction of factor loadings in a dataset with mental ability scores.
- Higher-order multivariate moments
- Latent factor model
- Minimum distance estimation
- Risk assessment
- Structural equation modelling