Abstract
We present new results for consistency of maximum likelihood estimators with a focus on multivariate mixed models. Our theory builds on the idea of using subsets of the full data to establish consistency of estimators based on the full data. It requires neither that the data consist of independent observations, nor that the observations can be modeled as a stationary stochastic process. Compared to existing asymptotic theory using the idea of subsets, we substantially weaken the assumptions, bringing them closer to what suffices in classical settings. We apply our theory in two multivariate mixed models for which it was unknown whether maximum likelihood estimators are consistent. The models we consider have nonstochastic predictors and multivariate responses which are possibly mixed-type (some discrete and some continuous).
| Original language | English (US) |
|---|---|
| Pages (from-to) | 932-952 |
| Number of pages | 21 |
| Journal | Annals of Statistics |
| Volume | 48 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2020 |
Bibliographical note
Funding Information:Acknowledgments. We thank an Associate Editor and two reviewers for suggestions that improved the article, and are grateful to Charles Doss and Charlie Geyer for their comments on an earlier version. The first author was supported by the American–Scandinavian Foundation.
Funding Information:
We thank an Associate Editor and two reviewers for suggestions that improved the article, and are grateful to Charles Doss and Charlie Geyer for their comments on an earlier version. The first author was supported by the American-Scandinavian Foundation.
Publisher Copyright:
© Institute of Mathematical Statistics, 2020
Keywords
- Consistency
- Crossed random effects
- GLMM
- MGLMM
- Maximum likelihood
- Subset argument