Structure selection for stochastic processes in high dimensions
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| Full text | |
| Author(s): |
Leonardi, Florencia
;
Carvalho, Rodrigo
;
Frondana, Iara
Total Authors: 3
|
| Document type: | Journal article |
| Source: | SCANDINAVIAN JOURNAL OF STATISTICS; v. N/A, p. 25-pg., 2023-08-14. |
| Abstract | |
We propose a penalized conditional likelihood criterion to estimate the basic neighborhood of each node in a discrete Markov random field that can be partially observed. We prove the convergence of the estimator in the case of a finite or countable infinite set of nodes. The estimated neighborhoods can be combined to estimate the underlying graph. In the finite case, the graph can be recovered with probability one. In contrast, we can recover any finite subgraph with probability one in the countable infinite case by allowing the candidate neighborhoods to grow as a function o(logn)$$ o\left(\log n\right) $$, with n$$ n $$ the sample size. Our method requires minimal assumptions on the probability distribution, and contrary to other approaches in the literature, the usual positivity condition is not needed. We evaluate the estimator's performance on simulated data and apply the methodology to a real dataset of stock index markets in different countries. (AU) | |
| FAPESP's process: | 19/17734-3 - Model selection in high dimensions: theoretical properties and applications |
| Grantee: | Florencia Graciela Leonardi |
| Support Opportunities: | Research Grants - eScience and Data Science Program - Regular Program Grants |
| FAPESP's process: | 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat |
| Grantee: | Oswaldo Baffa Filho |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |