Some results on maximum likelihood from incomplete data: finite sample properties and an improved M-estimator for resampling method
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Abstract This paper presents some results on the classical maximum likelihood (ML) parameter estimation from incomplete data. Finite sample properties of incomplete-data conditional observed information matrices are established. They possess positive def-initeness and the same Loewner partial ordering as the expected information matrices do. An explicit form of the observed Fisher information (OFI) is derived for the calculation of standard errors of the ML estimates. It simplifies Louis (1982) general formula for the OFI matrix. To prevent from getting an incorrect inverse of the OFI matrix, which may be attributed by the lack of sparsity and large size of the matrix, a monotone convergent recursive equation for the inverse of OFI matrix is developed which in turn generalizes the algorithm of Hero and Fessler (1994) for the Cramér-Rao lower bound. To improve the estimation, in particular when applying repeated sampling to incomplete data, a robust M-estimator is introduced. A closed form sandwich estimator of covariance matrix is proposed to provide the standard errors of the M-estimator. By the resulting loss of information presented in finite-sample incomplete data, the sandwich estimator produces smaller standard errors for the M-estimator than the ML estimates. In the case of complete information or absence of re-sampling, the M-estimator coincides with the ML estimates. Application to parameter estimation of a finite-mixture of Markov jump processes is discussed to verify the results. The simulation study confirms the accuracy and asymptotic properties of both the ML estimates and M-estimator. 2020 MSC: 60J20, 60J27, 62M09, 62H30
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.010 | 0.109 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it