Post-Parameter-Selection Maximum-Likelihood Estimation

Harel, Nadav; Routtenberg, Tirza

doi:10.1109/ssp49050.2021.9513852

Cited by 2 publications

(5 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, the assumed pdfs f I (x; θ) and f III (x; θ) are coherent with the selection approach. Coherency in estimation after model selection refers to the property that the estimation approach accounts for the model selection (see more in [5], [19], [20]). In our case, this coherency means that if it is assumed that the observations obey the kth model, then the assumed pdf is only determined by θ (k) .…”

Section: B Post-model-selection Estimation As Estimation Under Model ...mentioning

confidence: 99%

“…which is the MML estimator defined in (5), where (17) is the assumed pdf. By substituting (19) in (30) and using the fact that the log function is a monotonically increasing function, we obtain that the MSNL estimator can be written as…”

Section: Post-model-selection Estimatorsmentioning

confidence: 99%

“…f I (x; θ) = f II (x; θ) = f III (x; θ). Thus, in this case, the MSL, MSNL, and PSML estimators from (28), (30) and (36) are all reduced to the conventional MML estimator in (5).…”

Section: Post-model-selection Estimatorsmentioning

confidence: 99%

“…Bounds and estimation methods have been developed for post-parameter-selection estimation [3]- [5], where a subset of parameters of interest is selected, based on the data, prior to the estimation. In [6]- [8], the bounds and estimators were developed for cases where the informative data region is selected prior to the estimation.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Bayesian Post-Model-Selection Estimation

Harel

Routtenberg

2021

IEEE Signal Process. Lett.

View full text Add to dashboard Cite

In many parameter estimation problems, the exact model is unknown and is assumed to belong to a set of candidate models. In such cases, a predetermined data-based selection rule selects a parametric model from a set of candidates before the parameter estimation. The existing framework for estimation under model misspecification does not account for the selection process that led to the misspecified model. Moreover, in postmodel-selection estimation, there are multiple candidate models chosen based on the observations, making the interpretation of the assumed model in the misspecified setting non-trivial. In this work, we present three interpretations to address the problem of non-Bayesian post-model-selection estimation as an estimation under model misspecification problem: the naive interpretation, the normalized interpretation, and the selective inference interpretation, and discuss their properties. For each of these interpretations, we developed the corresponding misspecified maximum likelihood estimator and the misspecified Cramér-Rao-type lower bound. The relations between the estimators and the performance bounds, as well as their properties, are discussed. Finally, we demonstrate the performance of the proposed estimators and bounds via simulations of estimation after channel selection. We show that the proposed performance bounds are more informative than the oracle Cramér-Rao Bound (CRB), where the third interpretation (selective inference) results in the lowest mean-squared-error (MSE) among the estimators.

show abstract

Section: B Post-model-selection Estimation As Estimation Under Model ...mentioning

confidence: 99%

Section: Post-model-selection Estimatorsmentioning

confidence: 99%

“…f I (x; θ) = f II (x; θ) = f III (x; θ). Thus, in this case, the MSL, MSNL, and PSML estimators from (28), (30) and (36) are all reduced to the conventional MML estimator in (5).…”

Section: Post-model-selection Estimatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Bayesian Post-Model-Selection Estimation

Harel

Routtenberg

2021

IEEE Signal Process. Lett.

View full text Add to dashboard Cite

show abstract

“…The identification method described by the probability model (e.g. the maximum likelihood method (Harel and Routtenberg, 2021)) can deal with the problem of missing information. In this kind of identification method, the missing information can be regarded as latent variables and estimated in the framework of the probability model.…”

Section: Introductionmentioning

confidence: 99%

Identification of time-delay Markov jumps autoregressive system with recursive expectation maximum and convex optimization algorithm

Guo

2022

Transactions of the Institute of Measurement and Control

View full text Add to dashboard Cite

A novel proposed approach of the recursive expectation–maximization (REM)–convex optimization algorithm is developed to solve the parameter identification problem of the Markov jump autoregressive exogenous (MJARX) systems with unknown time delays. First, the REM algorithm is employed for identifying the unknown time delay of the system, based on which the time-delay sequence is obtained. Subsequently, the model parameter vector is determined by the convex optimization algorithm. Finally, the transition probability matrix and variance are calculated based on the minimized mean square error. A numerical example and simulated continuous fermentation reactor process are implemented to demonstrate the effectiveness of the proposed algorithm. The identification results are better than the expectation–maximization algorithm and REM algorithm results.

show abstract

Post-Parameter-Selection Maximum-Likelihood Estimation

Cited by 2 publications

References 15 publications

Bayesian Post-Model-Selection Estimation

Bayesian Post-Model-Selection Estimation

Identification of time-delay Markov jumps autoregressive system with recursive expectation maximum and convex optimization algorithm

Contact Info

Product

Resources

About