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Fundamental Principles of Parametric Estimation
Published in Anastasia Veloni, Nikolaos I. Miridakis, Erysso Boukouvala, Digital and Statistical Signal Processing, 2018
Anastasia Veloni, Nikolaos I. Miridakis, Erysso Boukouvala
We can draw some useful conclusions from this result: [F−1(θ)]11≥1/a=1/[F(θ)]11. Consequently, the presence of nuisance parameters may reduce the performance of the estimator.The magnitude of the performance reduction of the estimator is proportional to the amount of the information coupling between θ1 and θ2,⋯,θp.When the Fisher information matrix is diagonal, there is no reduction in the performance of the estimator.
Fundamentals of Estimation Theory
Published in Erchin Serpedin, Thomas Chen, Dinesh Rajan, Mathematical Foundations for SIGNAL PROCESSING, COMMUNICATIONS, AND NETWORKING, 2012
In general, the integration required for eliminating the nuisance parameter is not always possible. In this case, numerical methods or Monte Carlo techniques (such as importance sampling, Gibbs sampler, Metropolis-Hastings algorithm) are frequently used. Details on Monte Carlo statistical techniques are discussed in Chapter 12 of this book.
Estimating reliability parameters for inverse Gaussian distributions under complete and progressively type-II censored samples
Published in Quality Technology & Quantitative Management, 2023
Samadrita Bera, Nabakumar Jana
Different pseudo-likelihood methods are used to deal with the nuisance parameter in a model. The profile likelihood method is a simple method where we replace the nuisance parameter with its MLE or restricted MLE in the likelihood function. For details about profile likelihood and different pseudo likelihood methods, one may refer to Ventura and Racugno (2011), Severini (1998), Bera and Jana (2021). We derive the profile likelihood estimator of the common coefficient of variation in a similar way to Bera and Jana (2021). The restricted MLE of the nuisance parameter is , where , . The matching prior for is
Road geometry estimation using vehicle trails: a linear mixed model approach
Published in Journal of Intelligent Transportation Systems, 2023
Since and are rarely known, we need to consider the estimation of and by maximizing their joint likelihood based on the marginal distribution of y. The expectation-maximization (Laird & Ware, 1982) or Newton-Raphson algorithms (Lindstrom & Bates, 1988) may be done using either the ML for (11) or the REML for (12). However, this requires to estimate unknown parameters and simultaneously. If the fixed effects in (11) and (12) are replaced by their generalized least squares estimates in (9), both the log-likelihoods are free of the fixed effects and are functions of the random effects alone. This will simplify the convergence criterion and have better stability in the numerical solutions. To profile out the likelihood, we treat the unknown coefficients as nuisance parameters. We focus on the REML estimator for and The REML produces unbiased estimates of variance and covariance parameters so that the nuisance parameters have no effects on maximizing the likelihood function.
Probabilistic inference of reaction rate parameters from summary statistics
Published in Combustion Theory and Modelling, 2018
Mohammad Khalil, Habib N. Najm
The fitting of experimental data often involves nuisance parameters, i.e. parameters that are not of direct interest except inasmuch as they are needed in estimating the parameters of interest. In the present context of missing data, when one is only interested in inferring the unknown parameters and not the data, then the missing data vector acts as a nuisance parameter vector (and must be inferred jointly with the parameters as is outlined in the above subsections).