Robust Statistical Inference in Generalized Linear Models Based on Minimum Renyi’s Pseudodistance Estimators

Jaenada, María; Pardo, Leonardo

doi:10.3390/e24010123

Cited by 6 publications

(6 citation statements)

References 28 publications

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“…In addition to the abovementioned explanation, the GLM is a member of the exponential distribution family, which includes the Gaussian, Poisson, binomial, multinomial, and gamma distributions as special studies ( 42 ). The Gaussian family defines maximum likelihood as trying to minimize MSE.…”

Section: Data Properties and Methodologymentioning

confidence: 99%

Detailed Analysis of Aircraft Fuel Flow Using Data from Flight Data Recorder

Atasoy

2023

Transportation Research Record: Journal of the Transportation R

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This paper aims to perform accurate prediction of fuel flow (FF) by employing various models: deep learning (DL), random forest (RF), generalized linear model (GLM), and the Eurocontrol Base of Aircraft Data (BADA) model, and to examine the link between FF and different aircraft performance parameters. The flight data set used in this study is obtained from real turbofan engine narrow-body aircraft performing short-distance domestic subsonic flights, containing a total of 2,674 cruise flights between 31 city pairs. Several statistical error analyses are conducted to compare the performance of the models. Root mean square error, mean absolute error, and mean squared error values for DL are calculated to be 0.01, 0.008, and 0.0001, respectively. On the coefficient of determination ( [Formula: see text]) test for validation, the DL model has the highest value of 0.94. Results of the analysis in this paper show that the DL model offers the best ability to predict FF in all statistical tests, which makes it the best-suited model to estimate FF. These findings can provide the means to make more efficient trajectory planning and forecasts in air traffic management, and more accurately predict fuel consumption of aircraft, thereby decreasing emission levels of carbon gases and of various pollutants and airline operating expenses from fuel costs.

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Section: Data Properties and Methodologymentioning

confidence: 99%

Detailed Analysis of Aircraft Fuel Flow Using Data from Flight Data Recorder

Atasoy

2023

Transportation Research Record: Journal of the Transportation R

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“…In [19], the theoretical robustness properties of the RMDPDE were studied. In [20,21], the restricted Rényi pseudodistance estimator is considered, and robust Rao-type tests are derived from it and developed. More recently, in [22], the RMDPD under normal distributions is studied, and independence tests under the normal assumption are developed, and in [23] the RMDPDE is applied in the context of independent but not identically distributed variables under heterocedastic linear regression models.…”

Section: E θ [Y] = µ(θ) and Cov θ [Y] = σ(θ)mentioning

confidence: 99%

“…Distance-based test statistics are essentially of two types: Wald-type tests and Rao-type tests. Some applications of these tests can be seen at [8,[20][21][22][23][29][30][31][32][33][34][35][36][37] and references therein. In this section, we introduce the Rao-type tests based on RMDPDGE, and we study their asymptotic properties, proving the consistency of the tests.…”

Section: Rao-type Tests Based On Rmdpdgementioning

confidence: 99%

Restricted Distance-Type Gaussian Estimators Based on Density Power Divergence and Their Applications in Hypothesis Testing

et al. 2023

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In this paper, we introduce the restricted minimum density power divergence Gaussian estimator (MDPDGE) and study its main asymptotic properties. In addition, we examine it robustness through its influence function analysis. Restricted estimators are required in many practical situations, such as testing composite null hypotheses, and we provide in this case constrained estimators to inherent restrictions of the underlying distribution. Furthermore, we derive robust Rao-type test statistics based on the MDPDGE for testing a simple null hypothesis, and we deduce explicit expressions for some main important distributions. Finally, we empirically evaluate the efficiency and robustness of the method through a simulation study.

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“…Subsequently, Castilla et al [18] developed Wald-type tests based on MRPE for the MRM, and Castilla et al [19] studied the MRPE for the MRM in the ultra-high dimensional set-up. Further, Jaenada and Pardo [20,21] considered the MRPE and Wald-type test statistics for generalized linear models (GLM). Despite Wald-type test statistics, there exist others relevant test statistics having an important role in the statistical literature: the likelihood-ratio and Rao (or score) tests, which are based on restricted estimators, usually the RMLE.…”

Section: Minimum Rényi Pseudodistance Estimatorsmentioning

confidence: 99%

Robust Test Statistics Based on Restricted Minimum Rényi’s Pseudodistance Estimators

Jaenada

Miranda

Pardo

2022

Entropy

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The Rao’s score, Wald and likelihood ratio tests are the most common procedures for testing hypotheses in parametric models. None of the three test statistics is uniformly superior to the other two in relation with the power function, and moreover, they are first-order equivalent and asymptotically optimal. Conversely, these three classical tests present serious robustness problems, as they are based on the maximum likelihood estimator, which is highly non-robust. To overcome this drawback, some test statistics have been introduced in the literature based on robust estimators, such as robust generalized Wald-type and Rao-type tests based on minimum divergence estimators. In this paper, restricted minimum Rényi’s pseudodistance estimators are defined, and their asymptotic distribution and influence function are derived. Further, robust Rao-type and divergence-based tests based on minimum Rényi’s pseudodistance and restricted minimum Rényi’s pseudodistance estimators are considered, and the asymptotic properties of the new families of tests statistics are obtained. Finally, the robustness of the proposed estimators and test statistics is empirically examined through a simulation study, and illustrative applications in real-life data are analyzed.

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Robust Statistical Inference in Generalized Linear Models Based on Minimum Renyi’s Pseudodistance Estimators

Cited by 6 publications

References 28 publications

Detailed Analysis of Aircraft Fuel Flow Using Data from Flight Data Recorder

Detailed Analysis of Aircraft Fuel Flow Using Data from Flight Data Recorder

Restricted Distance-Type Gaussian Estimators Based on Density Power Divergence and Their Applications in Hypothesis Testing

Robust Test Statistics Based on Restricted Minimum Rényi’s Pseudodistance Estimators

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