arXiv subjects

Alessandra Salvan

Publications and source records attributed to Alessandra Salvan.

7 recordsLinked to original sources

arXiv2026

Focused median bias reduction

Median bias reduction of maximum likelihood estimators can substantially improve estimation and inference. Existing generally applicable methods are, however, typically implicit, requiring the solution of nonlinear systems of estimating equations, which is computationally demanding. They also require a fully specified nuisance parameterization, and their application to transformations of parameters involves tedious algebra and bespoke implementations. We develop an explicit median bias-corrected estimator for focus parameters that are smooth scalar transformations of a chosen reference parameterization. The estimator is obtained by solving, to the required order, an equation based on the Cornish-Fisher expansion of the centred and scaled maximum likelihood estimator of the focus parameter. It requires only the maximum likelihood or an asymptotically equivalent estimator at the reference parameterization, the gradient and Hessian of the transformation, and expectations of products of log-likelihood derivatives. These expectations are available for many models from the existing bias reduction literature and can also be estimated by Monte Carlo simulation. The resulting estimators are third-order median unbiased and provide one-step approximations to estimators from implicit median bias reduction when the focus parameter is included in the reference parameterization. The method improves standard asymptotic inference and integrates naturally with hull-based confidence procedures, yielding intervals with near nominal finite-sample coverage under median bias control. We demonstrate the framework through post-selection inference using the Focused Information Criterion, Mahalanobis distances, quantiles, and other scalar focus parameters in regression, circular, and stratified models.

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arXiv2022

Parametric bootstrap inference for stratified models with high-dimensional nuisance specifications

Inference about a scalar parameter of interest typically relies on the asymptotic normality of common likelihood pivots, such as the signed likelihood root, the score and Wald statistics. Nevertheless, the resulting inferential procedures are known to perform poorly when the dimension of the nuisance parameter is large relative to the sample size and when the information about the parameters is limited. In many such cases, the use of asymptotic normality of analytical modifications of the signed likelihood root is known to recover inferential performance. It is proved here that parametric bootstrap of standard likelihood pivots results in as accurate inferences as analytical modifications of the signed likelihood root do in stratified models with stratum specific nuisance parameters. We focus on the challenging case where the number of strata increases as fast or faster than the stratum samples size. It is also shown that this equivalence holds regardless of whether constrained or unconstrained bootstrap is used. This is in contrast to when the number of strata is fixed or increases slower than the stratum sample size, where we show that constrained bootstrap corrects inference to a higher order than unconstrained bootstrap. Simulation experiments support the theoretical findings and demonstrate the excellent performance of bootstrap in extreme scenarios.

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arXiv2020

Efficient implementation of median bias reduction with applications to general regression models

In numerous regular statistical models, median bias reduction (Kenne Pagui et al., 2017) has proven to be a noteworthy improvement over maximum likelihood, alternative to mean bias reduction. The estimator is obtained as solution to a modified score equation ensuring smaller asymptotic median bias than the maximum likelihood estimator. This paper provides a simplified algebraic form of the adjustment term for general regular models. With the new formula, the estimation procedure benefits from a considerable computational gain by avoiding multiple summations and thus allows an efficient implementation. More importantly, the new formulation allows to highlight how the median bias reduction adjustment can be obtained by adding an extra term to the mean bias reduction adjustment. Illustrations are provided through new applications of median bias reduction to two regression models not belonging to the generalized linear models class, extended beta regression and beta-binomial regression. Mean bias reduction is also provided here for the latter model. Simulation studies show remarkable componentwise median centering of the median bias reduced estimator, while variability and coverage of related confidence intervals are comparable with those of mean bias reduction. Moreover, empirical results for the beta-binomial model show that the method is successful in solving maximum likelihood boundary estimate problem.

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arXiv2020

Accurate inference in negative binomial regression

Negative binomial regression is commonly employed to analyze overdispersed count data. With small to moderate sample sizes, the maximum likelihood estimator of the dispersion parameter may be subject to a significant bias, that in turn affects inference on mean parameters. This paper proposes inference for negative binomial regression based on adjustments of the score function aimed at mean and median bias reduction. The resulting estimating equations are similar to those available for improved inference in generalized linear models and, in particular, can be solved using a suitable extension of iterative weighted least squares. Simulation studies show a remarkable performance of the new methods, which are also found to solve in many cases numerical problems of maximum likelihood estimates. The methods are illustrated and evaluated using two case studies: an Ames salmonella assay data set and data on epileptic seizures. Inference based on adjusted scores turns out to be generally preferable to explicit bias correction.

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arXiv2020

Median bias reduction in cumulative link models

This paper presents a novel estimation approach for cumulative link models, based on median bias reduction as developed in Kenne Pagui et al. (2017). The median bias reduced estimator is obtained as solution of an estimating equation based on an adjustment of the score. It allows to obtain higher-order median centering of maximum likelihood estimates without requiring their finiteness. Moreover, the estimator is equivariant under componentwise monotone reparameterizations and the method is effective in preventing boundary estimates. We evaluate the properties of the median bias reduced estimator through simulation studies and compare it with the two main competitors, the maximum likelihood and the mean bias reduced (Firth, 1993) estimators. Finally, we show an application where the proposed estimator is able to solve the boundary estimates problem.

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arXiv2020

Likelihood, Replicability and Robbins' Confidence Sequences

The widely claimed replicability crisis in science may lead to revised standards of significance. The customary frequentist confidence intervals, calibrated through hypothetical repetitions of the experiment that is supposed to have produced the data at hand, rely on a feeble concept of replicability. In particular, contradictory conclusions may be reached when a substantial enlargement of the study is undertaken. To redefine statistical confidence in such a way that inferential conclusions are non-contradictory, with large enough probability, under enlargements of the sample, we give a new reading of a proposal dating back to the 60's, namely Robbins' confidence sequences. Directly bounding the probability of reaching, in the future, conclusions that contradict the current ones, Robbins' confidence sequences ensure a clear-cut form of replicability when inference is performed on accumulating data. Their main frequentist property is easy to understand and to prove. We show that Robbins' confidence sequences may be justified under various views of inference: they are likelihood-based, can incorporate prior information, and obey the strong likelihood principle. They are easy to compute, even when inference is on a parameter of interest, especially using a closed-form approximation from normal asymptotic theory.

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arXiv2017

Median bias reduction of maximum likelihood estimates

For regular parametric problems, we show how median centering of the maximum likelihood estimate can be achieved by a simple modification of the score equation. For a scalar parameter of interest, the estimator is equivariant under interest respecting parameterizations and third-order median unbiased. With a vector parameter of interest, componentwise equivariance and third-order median centering are obtained. Like Firth's (1993, Biometrika) implicit method for bias reduction, the new method does not require finiteness of the maximum likelihood estimate and is effective in preventing infinite estimates. Simulation results for continuous and discrete models, including binary and beta regression, confirm that the method succeeds in achieving componentwise median centering and in solving the infinite estimate problem, while keeping comparable dispersion and the same approximate distribution as its main competitors.

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