Robust small area prediction for counts

Tzavidis, Nikos; Ranalli, Maria Giovanna; Salvati, Nicola; Dreassi, Emanuela; Chambers, Ray

doi:10.1177/0962280214520731

Cited by 30 publications

(29 citation statements)

References 36 publications

(53 reference statements)

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“…This latter, may offer a stable approximation of the actual MSE of the estimated relative risk. For example, an MSE estimator based on the semiparametric bootstrap (proposed also in Chambers et al 3 and Tzavidis et al 36 ) could be considered. Finally, the time dimension, as done for the spatial dimension, could be added into the proposed Semiparametric NB M-quantile model in order to provide robust estimates of the relative risk in space and time.…”

Section: Discussionmentioning

confidence: 99%

Semiparametric M-quantile regression for count data

Dreassi

Ranalli

Salvati

2014

Stat Methods Med Res

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Lung cancer incidence over 2005-2010 for 326 Local Authority Districts in England is investigated by ecological regression. Motivated from mis-specification of a Negative Binomial additive model, a semiparametric Negative Binomial M-quantile regression model is introduced. The additive part relates to those univariate or bivariate smoothing components, which are included in the model to capture nonlinearities in the predictor or to account for spatial dependence. All such components are estimated using penalized splines. The results show the capability of the semiparametric Negative Binomial M-quantile regression model to handle data with a strong spatial structure.

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Section: Discussionmentioning

confidence: 99%

Semiparametric M-quantile regression for count data

Dreassi

Ranalli

Salvati

2014

Stat Methods Med Res

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“…The MQ approach to small area prediction has been extended to discrete responses. In particular, Tzavidis et al () propose a small area predictor based on a new semiparametric MQ model for counts that extends the ideas of Cantoni & Ronchetti () and Chambers & Tzavidis (). This predictor can be viewed as an outlier robust alternative to the more commonly used conditional expectation predictor for counts that is based on a Poisson generalised linear mixed models with Gaussian random effects.…”

Section: A Review Of M‐quantile Models In Small Area Estimationmentioning

confidence: 99%

“…A number of papers on MQ regression that focus on theoretical developments (Tzavidis et al , ; Fabrizi et al , ; Salvati et al , ; Bianchi & Salvati, ; Chambers et al , ; Fabrizi et al , ; Tzavidis et al , ; Alfò et al , ), extensions to non‐linear models (Pratesi et al , ; Chambers et al , ; Dreassi et al , ; Tzavidis et al , ; Chambers et al , ) and various small area applications (Tzavidis et al , ; Pratesi et al , ; Salvati et al , ; Tzavidis et al , ; Fabrizi et al , ) have been published in recent years. In view of this growing number of studies, in this paper, we review MQ linear regression with special focus on its application to SAE.…”

Section: Introductionmentioning

confidence: 99%

Estimation and Testing in M‐quantile Regression with Applications to Small Area Estimation

Bianchi

Fabrizi

Salvati

et al. 2018

Int Statistical Rev

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In recent years, M-quantile regression has been applied to small area estimation to obtain reliable and outlier robust estimators without recourse to strong parametric assumptions. In this paper, after a review of M-quantile regression and its application to small area estimation, we cover several topics related to model specification and selection for M-quantile regression that received little attention so far. Specifically, a pseudo-R 2 goodness-of-fit measure is proposed, along with likelihood ratio and Wald type tests for model specification. A test to assess the presence of actual area heterogeneity in the data is also proposed. Finally, we introduce a new estimator of the scale of the regression residuals, motivated by a representation of the M-quantile regression estimation as a regression model with Generalised Asymmetric Least Informative distributed error terms. The Generalised Asymmetric Least Informative distribution, introduced in this paper, generalises the asymmetric Laplace distribution often associated to quantile regression. As the testing procedures discussed in the paper are motivated asymptotically, their finite sample properties are empirically assessed in Monte Carlo simulations. Although the proposed methods apply generally to Mquantile regression, in this paper, their use ar illustrated by means of an application to Small Area Estimation using a well known real dataset.

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“…Tzavidis et al () and Chambers et al () suggest almost identical approaches to calculating q ‐scores given data from a Poisson and a negative binomial distribution, respectively. The q ‐score

q_{i}^{*}

for a count datum y i is obtained as the solution to

m_{q_{i}^{*}, k} false(x_{i} false) = ({, \begin{matrix} array \min [1 - ϵ, \frac{1}{\exp ({falsefalse}_{x}^{i} {bold-italicβ}_{q = 0.5, k})}], & array if y_{i} = 0 \\ array y_{i}, & array if y_{i} = 1, 2, ⋯, \end{matrix})

where ϵ > 0 is a small pre‐specified constant.…”

Section: M‐quantile Models For Discrete Datamentioning

confidence: 99%

“…This means that their corresponding q i values be 0 regardless of their varying x i values, which is an undesirable property. Tzavidis et al (2015) and Chambers et al (2014) suggest almost identical approaches to calculating q-scores given data from a Poisson and a negative binomial distribution, respectively. The q-score q i for a count datum y i is obtained as the solution to…”

Section: Discrete Data and Q-scoresmentioning

confidence: 99%

Modelling Group Heterogeneity for Small Area Estimation Using M‐Quantiles

Dawber

Chambers

2018

Int Statistical Rev

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Summary Small area estimation typically requires model‐based methods that depend on isolating the contribution to overall population heterogeneity associated with group (i.e. small area) membership. One way of doing this is via random effects models with latent group effects. Alternatively, one can use an M‐quantile ensemble model that assigns indices to sampled individuals characterising their contribution to overall sample heterogeneity. These indices are then aggregated to form group effects. The aim of this article is to contrast these two approaches to characterising group effects and to illustrate them in the context of small area estimation. In doing so, we consider a range of different data types, including continuous data, count data and binary response data.

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Robust small area prediction for counts

Cited by 30 publications

References 36 publications

Semiparametric M-quantile regression for count data

Semiparametric M-quantile regression for count data

Estimation and Testing in M‐quantile Regression with Applications to Small Area Estimation

Modelling Group Heterogeneity for Small Area Estimation Using M‐Quantiles

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