1,721,091 research outputs found
Small area estimation via m-quantile geographically weighted regression
No full textThe effective use of spatial information, that is the geographic locations of population units, in a regression model-based approach to small area estimation is an important practical issue. One approach for incorporating such spatial information in a small area regression model is via Geographically Weighted Regression (GWR). In GWR the relationship between the outcome variable and the covariates is characterised by local rather than global parameters, where local is defined spatially. In this paper we investigate GWR-based small area estimation under the M-quantile modelling approach. In particular, we specify an M-quantile GWR model that is a local model for the M-quantiles of the conditional distribution of the outcome variable given the covariates. This model is then used to define a bias-robust predictor of the small area characteristic of interest that also accounts for spatial association in the data. An important spin-off from applying the M-quantile GWR small area model is that it can potentially offer more efficient synthetic estimation for out of sample areas. We demonstrate the usefulness of this framework through both model-based as well as design-based simulations, with the latter based on a realistic survey data set. The paper concludes with an illustrative application that focuses on estimation of average levels of Acid Neutralizing Capacity for lakes in the north-east of the USA.<br/
Quantile regression methods in poverty mapping: The case of the survey on life conditions in Ecuador
No full textParametric modeling of quantile regression coefficient functions with count data
No full textApplying quantile regression to count data presents logical and practical complications which are usually solved by artificially smoothing the discrete response variable through jittering. In this paper, we present an alternative approach in which the quantile regression coefficients are modeled by means of (flexible) parametric functions. The proposed method avoids jittering and presents numerous advantages over standard quantile regression in terms of computation, smoothness, efficiency, and ease of interpretation. Estimation is carried out by minimizing a “simultaneous” version of the loss function of ordinary quantile regression. Simulation results show that the described estimators are similar to those obtained with jittering, but are often preferable in terms of bias and efficiency. To exemplify our approach and provide guidelines for model building, we analyze data from the US National Medical Expenditure Survey. All the necessary software is implemented in the existing R package qrcm
Parametric modelling of M-quantile regression coefficient functions with application to small area estimation
Full text linkSmall area estimation methods can be used to obtain reliable estimates of a parameter of interest within an unplanned domain or subgroup of the population for which only a limited sample size is available. A standard approach to small area estimation is to use a linear mixed model in which the heterogeneity between areas is accounted for by area level effects. An alternative solution, which has gained popularity in recent years, is to use M-quantile regression models. This approach requires much weaker assumptions than the standard linear mixed model and enables computing outlier robust estimators of the area means. We introduce a new framework for M-quantile regression, in which the model coefficients, β(τ), are described by (flexible) parametric functions of τ. We illustrate the advantages of this approach and its application to small area estimation. Using the European Union Survey on Income and Living Conditions data, we estimate the average equivalized household income in three Italian regions. The paper is accompanied by an R package Mqrcm that implements the necessary procedures for estimation, inference and prediction
The geographical distribution of the consumption expenditure in Ecuador. Esimation and mapping of the regression quantiles
No full textThe real consumption expenditure of families provides important information about the welfare of people residing in a given administrative area. State policies designed to alleviate poverty and funding management plans rely on the ability of statistical models to provide detailed and correct information. It can be argued that mean regression alone does not provide a satisfactory picture of the distribution of the response. We explore the use of nonparametric quantile regression for geographically referenced data. The motivating example pertains the distribution of the consumption expenditure in Ecuador, whose shape, conditional on some predictors, varies across the locations and reveals that the spatial heterogeneity has a very different impact on the quantiles of the response
FIG. 11. — Mictaxius salvati n in Thalassinidea (Crustacea, Decapoda) from French Polynesia
No full textFIG. 11. — Mictaxius salvati n. sp., Mururoa, Tuamotu, holotype, hermaphrodite (MNHN Th 1417); A-C, pereopod 2-4; D, E, maxilliped 1 and 2; F, pleopod 1; G, pleopod 2; H, pleopod 3. Scale bars: A-C, F-H, 1 mm; D, E, 0.5 mm.Published as part of Ngoc-Ho, Nguyen, 2005, Thalassinidea (Crustacea, Decapoda) from French Polynesia, pp. 47-83 in Zoosystema 27 (1) on page 69, DOI: 10.5281/zenodo.540339
Outlier robust small domain estimation via bias correction and robust bootstrapping
Full text linkSeveral methods have been devised to mitigate the effects of outlier values on survey estimates. If outliers are a concern for estimation of population quantities, it is even more necessary to pay attention to them in a small area estimation (SAE) context,where sample size is usually very small and the estimation in often model based. In this paper we set two goals: The first is to review recent developments in outlier robust SAE. In particular, we focus on the use of partial bias corrections when outlier robust fitted values under a working model generate biased predictions from sample data containing representative outliers.Then we propose an outlier robust bootstrap MSE estimator for M-quantile based small area predictors which considers a bounded-block-bootstrap approach. We illustrate these methods through model based and design based simulations and in the context of a particular survey data set that has many of the outlier characteristics that are observed in business surveys
Robust Bayesian small area estimation based on quantile regression
No full textQuantile and M-quantile regression have been applied successfully to small area estimation within the frequentist approach. Quantile regression is applied in the same context but from a Bayesian perspective. Joint modelling of the quantile function is considered, adopting a non parametric assumption on the data generating process that nonetheless explicitly includes the normal distribution as a special case. A specification of the random part of the model that is simple and consistent with the predictive aim of small area estimation is proposed. Although the main output of the method is the estimation of the whole quantile function, estimators of the small area means based on the integration of the quantile function are proposed and discussed. A simulation exercise is used to assess the frequentist properties of these proposed predictors, that result at least as efficient as frequentist small area estimators based on quantile regression in scenarios characterized by the presence of outliers. The proposed method is illustrated using data from the European survey on Income and Living Conditions (EU-SILC)
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