Small area estimation based on M-quantile models in presence of outliers in auxiliary variables

When using small area estimation models, the presence of outlying observations in the response and/or in the auxiliary variables can severely affect the estimates of the model parameters, which can in turn affect the small area estimates produced using these models. In this paper we propose an M-quantile estimator of the small area mean that is robust to the presence of outliers in the response variable and in the continuous auxiliary variables. To estimate the variability of this estimator we propose a non-parametric bootstrap estimator. The performance of the proposed estimator is evaluated by means of model- and design-based simulations and by an application to real data. In these comparisons we also include the extension of the Robust EBLUP able to down-weight the outliers in the auxiliary variables. The results show that in the presence of outliers in the auxiliary variables the proposed estimator outperforms its traditional version that takes into account the presence of outliers only in the response variable

A Spatial Quantile Regression Hedonic Model of Agricultural Land Prices

Abstract Land price studies typically employ hedonic analysis to identify the impact of land characteristics on price. Owing to the spatial fixity of land, however, the question of possible spatial dependence in agricultural land prices arises. The presence of spatial dependence in agricultural land prices can have serious consequences for the hedonic model analysis. Ignoring spatial autocorrelation can lead to biased estimates in land price hedonic models. We propose using a flexible quantile regression-based estimation of the spatial lag hedonic model allowing for varying effects of the characteristics and, more importantly, varying degrees of spatial autocorrelation. In applying this approach to a sample of agricultural land sales in Northern Ireland we find that the market effectively consists of two relatively separate segments. The larger of these two segments conforms to the conventional hedonic model with no spatial lag dependence, while the smaller, much thinner market segment exhibits considerable spatial lag dependence. Un mod�le h�donique � r�gression quantile spatiale des prix des terrains agricoles R�sum� Les �tudes sur le prix des terrains font g�n�ralement usage d'une analyse h�donique pour identifier l'impact des caract�ristiques des terrains sur le prix. Toutefois, du fait de la fixit� spatiale des terrains, la question d'une �ventuelle d�pendance spatiale sur la valeur des terrains agricoles se pose. L'existence d'une d�pendance spatiale dans le prix des terrains agricoles peut avoir des cons�quences importantes sur l'analyse du mod�le h�donique. En ignorant cette corr�lation s�rielle, on s'expose au risque d'�valuations biais�es des mod�les h�doniques du prix des terrains. Nous proposons l'emploi d'une estimation � base de r�gression flexible du mod�le h�donique � d�calage spatial, tenant compte de diff�rents effets des caract�ristiques, et surtout de diff�rents degr�s de corr�lations s�rielles spatiales. En appliquant ce principe � un �chantillon de ventes de terrains agricoles en Irlande du Nord, nous d�couvrons que le march� se compose de deux segments relativement distincts. Le plus important de ces deux segments est conforme au mod�le h�donique traditionnel, sans d�pendance du d�calage spatial, tandis que le deuxi�me segment du march�, plus petit et beaucoup plus �troit, pr�sente une d�pendance consid�rable du d�calage spatial. Un modelo hed�nico de regresi�n cuantil espacial de los precios del terreno agr�cola Resumen T�picamente, los estudios del precio de la tierra emplean un an�lisis hed�nico para identificar el impacto de las caracter�sticas de la tierra sobre el precio. No obstante, debido a la fijeza espacial de la tierra, surge la cuesti�n de una posible dependencia espacial en los precios del terreno agr�cola. La presencia de dependencia espacial en los precios del terreno agr�cola puede tener consecuencias graves para el modelo de an�lisis hed�nico. Ignorar la autocorrelaci�n espacial puede conducir a estimados parciales en los modelos hed�nicos del precio de la tierra. Proponemos el uso de una valoraci�n basada en una regresi�n cuantil flexible del modelo hed�nico del lapso espacial que tenga en cuenta los diversos efectos de las caracter�sticas y, particularmente, los diversos grados de autocorrelaci�n espacial. Al aplicar este planteamiento a una muestra de ventas de terreno agr�cola en Irlanda del Norte, descubrimos que el mercado consiste efectivamente de dos segmento relativamente separados. El m�s grande de estos dos segmentos se ajusta al modelo hed�nico convencional sin dependencia del lapso espacial, mientras que el segmento m�s peque�o, y mucho m�s fino, muestra una dependencia considerable del lapso espacial.Spatial lag, quantile regression, hedonic model, C13, C14, C21, Q24,

A Framework for the Estimation of Disaggregated Statistical Indicators Using Tree-Based Machine Learning Methods

The thesis combines four papers that introduce a coherent framework based on MERFs for the estimation of spatially disaggregated economic and inequality indicators and associated uncertainties. Chapter 1 focusses on flexible domain prediction using MERFs. We discuss characteristics of semi-parametric point and uncertainty estimates for domain-specific means. Extensive model- and design-based simulations highlight advantages of MERFs in comparison to 'traditional' LMM-based SAE methods. Chapter 2 introduces the use of MERFs under limited covariate information. The access to population-level micro-data for auxiliary information imposes barriers for researchers and practitioners. We introduce an approach that adaptively incorporates aggregated auxiliary information using calibration-weights in the absence of unit-level auxiliary data. We apply the proposed method to German survey data and use aggregated covariate census information from the same year to estimate the average opportunity cost of care work for 96 planning regions in Germany. In Chapter 3, we discuss the estimation of non-linear poverty and inequality indicators. Our proposed method allows to estimate domain-specific cumulative distribution functions from which desired (non-linear) poverty estimators can be obtained. We evaluate proposed point and uncertainty estimators in a design-based simulation and focus on a case study uncovering spatial patterns of poverty for the Mexican state of Veracruz. Additionally, Chapter 3 informs a methodological discussion on differences and advantages between the use of predictive algorithms and (linear) statistical models in the context of SAE. The final Chapter 4 complements the previous research by implementing discussed methods for point and uncertainty estimates in the open-source R package SAEforest. The package facilitates the use of discussed methods and accessibly adds MERFs to the existing toolbox for SAE and official statistics. Overall, this work aims to synergize aspects from two statistical spheres (e.g. 'traditional' parametric models and nonparametric predictive algorithms) by critically discussing and adapting tree-based methods for applications in SAE. In this perspective, the thesis contributes to the existing literature along three dimensions: 1) The methodological development of alternative semi-parametric methods for the estimation of non-linear domain-specific indicators and means under unit-level and aggregated auxiliary covariates. 2) The proposition of a general framework that enables further discussions between 'traditional' and algorithmic approaches for SAE as well as an extensive comparison between LMM-based methods and MERFs in applications and several model and design-based simulations. 3) The provision of an open-source software package to facilitate the usability of methods and thus making MERFs and general SAE methodology accessible for tailored research applications of statistical, institutional and political practitioners

Moment conditions for the quadratic regression model with measurement error

We consider a new estimator for the quadratic errors-in-variables model that exploits higher-order moment conditions under the assumption that the distribution of the measurement error is symmetric and free of excess kurtosis. Our approach contributes to the literature by not requiring any side information and by straightforwardly allowing for one or more error-free control variables. We propose a Wald-type statistical test, based on an auxiliary method-of-moments estimator, to verify a necessary condition for our estimator's consistency. We derive the asymptotic properties of the estimator and the statistical test and illustrate their finite-sample properties by means of a simulation study and an empirical application to existing data from the literature. Our simulations show that the method-of-moments estimator performs well in terms of bias and variance and even exhibits a certain degree of robustness to the distributional assumptions about the measurement error. In the simulation experiments where such robustness is not present, our statistical test already has high power for relatively small samples

Maximum Likelihood Estimation of Latent Affine Processes

This article develops a direct filtration-based maximum likelihood methodology for estimating the parameters and realizations of latent affine processes. The equivalent of Bayes' rule is derived for recursively updating the joint characteristic function of latent variables and the data conditional upon past data. Likelihood functions can consequently be evaluated directly by Fourier inversion. An application to daily stock returns over 1953-96 reveals substantial divergences from EMM-based estimates: in particular, more substantial and time-varying jump risk.

Generalized Methods of Trimmed Moments

High breakdown-point regression estimators protect against large errors and data contamination. We adapt and generalize the concept of trimming used by many of these robust estimators so that it can be employed in the context of the generalized method of moments. The proposed generalized method of trimmed moments (GMTM) offers a globally robust estimation approach (contrary to existing only locally robust estimators) applicable in econometric models identified and estimated using moment conditions. We derive the consistency and asymptotic distribution of GMTM in a general setting, propose a robust test of overidentifying conditions, and demonstrate the application of GMTM in the instrumental variable regression. We also compare the finite-sample performance of GMTM and existing estimators by means of Monte Carlo simulation.asymptotic normality;generalized method of moments;instrumental variables regression;robust estimation;trimming