Maria Giovanna Ranalli

Non‐parametric small area estimation using penalized spline regression

We propose a new small area estimation approach that combines small area random effects with a smooth, nonparametrically specified trend. By using penalized splines as the representation for the nonparametric trend, it is possible to express the small area estimation problem as a mixed effect model regression. This model is readily fitted using existing model fitting approaches such as restricted maximum likelihood. We develop a corresponding bootstrap approach for model inference and estimation of the small area prediction mean squared error. The applicability of the method is demonstrated on a survey of lakes in the Northeastern US.

Small area estimation of the mean using non-parametric M-quantile regression: a comparison when a linear mixed model does not hold

The demand for reliable statistics in subpopulations, when only reduced sample sizes are available, has promoted the development of small area estimation methods. In particular, an approach that is now widely used is based on the seminal work by Battese et al. [An error-components model for prediction of county crop areas using survey and satellite data, J. Am. Statist. Assoc. 83 (1988), pp. 28–36] that uses linear mixed models (MM). We investigate alternatives when a linear MM does not hold because, on one side, linearity may not be assumed and/or, on the other, normality of the random effects may not be assumed. In particular, Opsomer et al. [Nonparametric small area estimation using penalized spline regression, J. R. Statist. Soc. Ser. B 70 (2008), pp. 265–283] propose an estimator that extends the linear MM approach to the case in which a linear relationship may not be assumed using penalized splines regression. From a very different perspective, Chambers and Tzavidis [M-quantile models for small area estimation, Biometrika 93 (2006), pp. 255–268] have recently proposed an approach for small-area estimation that is based on M-quantile (MQ) regression. This allows for models robust to outliers and to distributional assumptions on the errors and the area effects. However, when the functional form of the relationship between the qth MQ and the covariates is not linear, it can lead to biased estimates of the small area parameters. Pratesi et al. [Semiparametric M-quantile regression for estimating the proportion of acidic lakes in 8-digit HUCs of the Northeastern US, Environmetrics 19(7) (2008), pp. 687–701] apply an extended version of this approach for the estimation of the small area distribution function using a non-parametric specification of the conditional MQ of the response variable given the covariates [M. Pratesi, M.G. Ranalli, and N. Salvati, Nonparametric m-quantile regression using penalized splines, J. Nonparametric Stat. 21 (2009), pp. 287–304]. We will derive the small area estimator of the mean under this model, together with its mean-squared error estimator and compare its performance to the other estimators via simulations on both real and simulated data.

To misreport or not to report? The measurement of household financial wealth

The objective of the paper is to adjust for the bias due to unit non-response and measurement error in survey estimates of total household financial wealth. Sample surveys are a useful source of information on household wealth. Yet, survey estimates are affected by non-sampling errors. In particular, in the case of household wealth, unit non-response and measurement error can severely bias the estimates. Using the Italian Survey on Household Income and Wealth (SHIW), we exploit the available auxiliary information in order to assess the magnitude of this bias. We find evidence that for this kind of survey, non-sampling errors are a major issue, possibly more serious than sampling errors. Moreover, in the case of SHIW the potential bias due to measurement error seems to outweigh that induced by non-response.

A Mixed Model-assisted Regression Estimator that Uses Variables Employed at the Design Stage

The Generalized regression estimator (GREG) of a finite population mean or total has been shown to be asymptotically optimal when the working linear regression model upon which it is based includes variables related to the sampling design. In this paper a regression estimator assisted by a linear mixed superpopulation model is proposed. It accounts for the extra information coming from the design in the random component of the model and saves degrees of freedom in finite sample estimation. This procedure combines the larger asymptotic efficiency of the optimal estimator and the greater finite sample stability of the GREG. Design based properties of the proposed estimator are discussed and a small simulation study is conducted to explore its finite sample performance.

Modelling spatio-temporal air pollution data from a mobile monitoring station

ABSTRACT Environmental data is typically indexed in space and time. This work deals with modelling spatio-temporal air quality data, when multiple measurements are available for each space-time point. Typically this situation arises when different measurements referring to several response variables are observed in each space-time point, for example, different pollutants or size resolved data on particular matter. Nonetheless, such a kind of data also arises when using a mobile monitoring station moving along a path for a certain period of time. In this case, each spatio-temporal point has a number of measurements referring to the response variable observed several times over different locations in a close neighbourhood of the space-time point. We deal with this type of data within a hierarchical Bayesian framework, in which observed measurements are modelled in the first stage of the hierarchy, while the unobserved spatio-temporal process is considered in the following stages. The final model is very flexible and includes autoregressive terms in time, different structures for the variance-covariance matrix of the errors, and can manage covariates available at different space-time resolutions. This approach is motivated by the availability of data on urban pollution dynamics: fast measures of gases and size resolved particulate matter have been collected using an Optical Particle Counter located on a cabin of a public conveyance that moves on a monorail on a line transect of a town. Urban microclimate information is also available and included in the model. Simulation studies are conducted to evaluate the performance of the proposed model over existing alternatives that do not model data over the first stage of the hierarchy.

Bedside sonography assessment of extravascular lung water increase after major pulmonary resection in non-small cell lung cancer patients

Background Extra vascular lung water (EVLW) following pulmonary resection increases due to fluid infusion and rises in capillary surface and permeability of the alveolar capillary membranes. EVLW increase clinically correlates to pulmonary oedema and it may generate impairments of gas exchanges and acute lung injury. An early and reliable assessment of postoperative EVLW, especially following major pulmonary resection, is useful in terms of reducing the risk of postoperative complications. The currently used methods, though satisfying these criteria, tend to be invasive and cumbersome and these factors might limit its use. The presence and burden of EVLW has been reported to correlate with sonographic B-line artefacts (BLA) assessed by lung ultrasound (LUS). This observational study investigated if bedside LUS could detect EVLW increases after major pulmonary resection. Due to the clinical association between EVLW increase and impairment of gas exchange, secondary aims of the study included investigating for associations between any observed EVLW increases and both respiratory ratio (PaO2/FiO2) and fluid retention, measured by brain natriuretic peptide (BNP). Methods Overall, 74 major pulmonary resection patients underwent bedside LUS before surgery and at postoperative days 1 and 4, in the inviolate hemithorax which were divided into four quadrants. BLA were counted with a four-level method. The respiratory ratio PaO2/FiO2 and fluid retention were both assessed. Results BLA resulted being increased at postoperative day 1 (OR 9.25; 95% CI, 5.28-16.20; P<0.0001 vs. baseline), and decreased at day 4 (OR 0.50; 95% CI, 0.31-0.80; P=0.004 vs. day 1). Moreover, the BLA increase was associated with both increased BNP (OR 1.005; 95% CI, 1.003-1.008; P<0.0001) and body weight (OR 1.040; 95% CI, 1.008-1.073; P=0.015). Significant inverse correlations were observed between the BLA values and the PaO2/FiO2 respiratory ratios. Conclusions Our results suggest that LUS, due to its non-invasiveness, affordability and capacity to detect increases in EVLW, might be useful in better managing postoperative patients.

Metodi per correggere gli errori di copertura

Nel corso del processo in cui si progetta e realizza un’indagine le possibilita di errore non campionario sono molte. Gli errori di copertura sono i primi in cui si puo incorrere. Essi, definiti nel Par. 1.2.4, nascono dalla non corrispondenza tra le popolazioni obiettivo e frame e possono essere attribuiti a chi realizza l’indagine, perche non ha saputo trovare la giusta corrispondenza tra le due popolazioni, ma anche a cause estranee agli organizzatori della ricerca che dipendono, ad esempio, dalle particolari circostanze in cui l’indagine stessa viene a svolgersi, dalla specificita dei suoi obiettivi, dalla tipologia della popolazione oggetto di studio, dalla complessita del piano di campionamento e, non ultimo, dal metodo utilizzato per rilevare i dati. In sostanza, essi non sono imputabili direttamente all’oggetto dell’indagine e alle unita che si vogliono rilevare. Infatti, idealmente qualsiasi target o popolazione obiettivo, in presenza di risorse illimitate, potrebbe essere correttamente rappresentato dalla lista aggiornata e accurata degli elementi che lo compongono (frame).

L’impiego delle variabili ausiliarie per la costruzione degli stimatori

Nel capitolo precedente sono stati richiamati in modo schematico i principali piani di campionamento di uso corrente evidenziando il ruolo fondamentale delle informazioni disponibili nel frame. Ad esempio, conoscere la dislocazione territoriale delle unita statistiche consente di predisporre una stratificazione territoriale; oppure, nel caso sia nota la data di nascita degli individui e possibile definire una loro stratificazione per classe d’eta. Ancora, se per una popolazione di imprese e disponibile un archivio amministrativo con i dati sul settore di attivita produttiva e il numero degli addetti e possibile stratificare per settore e introdurre un campionamento con probabilita proporzionale al numero degli addetti. In questo capitolo, invece, verra trattato l’utilizzo delle informazioni sulla popolazione, anche provenienti da fonti alternative alla lista di campionamento, ai fini della costruzione dello stimatore da utilizzare, con l’obiettivo di accrescere l’efficienza del processo di stima.

Introduzione al campionamento da popolazioni finite

Lo scopo introduttivo di questo capitolo e quello di richiamare i concetti fondamentali del campionamento da popolazioni finite. Dopo alcune definizioni preliminari e una breve disquisizione sulla terminologia in uso, vengono ricordate le fasi di una indagine statistica e individuati gli errori che in ciascuna di esse possono aver origine. Come si vedra nei successivi capitoli di questo volume, dedicati proprio alle diverse tipologie di errore, l’impiego delle variabili ausiliarie per la individuazione e la correzione degli errori e fondamentale. Tuttavia, come e noto, ad esse si puo ricorrere anche per la costruzione del piano di campionamento. Questo non implica la correzione di alcun errore, ma una maggiore precisione ed aderenza alla realta che si vuole indagare e il ricorso alle variabili ausiliarie in questo caso puo essere inteso come un metodo preventivo degli errori. Non sempre e possibile disporre delle variabili ausiliarie per i diversi impieghi, puo allora essere necessario costruire ad hoc un data-set di tali variabili, per esempio con il campionamento a due fasi, che viene brevemente richiamato. Infine, vengono ricordati alcuni metodi di indagine che non seguono i canoni tradizionali del campionamento da popolazioni finite — sono i cosi detti campionamenti non probabilistici — alcuni molto in uso nelle indagini in ambito sociale. Anche se per essi non e possibile conoscere l’errore campionario, tuttavia, in questi casi, si puo ricorrere a metodi inferenziali diversi da quello tradizionale usato nel campionamento da popolazioni finite, noto come design-based.

I campionamenti probabilistici

Il presente capitolo riguarda i campioni probabilistici secondo la definizione fornita nel Par. 2.3 e fa riferimento a una situazione del tutto ideale. Cosi, si suppone che le unita delia popolazione frame, di numerosita nota e pari a N, coincidano con quelle della popolazione target e che tutte le unita comprese nel campione forniscano le risposte richieste.