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Lorsque des enquêtes sont effectuées, il est commun de faire face à de la non-réponse de la part des individus échantillonnés. Les estimateurs non-ajustés pouvant être biaisés en présence de données manquantes, on a habituellement recours à des méthodes d'imputation pour obtenir un fichier de données complété et réduire ainsi le biais de non-réponse. De plus, les estimateurs usuels de totaux ou moyennes de la population finie sont très sensibles à la présence de données influentes dans l'échantillon. Nous proposons une version efficace en présence de valeurs influentes des estimateurs multi-robustes, c'est-à-dire des estimateurs imputés par une méthode d'imputation multi-robuste. Pour ce faire, nous définissons le biais conditionnel d'une unité échantillonnée comme mesure de son influence. Nous présenterons les résultats d'une étude par simulation afin de montrer les gains de la méthode proposée en termes de biais et d'efficacité., Item nonresponse is a common issue in surveys. Because unadjusted estimators may be biased in the presence of nonresponse, it is common practice to impute the missing values, leading to the creation of a completed data file, in order to reduce the nonresponse bias. Moreover, the commonly used estimators of population totals/means are very unstable in the presence of influential units. We develop an efficient version, in the presence of influential units, of multiply robust estimators, which are estimators obtained after a multiply robust imputation method. To do so, we define the conditional bias of a sample unit as its measure of influence. We will present the results of a simulation study to show the benefits of the proposed method in terms of bias and efficiency.

Weather radar has become an invaluable tool for monitoring rainfall and studying its link to hydrological response. However, when it comes to accurately measuring small-scale rainfall extremes responsible for urban flooding, many challenges remain. The most important of them is that radar tends to underestimate rainfall compared to gauges. The hope is that by measuring at higher resolutions and making use of dual-polarization radar, these mismatches can be reduced. Each country has developed its own strategy for addressing this issue. However, since there is no common benchmark, improvements are hard to quantify objectively. This study sheds new light on current performances by conducting a multinational assessment of radar's ability to capture heavy rain events at scales of 5 min up to 2 h. The work is performed within the context of the joint experiment framework of project MUFFIN (Multiscale Urban Flood Forecasting), which aims at better understanding the link between rainfall and urban pluvial flooding across scales. In total, six different radar products in Denmark, the Netherlands, Finland and Sweden were considered. The top 50 events in a 10-year database of radar data were used to quantify the overall agreement between radar and gauges as well as the bias affecting the peaks. Results show that the overall agreement in heavy rain is fair (correlation coefficient 0.7–0.9), with apparent multiplicative biases on the order of 1.2–1.8 (17  %–44  % underestimation). However, after taking into account the different sampling volumes of radar and gauges, actual biases could be as low as 10 %. Differences in sampling volumes between radar and gauges play an important role in explaining the bias but are hard to quantify precisely due to the many post-processing steps applied to radar. Despite being adjusted for bias by gauges, five out of six radar products still exhibited a clear conditional bias, with intensities of about 1 %–2 % per mmh−1. As a result, peak rainfall intensities were severely underestimated (factor 1.8–3.0 or 44 %–67 %). The most likely reason for this is the use of a fixed Z–R relationship when estimating rainfall rates (R) from reflectivity (Z), which fails to account for natural variations in raindrop size distribution with intensity. Based on our findings, the easiest way to mitigate the bias in times of heavy rain is to perform frequent (e.g., hourly) bias adjustments with the help of rain gauges, as demonstrated by the Dutch C-band product. An even more promising strategy that does not require any gauge adjustments is to estimate rainfall rates using a combination of reflectivity (Z) and differential phase shift (Kdp), as done in the Finnish OSAPOL product. Both approaches lead to approximately similar performances, with an average bias (at 10 min resolution) of about 30 % and a peak intensity bias of about 45 %.

Une unité est considérée comme influente lorsque son inclusion ou son exclusion de l'échantillon a un effet important sur l'erreur due à l'échantillonnage. La présence d'unités influentes dans un échantillon rend les estimateurs classiques instables. Beaumont et al. (2013) ont montré que le biais conditionnel est un bon outil qui permet de mesurer l'influence d'une unité. Ils ont développé un estimateur robuste basé sur le biais conditionnel. Cet estimateur dépend d'une constante appelée "seuil de robustesse" déterminée de manière à minimiser le plus grand biais conditionnel estimé de l'estimateur robuste. Le but de ce travail est d'étudier d'autres critères permettant d'obtenir des estimateurs robustes ayant de bonnes propriétés en termes d'erreur quadratique moyenne., A unit is considered influential when its inclusion or exclusion from the sample has a significant effect on the sampling error. The presence of influential units in a sample makes classical estimators unstable. Beaumont et al. (2013) have shown that conditional bias is a good tool for measuring the influence of a unit. They developed a robust estimator based on conditional bias. The proposed estimator depends on a constant, called tuning constant, which is determined by minimizing the largest conditional bias of the robust estimator. The purpose of this work is to study other criteria for obtaining robust estimators with good properties in terms of mean square error.

Group sequential designs are widely used in clinical trials to determine whether a trial should be terminated early. In such trials, maximum likelihood estimates are often used to describe the difference in efficacy between the experimental and reference treatments; however, these are well known for displaying conditional and unconditional biases. Established bias-adjusted estimators include the conditional mean-adjusted estimator (CMAE), conditional median unbiased estimator, conditional uniformly minimum variance unbiased estimator (CUMVUE), and weighted estimator. However, their performances have been inadequately investigated. In this study, we review the characteristics of these bias-adjusted estimators and compare their conditional bias, overall bias, and conditional mean-squared errors in clinical trials with survival endpoints through simulation studies. The coverage probabilities of the confidence intervals for the four estimators are also evaluated. We find that the CMAE reduced conditional bias and showed relatively small conditional mean-squared errors when the trials terminated at the interim analysis. The conditional coverage probability of the conditional median unbiased estimator was well below the nominal value. In trials that did not terminate early, the CUMVUE performed with less bias and an acceptable conditional coverage probability than was observed for the other estimators. In conclusion, when planning an interim analysis, we recommend using the CUMVUE for trials that do not terminate early and the CMAE for those that terminate early. Copyright © 2017 John Wiley & Sons, Ltd.

Two post-real time precipitation products from the Integrated Multi-satellite Retrievals for Global Precipitation Measurement Mission (IMERG) are systematically evaluated over China with China daily Precipitation Analysis Product (CPAP) as reference. The IMERG products include the gauge-corrected IMERG product (IMERG_Cal) and the version of IMERG without direct gauge correction (IMERG_Uncal). The post-research TRMM Multisatellite Precipitation Analysis version 7 (TMPA-3B42V7) is also evaluated concurrently with IMERG for better perspective. In order to be consistent with CPAP, the evaluation and comparison of selected products are performed at 0.25° and daily resolutions from 12 March 2014 through 28 February 2015. The results show that: Both IMERG and 3B42V7 show similar performances. Compared to IMERG_Uncal, IMERG_Cal shows significant improvement in overall and conditional bias and in the correlation coefficient. Both IMERG_Cal and IMERG_Uncal perform relatively poor in winter and over-detect slight precipitation events in northwestern China. As an early validation of the GPM-era IMERG products that inherit the TRMM-era global satellite precipitation products, these findings will provide useful feedbacks and insights for algorithm developers and data users over China and beyond.

In many signal processing applications of Kalman filter (KF) and its variants and extensions, accurate estimation of extreme states is often of great importance. When the observations used are uncertain, however, KF suffers from conditional bias (CB) which results in consistent under- and overestimation of extremes in the right and left tails, respectively. Recently, CB-penalized KF, or CBPKF, has been developed to address CB. In this paper, we present an alternative formulation based on variance-inflated KF to reduce computation and algorithmic complexity, and describe adaptive implementation to improve unconditional performance. For theoretical basis and context, we also provide a complete self-contained description of CB-penalized Fisher-like estimation and CBPKF. The results from 1-dimensional synthetic experiments for a linear system with varying degrees of nonstationarity show that adaptive CBPKF reduces root mean square error at the extreme tail ends by 20 to 30% over KF while performing comparably to KF in the unconditional sense. The alternative formulation is found to approximate the original formulation very closely while reducing computing time to 1.5 to 3.5 times of that for KF depending on the dimensionality of the problem. Adaptive CBPKF hence offers a significant addition to the dynamic filtering methods for general application in signal processing when accurate estimation of extremes is of importance., Comment: 9 pages, 5 figures, 3 tables

In recent years, there has been a prominent discussion in the literature about the potential for overestimation of the treatment effect when a clinical trial stops at an interim analysis due to the experimental treatment showing a benefit over the control. However, there has been much less attention paid to the converse issue, namely, that sequentially monitored clinical trials which did not stop early for benefit tend to underestimate the treatment effect. In meta-analyses of many studies, these two sources of bias will tend to balance each other to produce an unbiased estimate of the treatment effect. However, for the interpretation of a single study in isolation, underestimation due to interim analysis may be an important consideration. In this paper, we discuss the nature of this underestimation, including theoretical and simulation results demonstrating that it can be substantial in some contexts. Furthermore, we show how a conditional approach to estimation, in which we condition on the study reaching its final analysis, may be used to validly inflate the observed treatment difference from a sequentially monitored clinical trial. Expressions for the conditional bias and information are derived, and these are used in supplied R code that computes the bias-adjusted estimate and an associated confidence interval. As well as simulation results demonstrating the validity of the methods, we present a data analysis example from a pivotal clinical trial in cardiovascular disease. The methods will be most useful when an unbiased treatment effect estimate is critical, such as in cost-effectiveness analysis or risk prediction.

Background: The primary purpose of prescription drug labeling is to give healthcare professionals the information needed to prescribe drugs appropriately. Therefore, labeling typically reports the effects that the treatment might be expected to have on several efficacy measures, including not only the primary endpoint used to establish effectiveness but also a number of key secondary endpoints that are important to practitioners and patients. Methods: One possible regulatory approach to drug labeling is to include results on important secondary efficacy endpoints in labeling only if there is statistical evidence of a treatment effect and a clinically meaningful estimated effect. We evaluate the statistical consequences of this approach by deriving and discussing the potential bias in point estimates and deviation from nominal coverage in confidence intervals that are reported in labeling. Results: Such an approach can lead to substantial conditional bias in point estimates (toward spuriously greater effects than the truth) and undercoverage in confidence intervals. Conclusion: These statistical properties may have important and undesirable regulatory and public health implications. We discuss an alternative approach to include results in labeling for a selected set of reliably ascertained, clinically important endpoints whether or not there is evidence of a treatment effect.

In this thesis, we address the problem of robust estimation of mean or total electricity consumption curves by sampling in a finite population for the entire population and for small areas. We are also interested in estimating mean curves by sampling in presence of partially missing trajectories.Indeed, many studies carried out in the French electricity company EDF, for marketing or power grid management purposes, are based on the analysis of mean or total electricity consumption curves at a fine time scale, for different groups of clients sharing some common characteristics.Because of privacy issues and financial costs, it is not possible to measure the electricity consumption curve of each customer so these mean curves are estimated using samples. In this thesis, we extend the work of Lardin (2012) on mean curve estimation by sampling by focusing on specific aspects of this problem such as robustness to influential units, small area estimation and estimation in presence of partially or totally unobserved curves.In order to build robust estimators of mean curves we adapt the unified approach to robust estimation in finite population proposed by Beaumont et al (2013) to the context of functional data. To that purpose we propose three approaches : application of the usual method for real variables on discretised curves, projection on Functional Spherical Principal Components or on a Wavelets basis and thirdly functional truncation of conditional biases based on the notion of depth.These methods are tested and compared to each other on real datasets and Mean Squared Error estimators are also proposed.Secondly we address the problem of small area estimation for functional means or totals. We introduce three methods: unit level linear mixed model applied on the scores of functional principal components analysis or on wavelets coefficients, functional regression and aggregation of individual curves predictions by functional regression trees or functional random forests. Robust versions of these estimators are then proposed by following the approach to robust estimation based on conditional biais presented before.Finally, we suggest four estimators of mean curves by sampling in presence of partially or totally unobserved trajectories. The first estimator is a reweighting estimator where the weights are determined using a temporal non parametric kernel smoothing adapted to the context of finite population and missing data and the other ones rely on imputation of missing data. Missing parts of the curves are determined either by using the smoothing estimator presented before, or by nearest neighbours imputation adapted to functional data or by a variant of linear interpolation which takes into account the mean trajectory of the entire sample. Variance approximations are proposed for each method and all the estimators are compared to each other on real datasets for various missing data scenarios.; Dans cette thèse, nous nous intéressons à l'estimation robuste de courbes moyennes ou totales de consommation électrique par sondage en population finie, pour l'ensemble de la population ainsi que pour des petites sous-populations, en présence ou non de courbes partiellement inobservées.En effet, de nombreuses études réalisées dans le groupe EDF, que ce soit dans une optique commerciale ou de gestion du réseau de distribution par Enedis, se basent sur l'analyse de courbes de consommation électrique moyennes ou totales, pour différents groupes de clients partageant des caractéristiques communes. L'ensemble des consommations électriques de chacun des 35 millions de clients résidentiels et professionnels Français ne pouvant être mesurées pour des raisons de coût et de protection de la vie privée, ces courbes de consommation moyennes sont estimées par sondage à partir de panels. Nous prolongeons les travaux de Lardin (2012) sur l'estimation de courbes moyennes par sondage en nous intéressant à des aspects spécifiques de cette problématique, à savoir l'estimation robuste aux unités influentes, l'estimation sur des petits domaines, et l'estimation en présence de courbes partiellement ou totalement inobservées.Pour proposer des estimateurs robustes de courbes moyennes, nous adaptons au cadre fonctionnel l'approche unifiée d'estimation robuste en sondages basée sur le biais conditionnel proposée par Beaumont (2013). Pour cela, nous proposons et comparons sur des jeux de données réelles trois approches : l'application des méthodes usuelles sur les courbes discrétisées, la projection sur des bases de dimension finie (Ondelettes ou Composantes Principales de l'Analyse en Composantes Principales Sphériques Fonctionnelle en particulier) et la troncature fonctionnelle des biais conditionnels basée sur la notion de profondeur d'une courbe dans un jeu de données fonctionnelles. Des estimateurs d'erreur quadratique moyenne instantanée, explicites et par bootstrap, sont également proposés.Nous traitons ensuite la problématique de l'estimation sur de petites sous-populations. Dans ce cadre, nous proposons trois méthodes : les modèles linéaires mixtes au niveau unité appliqués sur les scores de l'Analyse en Composantes Principales ou les coefficients d'ondelettes, la régression fonctionnelle et enfin l'agrégation de prédictions de courbes individuelles réalisées à l'aide d'arbres de régression ou de forêts aléatoires pour une variable cible fonctionnelle. Des versions robustes de ces différents estimateurs sont ensuite proposées en déclinant la démarche d'estimation robuste basée sur les biais conditionnels proposée précédemment.Enfin, nous proposons quatre estimateurs de courbes moyennes en présence de courbes partiellement ou totalement inobservées. Le premier est un estimateur par repondération par lissage temporel non paramétrique adapté au contexte des sondages et de la non réponse et les suivants reposent sur des méthodes d'imputation. Les portions manquantes des courbes sont alors déterminées soit en utilisant l'estimateur par lissage précédemment cité, soit par imputation par les plus proches voisins adaptée au cadre fonctionnel ou enfin par une variante de l'interpolation linéaire permettant de prendre en compte le comportement moyen de l'ensemble des unités de l'échantillon. Des approximations de variance sont proposées dans chaque cas et l'ensemble des méthodes sont comparées sur des jeux de données réelles, pour des scénarios variés de valeurs manquantes.

Ordinary kriging and non-linear geostatistical estimators are now well accepted methods in mining grade control and mine reserve estimation. In kriging, the search volume or ‘kriging neighbourhood’ is defined by the user. The definition of the search space can have a significant impact on the outcome of the kriging estimate. In particular, too restrictive neighbourhood, can result in serious conditional bias. Kriging is commonly described as a ‘minimum variance estimator’ but this is only true when the neighbourhood is properly selected. Arbitrary decisions about search space are highly risky. The criteria to consider when evaluating a particular kriging neighbourhood are the slope of the regression of the ‘true’ and ‘estimated’ block grades, the number of kriging negative weights and the kriging variance. Search radius is one of the most important parameters of search volume which often is determined on the basis of influence of the variogram. In this paper the above-mentioned parameters are used to determine optimal search radius.

Mineral resource estimation has long been plagued with the inherent challenge of conditional bias. Estimation requires the specification of a number of parameters such as block model block size, minimum and maximum number of data used to estimate a block, and search ellipsoid radii. The choice of estimation parameters is not an objective procedure that can be followed from one deposit to the next. Several measures have been proposed to assist in the choice of kriging estimation parameters to lower the conditional bias. These include the slope of regression and kriging efficiency.

This paper constitutes a write-up of the first Professor Danie Krige memorial lecture in 2014, which was organized by the University of the Witwatersrand in collaboration with the Southern African Institute of Mining and Metallurgy (SAIMM) and the Geostatistical Association of Southern Africa, at which his wife, Mrs Ansie Krige, the SAIMM, and Professor RCA Minnitt also spoke. The memorial lecture was presented by his previous PhD graduate student, Dr Winfred Assibey-Bonsu. During that inaugural memorial lecture, the SAIMM highlighted three activities that the Institute would undertake going forward, so as to remember this great South African mining pioneer: ►The publication of a Danie Krige Commemorative Volume of the SAIMM Journal ►An annual Danie Krige Memorial Lecture to be facilitated by the School of Mining Engineering at the University of the Witwatersrand ►The annual award of a Danie Krige Medal. What follows is both a tribute to his work and a testimony to the great man's deep personal integrity, belief in family, humility, and faith in Christ: all of which led him to become a giant not only in the South African mining industry, but indeed worldwide

Cette thèse comporte trois articles dont un est publié et deux en préparation. Le sujet central de la thèse porte sur le traitement des valeurs aberrantes représentatives dans deux aspects importants des enquêtes que sont : l’estimation des petits domaines et l’imputation en présence de non-réponse partielle. En ce qui concerne les petits domaines, les estimateurs robustes dans le cadre des modèles au niveau des unités ont été étudiés. Sinha & Rao (2009) proposent une version robuste du meilleur prédicteur linéaire sans biais empirique pour la moyenne des petits domaines. Leur estimateur robuste est de type «plugin», et à la lumière des travaux de Chambers (1986), cet estimateur peut être biaisé dans certaines situations. Chambers et al. (2014) proposent un estimateur corrigé du biais. En outre, un estimateur de l’erreur quadratique moyenne a été associé à ces estimateurs ponctuels. Sinha & Rao (2009) proposent une procédure bootstrap paramétrique pour estimer l’erreur quadratique moyenne. Des méthodes analytiques sont proposées dans Chambers et al. (2014). Cependant, leur validité théorique n’a pas été établie et leurs performances empiriques ne sont pas pleinement satisfaisantes. Ici, nous examinons deux nouvelles approches pour obtenir une version robuste du meilleur prédicteur linéaire sans biais empirique : la première est fondée sur les travaux de Chambers (1986), et la deuxième est basée sur le concept de biais conditionnel comme mesure de l’influence d’une unité de la population. Ces deux classes d’estimateurs robustes des petits domaines incluent également un terme de correction pour le biais. Cependant, ils utilisent tous les deux l’information disponible dans tous les domaines contrairement à celui de Chambers et al. (2014) qui utilise uniquement l’information disponible dans le domaine d’intérêt. Dans certaines situations, un biais non négligeable est possible pour l’estimateur de Sinha & Rao (2009), alors que les estimateurs proposés exhibent un faible biais pour un choix approprié de la fonction d’influence et de la constante de robustesse. Les simulations Monte Carlo sont effectuées, et les comparaisons sont faites entre les estimateurs proposés et ceux de Sinha & Rao (2009) et de Chambers et al. (2014). Les résultats montrent que les estimateurs de Sinha & Rao (2009) et de Chambers et al. (2014) peuvent avoir un biais important, alors que les estimateurs proposés ont une meilleure performance en termes de biais et d’erreur quadratique moyenne. En outre, nous proposons une nouvelle procédure bootstrap pour l’estimation de l’erreur quadratique moyenne des estimateurs robustes des petits domaines. Contrairement aux procédures existantes, nous montrons formellement la validité asymptotique de la méthode bootstrap proposée. Par ailleurs, la méthode proposée est semi-paramétrique, c’est-à-dire, elle n’est pas assujettie à une hypothèse sur les distributions des erreurs ou des effets aléatoires. Ainsi, elle est particulièrement attrayante et plus largement applicable. Nous examinons les performances de notre procédure bootstrap avec les simulations Monte Carlo. Les résultats montrent que notre procédure performe bien et surtout performe mieux que tous les compétiteurs étudiés. Une application de la méthode proposée est illustrée en analysant les données réelles contenant des valeurs aberrantes de Battese, Harter & Fuller (1988). S’agissant de l’imputation en présence de non-réponse partielle, certaines formes d’imputation simple ont été étudiées. L’imputation par la régression déterministe entre les classes, qui inclut l’imputation par le ratio et l’imputation par la moyenne sont souvent utilisées dans les enquêtes. Ces méthodes d’imputation peuvent conduire à des estimateurs imputés biaisés si le modèle d’imputation ou le modèle de non-réponse n’est pas correctement spécifié. Des estimateurs doublement robustes ont été développés dans les années récentes. Ces estimateurs sont sans biais si l’un au moins des modèles d’imputation ou de non-réponse est bien spécifié. Cependant, en présence des valeurs aberrantes, les estimateurs imputés doublement robustes peuvent être très instables. En utilisant le concept de biais conditionnel, nous proposons une version robuste aux valeurs aberrantes de l’estimateur doublement robuste. Les résultats des études par simulations montrent que l’estimateur proposé performe bien pour un choix approprié de la constante de robustesse., This thesis focuses on the treatment of representative outliers in two important aspects of surveys: small area estimation and imputation for item non-response. Concerning small area estimation, robust estimators in unit-level models have been studied. Sinha & Rao (2009) proposed estimation procedures designed for small area means, based on robustified maximum likelihood parameters estimates of linear mixed model and robust empirical best linear unbiased predictors of the random effect of the underlying model. Their robust methods for estimating area means are of the plug-in type, and in view of the results of Chambers (1986), the resulting robust estimators may be biased in some situations. Biascorrected estimators have been proposed by Chambers et al. (2014). In addition, these robust small area estimators were associated with the estimation of the Mean Square Error (MSE). Sinha & Rao (2009) proposed a parametric bootstrap procedure based on the robust estimates of the parameters of the underlying linear mixed model to estimate the MSE. Analytical procedures for the estimation of the MSE have been proposed in Chambers et al. (2014). However, their theoretical validity has not been formally established and their empirical performances are not fully satisfactorily. Here, we investigate two new approaches for the robust version the best empirical unbiased estimator: the first one relies on the work of Chambers (1986), while the second proposal uses the concept of conditional bias as an influence measure to assess the impact of units in the population. These two classes of robust small area estimators also include a correction term for the bias. However, they are both fully bias-corrected, in the sense that the correction term takes into account the potential impact of the other domains on the small area of interest unlike the one of Chambers et al. (2014) which focuses only on the domain of interest. Under certain conditions, non-negligible bias is expected for the Sinha-Rao method, while the proposed methods exhibit significant bias reduction, controlled by appropriate choices of the influence function and tuning constants. Monte Carlo simulations are conducted, and comparisons are made between: the new robust estimators, the Sinha-Rao estimator, and the bias-corrected estimator. Empirical results suggest that the Sinha-Rao method and the bias-adjusted estimator of Chambers et al (2014) may exhibit a large bias, while the new procedures offer often better performances in terms of bias and mean squared error. In addition, we propose a new bootstrap procedure for MSE estimation of robust small area predictors. Unlike existing approaches, we formally prove the asymptotic validity of the proposed bootstrap method. Moreover, the proposed method is semi-parametric, i.e., it does not rely on specific distributional assumptions about the errors and random effects of the unit-level model underlying the small-area estimation, thus it is particularly attractive and more widely applicable. We assess the finite sample performance of our bootstrap estimator through Monte Carlo simulations. The results show that our procedure performs satisfactorily well and outperforms existing ones. Application of the proposed method is illustrated by analyzing a well-known outlier-contaminated small county crops area data from North-Central Iowa farms and Landsat satellite images. Concerning imputation in the presence of item non-response, some single imputation methods have been studied. The deterministic regression imputation, which includes the ratio imputation and mean imputation are often used in surveys. These imputation methods may lead to biased imputed estimators if the imputation model or the non-response model is not properly specified. Recently, doubly robust imputed estimators have been developed. However, in the presence of outliers, the doubly robust imputed estimators can be very unstable. Using the concept of conditional bias as a measure of influence (Beaumont, Haziza and Ruiz-Gazen, 2013), we propose an outlier robust version of the doubly robust imputed estimator. Thus this estimator is denoted as a triple robust imputed estimator. The results of simulation studies show that the proposed estimator performs satisfactorily well for an appropriate choice of the tuning constant.

We propose a method with better predictions at extreme values than the standard method of Kriging. We construct our predictor in two ways: by penalizing the mean squared error through conditional bias and by penalizing the conditional likelihood at the target function value. Our prediction exhibits robustness to the model mismatch in the covariance parameters, a desirable feature for computer simulations with a restricted number of data points. Applications on several functions show that our predictor is robust to the non-Gaussianity of the function.

Repeated significance testing in a sequential experiment not only increases the overall type I error rate of the false positive conclusion but also causes biases in estimating the unknown parameter. In general, the test statistics in a sequential trial can be properly approximated by a Brownian motion with a drift parameter at interim looks. The unadjusted maximum likelihood estimator can be potentially very biased due to the possible early stopping rule at any interim. In this paper, we investigate the conditional and marginal biases with focus on the conditional one upon the stopping time in estimating the Brownian motion drift parameter. It is found that the conditional bias may be very serious for existing point estimation methods, even if the unconditional bias is satisfactory. New conditional estimators are thus proposed, which can significantly reduce the conditional bias from unconditional estimators. The results of Monte-Carlo studies show that the proposed estimators can provide a much smaller conditional bias and MSE than the naive MLE and a Whitebead's bias reduced estimator.

International audience; In business surveys, it is not unusual to collect economic variables for which the distribution is highly skewed. In this context, winsorization is often used to treat the problem of influential values. This technique requires the determination of a constant that corresponds to the threshold above which large values are reduced. In this paper, we consider a method of determining the constant which involves minimizing the largest estimated conditional bias in the sample. In the context of domain estimation, we also propose a method of ensuring consistency between the domain-level winsorized estimates and the population-level winsorized estimate. The results of two simulation studies suggest that the proposed methods lead to winsorized estimators that have good bias and relative efficiency properties.

One of the seminal pioneering papers in reserve evaluation was published by Danie Krige in 1951. In that paper he introduced the concept of regression techniques in providing better estimates for stope grades and correcting for what later became known as the 'conditional bias'. In South Africa, the development of this approach led to the phenomenon being dubbed the 'regression effect', and regression techniques ultimately formed the basis of simple kriging in Krige's later papers. In the late 1950s and early 1960s, Georges Matheron (1965) formulated the general theory of 'regionalized variables' and included copious discussion on what he termed the 'volume-variance' effect. Matheron defined mathematically the reason for, and quantification of, the difference in variability between estimated values and the actual unknown values. In 1983, this author published a paper that combined these two philosophies so that the 'regression effect' could be quantified before actual mining block values were available. In 1996 and in some earlier presentations, Krige revisited the regression effect in terms of the conditional bias and suggested two measures that might enable a practitioner of geostatistics to assess the 'efficiency' of the kriging estimator in any particular case. In this article, we revisit the trail from 'regression effect' to 'kriging efficiency' in conceptual terms and endeavour to explain exactly what is measured by these parameters and how to use (or abuse) them in practical cases.

SYNOPSIS A localized nonlinear recoverable resource estimate technique has been applied using typical feasibility or new mining drilling data configurations drawn from a massive database from a mined-out area on a hydrothermal gold deposit. The results were then compared with the corresponding 8 m W 5 m grid grade-control data in order to determine the efficiency of the approach and the validity of the recoverable resource estimates for mine planning and financial forecasts.

The goal of this study is to improve understanding of the optimization criteria for radar rainfall (RR) products. Conditional bias (CB) is formally defined and discussed. The CB is defined as the difference between a given rain rate and the conditional average of its estimates. A simple analytical model is used to study the behavior of CB and its effect on the relationship between the estimates and the truth. This study shows the measurement errors of near-surface radar reflectivity and the natural reflectivity–rainfall rate variability can affect CB. This RR estimation error component is also compared with the commonly used mean-square error (MSE). A dilemma between the minimization of these two errors is demonstrated. Removing CB from the estimates significantly increases MSE, but minimizing MSE results in a large CB that manifests itself in underestimation of strong rainfalls.

Summary In survey sampling, auxiliary information on the population is often available. The aim of this paper is to develop a method which allows one to take into account such auxiliary information at the estimation stage by means of conditional bias adjustment. The basic idea is to attempt to construct a conditionally unbiased estimator. Four estimators that have a small conditional bias with respect to a statistic are proposed. It is shown that many of the estimators used in the literature in the case of simple random sampling can be obtained by using this estimation principle. The problem of simple random sampling with replacement, poststratification, and adjustment of a 2 x 2 dimensional contingency table to marginal totals are discussed in the conditional framework. Finally it is shown that the regression estimator can be viewed as an approximation of an application of the conditional principle. Resume Dans les enquetes par sondage, une information auxiliaire sur l'ensemble de la population est souvent disponible. Le but de cent aticle est de developper une methode qui permet de prendre en compte cette information auxiliaire a l'etape de l'estimation au moyen d'un ajustement du biais conditionnel. L'idee de base estde tenter de constuire un estimateur sans biaisconditionnel. Quatre estimateurs ayant un faible biais conditionnel sont proposes. On montre ensuite que beaucoup d'estimateus presentes dans la litterature dans le cas du plan simple sans remise peuvent etre obtenus en utilisant ce principe d'estimation. Les problemes du sondage aleatoire simple avec remise, de la poststratification, de l'ajustement d'un tableau de contigence de dimension 2 × 2 sont discutes dans le contexte de l'estimation conditionnelle. Finalement on montre que l'estimateur par la regression peut etre obtenu en cherchant une approximation de ce principe conditionnel.

This paper studies the behaviour of the bias corrected LSDV estimator and GMM-based estimators in dynamic panel data models with endogenous regressors. We obtain an expansion of the conditional bias of the LSDV estimator with the leading term coinciding with the one in the expansion from (Kiviet, 1995) and (Kiviet, 1999). Nevertheless, our simulations suggest that in the presence of endogenous regressors the performance of the corrected LSDV estimator can be low. This indicates that although the bias has similar structure whether or not the exogeneity assumption holds, the approximation technique that the LSDVc estimator is based on can work poorly in the endogenous case. GMM-based estimators also have low performance in our experiment.

This study explores whether gender stereotypes about math ability shape high school teachers’ assessments of the students with whom they interact daily, resulting in the presence of conditional bias. It builds on theories of intersectionality by exploring teachers’ perceptions of students in different gender and racial/ethnic subgroups and advances the literature on the salience of gender across contexts by considering variation across levels of math course-taking in the academic hierarchy. Analyses of nationally representative data from the Education Longitudinal Study of 2002 (ELS) reveal that disparities in teachers’ perceptions of ability that favored white males over minority students of both genders are explained away by student achievement in the form of test scores and grades. However, we find evidence of a consistent bias against white females, which although relatively small in magnitude, suggests that teachers hold the belief that math is just easier for white males than it is for white females. In addition, we find some evidence of variation across course level contexts with regard to bias. We conclude by discussing the implications of our findings for research on the construction of gender inequality.

As researchers try to move from cybernetics to neural reality, it is time to look at the match between the back propagation strategy and the functional parameters of neurons. Traditionally, the “bias value” in the back propagation activation function has served a mathematical rather than a biological function. By incorporating a production system into the activation logic at the hidden layer, we are able to arrive at a conditional bias value that approximates the function of thresholds in biological neurons.

This paper shows, through a case study, the impact of multivariate grade modelling upon mine design and mine planning. A deposit explored by drill holes is considered, in which the grades of five elements (copper, silver, molybdenum, arsenic, and antimony) are of interest. Forty alternative models of the deposit are constructed by fitting the joint correlation structure of the grade variables and using conditional cosimulation. In addition, a reference model, obtained by averaging the alternative models, is also considered. The study shows that the resulting mine design (final pit characteristics and production schedules) is sensitive to the grade model under consideration, and that the design based on the reference model may not be optimal when compared to the alternative models based on cosimulation. However, when assuming a given long-term plan and extraction sequence, the grades and net present value (NPV) calculated on the reference model are unbiased with respect to those calculated on the alternative models with the same extraction sequence. The latter allow assessing the possible dispersion of the actual grades and NPV around their expected values, and are useful for the planner in order to determine the probability of meeting given production targets and of exceeding or falling short of given threshold grades. Additionally, unlike cosimulation, the separate simulation of each grade variable leads to unrealistic resource models and to biased results in mine design and mine planning. This approach should therefore be avoided, unless the grade variables are spatially uncorrelated.

[1] In the East Asian-western Pacific (EAWP) region, six climate prediction models which are currently used in APEC Climate Center (APCC) Multi-Model Ensemble (MME) prediction system show low skill in predicting summer precipitation. In order to diagnose the dominant error in the prediction, an error decomposition method is developed. Using this method, the total error is decomposed into three parts: errors due to conditional bias, unconditional bias and atmospheric internal processes (AIP). The bias-error can be corrected while the AIP error cannot. It is found that the sum of both bias-errors is about 3 to 20 times larger than the AIP error over the EAWP region for these models. This suggests that the AIP error is not the main cause for the loss of predictability, therefore there is potential to improve the predictions by correcting the bias-errors.

One of the a,rea~s of Statistics in ~ hich the influence a, nalysis has been ~ idely stu.died in the multiple linear regression model. Nevertheless, the influence diagnostics propo,sed in this context cannot be applied to regression in complex survey, under randomized inference, s.ince the i.i.d, ca.se does not incorporate any probability weighting or population structure, such as clust, ering~ stratification or measures of size i~,to the analysis. In this paper we introduce ~)me influence diagnostics in regression in complex survey, They are built on the condition.al bias concept (Moreno-R, ebollo el, a,l,, 1999). We emphasize the similarities an.d differences of the propo.sed measures with respect to the existing ones for the i.i,d, case.

The postprocessing algorithm introduced by Yao for imposing the spectral amplitudes of a target covariance model is shown to be efficient in correcting the smoothing effect of estimation maps, whether obtained by kriging or any other interpolation technique. As opposed to stochastic simulation, Yao's algorithm yields a unique map starting from an original, typically smooth, estimation map. Most importantly it is shown that reproduction of a covariance/semivariogram model (global accuracy) is necessarily obtained at the cost of local accuracy reduction and increase in conditional bias. When working on one location at a time, kriging remains the most accurate (in the least squared error sense) estimator. However, kriging estimates should only be listed, not mapped, since they do not reflect the correct (target) spatial autocorrelation. This mismatch in spatial autocorrelation can be corrected via stochastic simulation, or can be imposed a posteriori via Yao's algorithm.

For small sample random effects models, results are derived which show in certain cases, and indicate in general, that an estimated random effects variance matrix may be used in the weight matrices without causing undue error in the empirically weighted mean. Exact error variances are derived mathematically for the empirically weighted mean for the two sample case in one and two dimensions. Simulation is used to determine errors for a practical example of six five-variate samples. For estimation of their mean, the differences between the samples are ancillary. The biases of the average and weighted mean estimators conditional on these ancillaries is illustrated in a diagram plotting values obtained by simulation. A curious range anomaly is illustrated which arises if random effects are ignored when present.

Small sample support sizes certainly tend to have higher nugget effects and if the kriging of an ore block is then done with an inadequate data search routine, the problem of ‘conditional biases’ will be exaggerated. Block estimates done on this basis should not be labeled ‘kriging’ or even ‘geostatistics’. Conditional biases occur whatever the individual sample support size and arises basically from an inadequate data search routine when estimating the grades of ore units (blocks). Dr. Manns’ connection between ‘conditional bias’ and a ‘random …