Robust estimating functions and bias correction for longitudinal data analysis

Robust methods are useful in making reliable statistical inferences when there are small deviations from the model assumptions. The widely used method of the generalized estimating equations can be "robustified" by replacing the standardized residuals with the M-residuals. If the Pearson residuals are assumed to be unbiased from zero, parameter estimators from the robust approach are asymptotically biased when error distributions are not symmetric. We propose a distribution-free method for correcting this bias. Our extensive numerical studies show that the proposed method can reduce the bias substantially. Examples are given for illustration.

Assessing severe Drought and wet events over India in a future climate using a nested bias-correction approach

General circulation models (GCMs) are routinely used to simulate future climatic conditions. However, rainfall outputs from GCMs are highly uncertain in preserving temporal correlations, frequencies, and intensity distributions, which limits their direct application for downscaling and hydrological modeling studies. To address these limitations, raw outputs of GCMs or regional climate models are often bias corrected using past observations. In this paper, a methodology is presented for using a nested bias-correction approach to predict the frequencies and occurrences of severe droughts and wet conditions across India for a 48-year period (2050-2099) centered at 2075. Specifically, monthly time series of rainfall from 17 GCMs are used to draw conclusions for extreme events. An increasing trend in the frequencies of droughts and wet events is observed. The northern part of India and coastal regions show maximum increase in the frequency of wet events. Drought events are expected to increase in the west central, peninsular, and central northeast regions of India. (C) 2013 American Society of Civil Engineers.

Calibration and bias correction of climate projections for crop modelling: an idealised case study over Europe

Producing projections of future crop yields requires careful thought about the appropriate use of atmosphere-ocean global climate model (AOGCM) simulations. Here we describe and demonstrate multiple methods for ‘calibrating’ climate projections using an ensemble of AOGCM simulations in a ‘perfect sibling’ framework. Crucially, this type of analysis assesses the ability of each calibration methodology to produce reliable estimates of future climate, which is not possible just using historical observations. This type of approach could be more widely adopted for assessing calibration methodologies for crop modelling. The calibration methods assessed include the commonly used ‘delta’ (change factor) and ‘nudging’ (bias correction) approaches. We focus on daily maximum temperature in summer over Europe for this idealised case study, but the methods can be generalised to other variables and other regions. The calibration methods, which are relatively easy to implement given appropriate observations, produce more robust projections of future daily maximum temperatures and heat stress than using raw model output. The choice over which calibration method to use will likely depend on the situation, but change factor approaches tend to perform best in our examples. Finally, we demonstrate that the uncertainty due to the choice of calibration methodology is a significant contributor to the total uncertainty in future climate projections for impact studies. We conclude that utilising a variety of calibration methods on output from a wide range of AOGCMs is essential to produce climate data that will ensure robust and reliable crop yield projections.

Bias correction in a multivariate normal regression model with general parameterization

This paper derives the second-order biases Of maximum likelihood estimates from a multivariate normal model where the mean vector and the covariance matrix have parameters in common. We show that the second order bias can always be obtained by means of ordinary weighted least-squares regressions. We conduct simulation studies which indicate that the bias correction scheme yields nearly unbiased estimators. (C) 2009 Elsevier B.V. All rights reserved.

Reproducibility and day time bias correction of optoelectronic leg volumetry: a prospective cohort study

Background Leg edema is a common manifestation of various underlying pathologies. Reliable measurement tools are required to quantify edema and monitor therapeutic interventions. Aim of the present work was to investigate the reproducibility of optoelectronic leg volumetry over 3 weeks' time period and to eliminate daytime related within-individual variability. Methods Optoelectronic leg volumetry was performed in 63 hairdressers (mean age 45 ± 16 years, 85.7% female) in standing position twice within a minute for each leg and repeated after 3 weeks. Both lower leg (legBD) and whole limb (limbBF) volumetry were analysed. Reproducibility was expressed as analytical and within-individual coefficients of variance (CVA, CVW), and as intra-class correlation coefficients (ICC). Results A total of 492 leg volume measurements were analysed. Both legBD and limbBF volumetry were highly reproducible with CVA of 0.5% and 0.7%, respectively. Within-individual reproducibility of legBD and limbBF volumetry over a three weeks' period was high (CVW 1.3% for both; ICC 0.99 for both). At both visits, the second measurement revealed a significantly higher volume compared to the first measurement with a mean increase of 7.3 ml ± 14.1 (0.33% ± 0.58%) for legBD and 30.1 ml ± 48.5 ml (0.52% ± 0.79%) for limbBF volume. A significant linear correlation between absolute and relative leg volume differences and the difference of exact day time of measurement between the two study visits was found (P < .001). A therefore determined time-correction formula permitted further improvement of CVW. Conclusions Leg volume changes can be reliably assessed by optoelectronic leg volumetry at a single time point and over a 3 weeks' time period. However, volumetry results are biased by orthostatic and daytime-related volume changes. The bias for day-time related volume changes can be minimized by a time-correction formula.

Lidar uncertainty in complex terrain development of a bias correction methodology

El autor ha trabajado como parte del equipo de investigación en mediciones de viento en el Centro Nacional de Energías Renovables (CENER), España, en cooperación con la Universidad Politécnica de Madrid y la Universidad Técnica de Dinamarca. El presente reporte recapitula el trabajo de investigación realizado durante los últimos 4.5 años en el estudio de las fuentes de error de los sistemas de medición remota de viento, basados en la tecnología lidar, enfocado al error causado por los efectos del terreno complejo. Este trabajo corresponde a una tarea del paquete de trabajo dedicado al estudio de sistemas remotos de medición de viento, perteneciente al proyecto de intestigación europeo del 7mo programa marco WAUDIT. Adicionalmente, los datos de viento reales han sido obtenidos durante las campañas de medición en terreno llano y terreno complejo, pertenecientes al también proyecto de intestigación europeo del 7mo programa marco SAFEWIND. El principal objetivo de este trabajo de investigación es determinar los efectos del terreno complejo en el error de medición de la velocidad del viento obtenida con los sistemas de medición remota lidar. Con este conocimiento, es posible proponer una metodología de corrección del error de las mediciones del lidar. Esta metodología está basada en la estimación de las variaciones del campo de viento no uniforme dentro del volumen de medición del lidar. Las variaciones promedio del campo de viento son predichas a partir de los resultados de las simulaciones computacionales de viento RANS, realizadas para el parque experimental de Alaiz. La metodología de corrección es verificada con los resultados de las simulaciones RANS y validadas con las mediciones reales adquiridas en la campaña de medición en terreno complejo. Al inicio de este reporte, el marco teórico describiendo el principio de medición de la tecnología lidar utilizada, es presentado con el fin de familiarizar al lector con los principales conceptos a utilizar a lo largo de este trabajo. Posteriormente, el estado del arte es presentado en donde se describe los avances realizados en el desarrollo de la la tecnología lidar aplicados al sector de la energía eólica. En la parte experimental de este trabajo de investigación se ha estudiado los datos adquiridos durante las dos campañas de medición realizadas. Estas campañas has sido realizadas en terreno llano y complejo, con el fin de complementar los conocimiento adquiridos en casa una de ellas y poder comparar los efectos del terreno en las mediciones de viento realizadas con sistemas remotos lidar. La primer campaña experimental se desarrollo en terreno llano, en el parque de ensayos de aerogeneradores H0vs0re, propiedad de DTU Wind Energy (anteriormente Ris0). La segunda campaña experimental se llevó a cabo en el parque de ensayos de aerogeneradores Alaiz, propiedad de CENER. Exactamente los mismos dos equipos lidar fueron utilizados en estas campañas, haciendo de estos experimentos altamente relevantes en el contexto de evaluación del recurso eólico. Un equipo lidar está basado en tecnología de onda continua, mientras que el otro está basado en tecnología de onda pulsada. La velocidad del viento fue medida, además de con los equipos lidar, con anemómetros de cazoletas, veletas y anemómetros verticales, instalados en mástiles meteorológicos. Los sensores del mástil meteorológico son considerados como las mediciones de referencia en el presente estudio. En primera instancia, se han analizado los promedios diez minútales de las medidas de viento. El objetivo es identificar las principales fuentes de error en las mediciones de los equipos lidar causadas por diferentes condiciones atmosféricas y por el flujo no uniforme de viento causado por el terreno complejo. El error del lidar ha sido estudiado como función de varias propiedades estadísticas del viento, como lo son el ángulo vertical de inclinación, la intensidad de turbulencia, la velocidad vertical, la estabilidad atmosférica y las características del terreno. El propósito es usar este conocimiento con el fin de definir criterios de filtrado de datos. Seguidamente, se propone una metodología para corregir el error del lidar causado por el campo de viento no uniforme, producido por la presencia de terreno complejo. Esta metodología está basada en el análisis matemático inicial sobre el proceso de cálculo de la velocidad de viento por los equipos lidar de onda continua. La metodología de corrección propuesta hace uso de las variaciones de viento calculadas a partir de las simulaciones RANS realizadas para el parque experimental de Alaiz. Una ventaja importante que presenta esta metodología es que las propiedades el campo de viento real, presentes en las mediciones instantáneas del lidar de onda continua, puede dar paso a análisis adicionales como parte del trabajo a futuro. Dentro del marco del proyecto, el trabajo diario se realizó en las instalaciones de CENER, con supervisión cercana de la UPM, incluyendo una estancia de 1.5 meses en la universidad. Durante esta estancia, se definió el análisis matemático de las mediciones de viento realizadas por el equipo lidar de onda continua. Adicionalmente, los efectos del campo de viento no uniforme sobre el error de medición del lidar fueron analíticamente definidos, después de asumir algunas simplificaciones. Adicionalmente, durante la etapa inicial de este proyecto se desarrollo una importante trabajo de cooperación con DTU Wind Energy. Gracias a esto, el autor realizó una estancia de 1.5 meses en Dinamarca. Durante esta estancia, el autor realizó una visita a la campaña de medición en terreno llano con el fin de aprender los aspectos básicos del diseño de campañas de medidas experimentales, el estudio del terreno y los alrededores y familiarizarse con la instrumentación del mástil meteorológico, el sistema de adquisición y almacenamiento de datos, así como de el estudio y reporte del análisis de mediciones. ABSTRACT The present report summarizes the research work performed during last 4.5 years of investigation on the sources of lidar bias due to complex terrain. This work corresponds to one task of the remote sensing work package, belonging to the FP7 WAUDIT project. Furthermore, the field data from the wind velocity measurement campaigns of the FP7 SafeWind project have been used in this report. The main objective of this research work is to determine the terrain effects on the lidar bias in the measured wind velocity. With this knowledge, it is possible to propose a lidar bias correction methodology. This methodology is based on an estimation of the wind field variations within the lidar scan volume. The wind field variations are calculated from RANS simulations performed from the Alaiz test site. The methodology is validated against real scale measurements recorded during an eight month measurement campaign at the Alaiz test site. Firstly, the mathematical framework of the lidar sensing principle is introduced and an overview of the state of the art is presented. The experimental part includes the study of two different, but complementary experiments. The first experiment was a measurement campaign performed in flat terrain, at DTU Wind Energy H0vs0re test site, while the second experiment was performed in complex terrain at CENER Alaiz test site. Exactly the same two lidar devices, based on continuous wave and pulsed wave systems, have been used in the two consecutive measurement campaigns, making this a relevant experiment in the context of wind resource assessment. The wind velocity was sensed by the lidars and standard cup anemometry and wind vanes (installed on a met mast). The met mast sensors are considered as the reference wind velocity measurements. The first analysis of the experimental data is dedicated to identify the main sources of lidar bias present in the 10 minute average values. The purpose is to identify the bias magnitude introduced by different atmospheric conditions and by the non-uniform wind flow resultant of the terrain irregularities. The lidar bias as function of several statistical properties of the wind flow like the tilt angle, turbulence intensity, vertical velocity, atmospheric stability and the terrain characteristics have been studied. The aim of this exercise is to use this knowledge in order to define useful lidar bias data filters. Then, a methodology to correct the lidar bias caused by non-uniform wind flow is proposed, based on the initial mathematical analysis of the lidar measurements. The proposed lidar bias correction methodology has been developed focusing on the the continuous wave lidar system. In a last step, the proposed lidar bias correction methodology is validated with the data of the complex terrain measurement campaign. The methodology makes use of the wind field variations obtained from the RANS analysis. The results are presented and discussed. The advantage of this methodology is that the wind field properties at the Alaiz test site can be studied with more detail, based on the instantaneous measurements of the CW lidar. Within the project framework, the daily basis work has been done at CENER, with close guidance and support from the UPM, including an exchange period of 1.5 months. During this exchange period, the mathematical analysis of the lidar sensing of the wind velocity was defined. Furthermore, the effects of non-uniform wind fields on the lidar bias were analytically defined, after making some assumptions for the sake of simplification. Moreover, there has been an important cooperation with DTU Wind Energy, where a secondment period of 1.5 months has been done as well. During the secondment period at DTU Wind Energy, an important introductory learning has taken place. The learned aspects include the design of an experimental measurement campaign in flat terrain, the site assessment study of obstacles and terrain conditions, the data acquisition and processing, as well as the study and reporting of the measurement analysis.

And yet it shrinks: A novel method for correcting bias in forest tree growth estimates caused by water-induced fluctuations

Accuracy in tree woody growth estimates is important to global carbon budget estimation and climate-change science. Tree growth in permanent sampling plots (PSPs) is commonly estimated by measuring stem diameter changes, but this method is susceptible to bias resulting from water-induced reversible stem shrinkage. In the absence of bias correction, temporal variability in growth is likely to be overestimated and incorrectly attributed to fluctuations in resource availability, especially in forests with high seasonal and inter-annual variability in water. We propose and test a novel approach for estimating and correcting this bias at the community level. In a 50-ha PSP from a seasonally dry tropical forest in southern India, where tape measurements have been taken every four years from 1988 to 2012, for nine trees we estimated bias due to reversible stem shrinkage as the difference between woody growth measured using tree rings and that estimated from tape. We tested if the bias estimated from these trees could be used as a proxy to correct bias in tape-based growth estimates at the PSP scale. We observed significant shrinkage-related bias in the growth estimates of the nine trees in some censuses. This bias was strongly linearly related to tape-based growth estimates at the level of the PSP, and could be used as a proxy. After bias was corrected, the temporal variance in growth rates of the PSP decreased, while the effect of exceptionally dry or wet periods was retained, indicating that at least a part of the temporal variability arose from reversible shrinkage-related bias. We also suggest that the efficacy of the bias correction could be improved by measuring the proxy on trees that belong to different size classes and census timing, but not necessarily to different species. Our approach allows for reanalysis - and possible reinterpretation of temporal trends in tree growth, above ground biomass change, or carbon fluxes in forests, and their relationships with resource availability in the context of climate change. (C) 2014 Elsevier B.V. All rights reserved.

Improved Arctic sea-ice thickness projections using bias corrected CMIP5 simulations

Projections of Arctic sea ice thickness (SIT) have the potential to inform stakeholders about accessibility to the region, but are currently rather uncertain. The latest suite of CMIP5 Global Climate Models (GCMs) produce a wide range of simulated SIT in the historical period (1979–2014) and exhibit various biases when compared with the Pan-Arctic Ice Ocean Modelling and Assimilation System (PIOMAS) sea ice reanalysis. We present a new method to constrain such GCM simulations of SIT via a statistical bias correction technique. The bias correction successfully constrains the spatial SIT distribution and temporal variability in the CMIP5 projections whilst retaining the climatic fluctuations from individual ensemble members. The bias correction acts to reduce the spread in projections of SIT and reveals the significant contributions of climate internal variability in the first half of the century and of scenario uncertainty from mid-century onwards. The projected date of ice-free conditions in the Arctic under the RCP8.5 high emission scenario occurs in the 2050s, which is a decade earlier than without the bias correction, with potentially significant implications for stakeholders in the Arctic such as the shipping industry. The bias correction methodology developed could be similarly applied to other variables to reduce spread in climate projections more generally.

Bias-corrected estimators for dispersion models with dispersion covariates

In this paper we discuss bias-corrected estimators for the regression and the dispersion parameters in an extended class of dispersion models (Jorgensen, 1997b). This class extends the regular dispersion models by letting the dispersion parameter vary throughout the observations, and contains the dispersion models as particular case. General formulae for the O(n(-1)) bias are obtained explicitly in dispersion models with dispersion covariates, which generalize previous results obtained by Botter and Cordeiro (1998), Cordeiro and McCullagh (1991), Cordeiro and Vasconcellos (1999), and Paula (1992). The practical use of the formulae is that we can derive closed-form expressions for the O(n(-1)) biases of the maximum likelihood estimators of the regression and dispersion parameters when the information matrix has a closed-form. Various expressions for the O(n(-1)) biases are given for special models. The formulae have advantages for numerical purposes because they require only a supplementary weighted linear regression. We also compare these bias-corrected estimators with two different estimators which are also bias-free to order O(n(-1)) that are based on bootstrap methods. These estimators are compared by simulation. (C) 2011 Elsevier B.V. All rights reserved.

BIAS-CORRECTED MAXIMUM LIKELIHOOD ESTIMATION OF THE PARAMETERS OF THE WEIGHTED LINDLEY DISTRIBUTION

This report discusses the calculation of analytic second-order bias techniques for the maximum likelihood estimates (for short, MLEs) of the unknown parameters of the distribution in quality and reliability analysis. It is well-known that the MLEs are widely used to estimate the unknown parameters of the probability distributions due to their various desirable properties; for example, the MLEs are asymptotically unbiased, consistent, and asymptotically normal. However, many of these properties depend on an extremely large sample sizes. Those properties, such as unbiasedness, may not be valid for small or even moderate sample sizes, which are more practical in real data applications. Therefore, some bias-corrected techniques for the MLEs are desired in practice, especially when the sample size is small. Two commonly used popular techniques to reduce the bias of the MLEs, are ‘preventive’ and ‘corrective’ approaches. They both can reduce the bias of the MLEs to order O(n−2), whereas the ‘preventive’ approach does not have an explicit closed form expression. Consequently, we mainly focus on the ‘corrective’ approach in this report. To illustrate the importance of the bias-correction in practice, we apply the bias-corrected method to two popular lifetime distributions: the inverse Lindley distribution and the weighted Lindley distribution. Numerical studies based on the two distributions show that the considered bias-corrected technique is highly recommended over other commonly used estimators without bias-correction. Therefore, special attention should be paid when we estimate the unknown parameters of the probability distributions under the scenario in which the sample size is small or moderate.

Assessing GCM Convergence for India Using the Variable Convergence Score

General circulation models (GCMs) use transient climate simulations to predict climate conditions in the future. Coarse-grid resolutions and process uncertainties necessitate the use of downscaling models to simulate precipitation. However, in the downscaling models, with multiple GCMs now available, selecting an atmospheric variable from a particular model which is representative of the ensemble mean becomes an important consideration. The variable convergence score (VCS) provides a simple yet meaningful approach to address this issue, providing a mechanism to evaluate variables against each other with respect to the stability they exhibit in future climate simulations. In this study, VCS methodology is applied to 10 atmospheric variables of particular interest in downscaling precipitation over India and also on a regional basis. The nested bias-correction methodology is used to remove the systematic biases in the GCMs simulations, and a single VCS curve is developed for the entire country. The generated VCS curve is expected to assist in quantifying the variable performance across different GCMs, thus reducing the uncertainty in climate impact-assessment studies. The results indicate higher consistency across GCMs for pressure and temperature, and lower consistency for precipitation and related variables. Regional assessments, while broadly consistent with the overall results, indicate low convergence in atmospheric attributes for the Northeastern parts of India.

Ranking of global climate models for India using multicriterion analysis

Eleven GCMs (BCCR-BCCM2.0, INGV-ECHAM4, GFDL2.0, GFDL2.1, GISS, IPSL-CM4, MIROC3, MRI-CGCM2, NCAR-PCMI, UKMO-HADCM3 and UKMO-HADGEM1) were evaluated for India (covering 73 grid points of 2.5 degrees x 2.5 degrees) for the climate variable `precipitation rate' using 5 performance indicators. Performance indicators used were the correlation coefficient, normalised root mean square error, absolute normalised mean bias error, average absolute relative error and skill score. We used a nested bias correction methodology to remove the systematic biases in GCM simulations. The Entropy method was employed to obtain weights of these 5 indicators. Ranks of the 11 GCMs were obtained through a multicriterion decision-making outranking method, PROMETHEE-2 (Preference Ranking Organisation Method of Enrichment Evaluation). An equal weight scenario (assigning 0.2 weight for each indicator) was also used to rank the GCMs. An effort was also made to rank GCMs for 4 river basins (Godavari, Krishna, Mahanadi and Cauvery) in peninsular India. The upper Malaprabha catchment in Karnataka, India, was chosen to demonstrate the Entropy and PROMETHEE-2 methods. The Spearman rank correlation coefficient was employed to assess the association between the ranking patterns. Our results suggest that the ensemble of GFDL2.0, MIROC3, BCCR-BCCM2.0, UKMO-HADCM3, MPIECHAM4 and UKMO-HADGEM1 is suitable for India. The methodology proposed can be extended to rank GCMs for any selected region.

Smart meter devices and the effect of feedback on residential electricity consumption: Evidence from a natural experiment in Northern Ireland

Using a unique set of data and exploiting a large-scale natural experiment, we estimate the effect of real-time usage information on residential electricity consumption in Northern Ireland. Starting in April 2002, the utility replaced prepayment meters with advanced meters that allow the consumer to track usage in real-time. We rely on this event, account for the endogeneity of price and payment plan with consumption through a plan selection correction term, and find that the provision of information is associated with a decline in electricity consumption of 11-17%. We find that the reduction is robust to different specifications, selection-bias correction methods and subsamples of the original data. The advanced metering program delivers reasonably cost-effective reductions in carbon dioxide emissions, even under the most conservative usage reduction scenarios.