Absolute Relative Bias Research Articles

An Empirical Comparison of Some Product Estimators

In this paper, we undertake an extensive comparative study of some biased, almost unbiased and unbiased product estimators on the ground of different performance measures through Monte Carlo simulation that has not yet been initiated in the survey sampling literature. The simulation experiment is conducted using data on 20 natural populations available in the literature, and the performance indicators taken into consideration are the absolute relative bias, percentage relative efficiency, coverage rate of confidence intervals, standard deviation of the student t-statistic, and approach to symmetry (normality). This empirical study will not only facilitate to assess the overall relative performance of different competing product or product-type estimators but will also be beneficial to provide some guidelines towards further research in this direction.

Error Characteristic Analysis of Satellite-Based Precipitation Products over Mainland China

Satellite-based precipitation products (SPPs) provide valuable precipitation information for various applications. Their performance, however, varies significantly from region to region due to various data sources and production processes. This paper aims to evaluate four selected SPPs (Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks Climate Data Record (PERSIANN-CDR), Multi-Source Weighted-Ensemble Precipitation (MSWEP), Gauge-adjusted Global Satellite Mapping of Precipitation (GSMAP-gauge), and Global Precipitation Measurement (GPM)) over mainland China from 2016 to 2019. Both conventional statistical indicators (e.g., correlation coefficients (CC), root mean square error (RMSE), mean absolute error (MAE), relative bias (RB), and Nash–Sutcliffe efficiency (NSE)) and categorical indicators (probability of detection (POD), probability of true detection (POTD), false-alarm rate (FAR), and critical success index (CSI)) are used for quantitative analysis. The results show that: (1) GSMAP-gauge and GPM perform best in reproducing the spatial distribution pattern of precipitation over mainland China, whereas SPPs generally underestimate summer precipitation with a high frequency of no-rain cases. (2) MSWEP has the best capability for recording precipitation events, although some parts of northern China exhibit abnormal overestimations for winter precipitation. (3) All SPPs, especially the PERSIANN-CDR, significantly underestimate the precipitation in the mountainous areas of southwestern China. (4) The GSMAP-gauge and GPM outperformed the other two of the four SPPs, in terms of the probability density function of daily precipitation for cases (PDFc) and the probability density function of daily precipitation for volume (PDFv). Generally, PERSIANN-CDR shows the poorest performance when compared to the other three products. The product’s algorithm for estimating heavy precipitation and mountainous precipitation needs further improvement.

Analyzing the overall effects of the microbiome abundance data with a Bayesian predictive value approach.

The microbiome abundance data is known to be over-dispersed and sparse count data. Among various zero-inflated models, zero-inflated negative binomial (ZINB) model and zero-inflated beta binomial (ZIBB) model are the methods to analyze the microbiome abundance data. ZINB and ZIBB have two sets of parameters, which are for modeling the zero-inflation part and the count part separately. Most previous methods have focused on making inferences in terms of separate case-control effect for the zero-inflation part and the count part. However, in a case-control study, the primary interest is normally focused on the inference and a single interpretation of the overall unconditional mean (also known as the overall effect) of the microbiome abundance in microbiome studies. Here, we propose a Bayesian predictive value (BPV) approach to estimate the overall effect of the microbiome abundance. This approach is implemented based on R package brms. Hence, the parameters in the models will be estimated with two Markov chain Monte Carlo (MCMC) algorithms used in Stan. We performed simulations and real data applications to compare the proposed approach and R package glmmTMB with simulation method in the estimation and inference in terms of the ratio function between the overall effects from two groups in a case-control study. The results show that the performance of the BPV approach is better than R package glmmTMB with the simulation method in terms of lower absolute biases and relative absolute biases, and coverage probability being closer to the nominal level especially when the sample size is small and zero-inflation rate is high.

Assessing the Performance of ELL and EBP Models in Estimating District Level Poverty Indices in The Presence of Outliers in the Northern Region of Ghana.

The objective of this study was to assess the performance of the Elbers, Lanjouw and Lanjouw (ELL) and the Empirical Best Predictor (EBP) Small Area Estimation (SAE) models in estimating the Foster-Greer-Thobecke (FGT) poverty indices for the Northern Region of Ghana in the presence of outliers. The sixth round of the Ghana Living Standard Survey (GLSS) data and the  Population and Housing Census ( PHC) data were used for the study. The performances of these SAE models under normality and non-normality assumptions were evaluated by computing and comparing their Absolute Relative Biases and Relative Root Mean Squared Errors values under both conditions by conducting a model-based simulation study in the absence and presence of outlier contaminated data. Results from the study showed that no matter the level of contamination, the EBP model is a better performer and more stable than the ELL model in estimating all the FGT poverty indicators for the Region. Therefore, it was recommended that in future poverty estimating exercises, the EBP model be used to estimate the FGT poverty indicators for the Northern Region of Ghana.

Efficiency Comparisons of Robust and Non-Robust Estimators for Seemingly Unrelated Regressions Model

This paper studies and reviews several procedures for developing robust regression estimators of the seemingly unrelated regressions (SUR) model, when the variables are affected by outliers. To compare the robust estimators (M-estimation, S-estimation, and MM-estimation) with non-robust (traditional maximum likelihood and feasible generalized least squares) estimators of this model with outliers, the Monte Carlo simulation study has been performed. The simulation factors of our study are the number of equations in the system, the number of observations, the contemporaneous correlation among equations, the number of regression parameters, and the percentages of outliers in the dataset. The simulation results showed that, based on total mean squared error (TMSE), total mean absolute error (TMAE) and relative absolute bias (RAB) criteria, robust estimators give better performance than non-robust estimators; specifically, the MM-estimator is more efficient than other estimators. While when the dataset does not contain outliers, the results showed that the unbiased SUR estimator (feasible generalized least squares estimator) is more efficient than other estimators.

Scale-dependence of observational and modelling uncertainties in forensic flash flood analysis

The mismatch between the space–time scales of flash flood occurrence and those of the typical hydro-meteorological monitoring networks has stimulated the development of forensic flash flood analysis, which involves post-flood indirect peak discharge estimation in ungauged channels and flood response modelling driven by weather-radar rainfall estimates. However, both approaches are potentially affected by significant uncertainties. Assessment of scale dependence of such uncertainties is important to identify how uncertainty affecting forensic flash flood analysis increases with decreasing basin size. In this work, we apply the forensic methodology to the flash flood of November 18, 2013 in Sardinia (Italy). We introduce the ‘flash flood forensic consistency index’ as a tool to compare the probability distribution of peak discharge uncertainties from observational and model estimates, and to determine the scale effects of the forensic analysis concept. Uncertainties in field-based peak flow estimates are evaluated through a first-order error analysis of the Taylor-series approximation of the slope-conveyance method, whereas uncertainties in flash flood modelling are based on the Generalized Likelihood Uncertainty Estimation methodology using a distributed hydrologic model. Results show no significant relationship between observational and modelling uncertainties, considered independently, and basin area and channel bed slope. Conversely, when considering the interaction between the two uncertainty distributions, a relationship arises between their degree of overlap and basin size. In particular, with decreasing basin area or increasing channel bed slope, the absolute relative bias between the estimated peak flow values increases more than their relative uncertainties, decreasing the consistency index. This calls for more robust approaches for the analysis of flash flood response in small-sized rugged-relief mountain basins, which are of high interest for flood risk management.

Estimation of Parameters of Lomax Distribution by Using Maximum Product Spacings Method

Abstract: The objective of this paper is to estimate the parameters of Lomax distribution with shape parameter(α) and scale parameter(λ). In this heuristic algorithm, the Maximum Product Spacings Method is used to Estimates the parameters of Lomax Distribution. We also computed Average Estimate (AE), Variance (VAR), Mean Absolute Deviation (MAD), Mean Square Error (MSE), Relative Error (RE) and Relative Absolute Bias (RAB) for both the parameters under grouped sample based on 1000 simulations to assess the performance of the estimators. And also compare Maximum Product Spacings Method with Least Squares Regression Method and Median Rank Regression Method. Keywords: Lomax Parameters, Grouped sample, Maximum Product Spacings method, simulation

Parameter Estimation Based on Double Ranked Set Samples with Applications to Weibull Distribution

In this paper, the likelihood function for parameter estimation based on double ranked set sampling (DRSS) schemes is introduced. The proposed likelihood function is used for the estimation of the Weibull distribution parameters. The maximum likelihood estimators (MLEs) are investigated and compared to the corresponding ones based on simple random sampling (SRS) and ranked set sampling (RSS) schemes. A Monte Carlo simulation is conducted and the absolute relative biases, mean square errors, and efficiencies are compared for the different schemes. It is found that, the MLEs based on DRSS is more efficient than MLE using SRS and RSS for estimating the two parameters of the Weibull distribution (WD).

Triple collocation-based error estimation and data fusion of global gridded precipitation products over the Yangtze River basin

Error estimation and data fusion are critical to improving the accuracy of global model- and satellite-based precipitation products for practical applications. However, they face challenges over vast areas of the world due to limited ground observations. Triple collocation (TC) method can overcome this limitation and provide an efficient way for error estimation without the “ground truth” and thus also for data fusion, by leveraging multi-source observations and model outputs, which have been increasingly available in recent years. In this work, we conducted a comprehensive study on error estimation and data fusion of a number of global gridded precipitation products over the Yangtze River basin from 2015 to 2018 using TC and multiplicative TC (MTC) methods. We use three satellite-based precipitation products such as the IMERG Final (IMERG-F), PERSIANN-CDR (PCDR) and SM2RAIN-ASCAT (SM2R), and one reanalysis dataset ERA5 which contains precipitation estimates. They were grouped into two TC triplets based on different combinations: IMERG-F + SM2R + ERA5 and PCDR + SM2R + ERA5. For performance evaluation, the TC-based error estimation methods were compared to the traditional method using rain gauge data, and the TC-based data fusion methods were compared with two widely-used data fusion methods Bayesian Model Averaging (BMA) and Random Forest based MErging Procedure (RF-MEP). Results showed that ERA5 had the best performance with the largest correlation coefficient (CC, 0.435), while PCDR had the worst accuracy with the smallest CC (0.304) and the largest absolute relative bias (RB, 0.365). TC tended to underestimate the root mean square error (RMSE) with respect to the traditional gauged-based method, but MTC showed a consistent result owing to the employment of a multiplicative error model. The performance of TC-based data fusion methods had no significant difference from BMA and RF-MEP. All data fusion results were better than the original triplets, as the mean CC value increased from 0.38 to 0.47 and the mean RMSE decreased from 15.0 to 13.5 mm/day. In addition, we found that the zero value replacement in MTC had great influence on error estimation, while had limited impacts on data fusion.

Estimation of Parameters of Pert Distribution by Using Method of Moments

Abstract: The method of moments has been widely used for estimating the parameters of a distribution. Usually lower order moments are wont to find the parameter estimates as they're known to possess less sampling variability. The method of moments may be a technique for estimating the parameters of a statistical model. It works by finding values of the parameters that end in a match between the sample moments and therefore the population moments (as implied by the model). the Method of moment Estimator is used to find out Estimates the parameters of PERT Distribution. We also compare equispaced and unequispaced Optimally Constructed Grouped data by the method of an Asymptotically Relative Efficiency. We also computed Average Estimate (AE), Variance (VAR), Standard Deviation (STD), Mean Absolute Deviation (MAD), Mean Square Error (MSE), Simulated Error (SE) and Relative Absolute Bias (RAB) for both the parameters under grouped sample supported 1000 simulations to assess the performance of the estimators. Keywords: Method of Moments, PERT Distribution, equispaced and unequipped Optimal Grouped sample

28-LB: RTCGM Performance at Different Sensor Wear Sites during Prolonged Aerobic Exercise

Strenuous exercise may disrupt the local equilibria between vascular and interstitial glucose concentrations. We measured interstitial glucose levels during aerobic exercise in different anatomical regions with continuous glucose monitoring (CGM) sensors and compared them to capillary blood glucose (BG) levels. We enrolled 10 individuals, 7 with type 1 diabetes (T1D) and 3 without (healthy volunteers), for a 50-mile bicycle ride. Three CGM sensors (Dexcom G6) were placed on each participant, with one each in the upper arm, abdomen and thigh. BG values were obtained at the start of the ride and every 30 minutes thereafter. Accuracy of CGM levels was assessed for each insertion site as the mean absolute relative difference (MARD) and bias versus contemporaneous BG levels. Table shows that arm-worn sensors were more accurate in terms of MARD, and also had smaller numerical bias, than sensors placed in either the abdomen or thigh. Sensor accuracy was not significantly affected by the presence or absence of a diabetes diagnosis and accuracy metrics were consistent with those reported in the device’s instructions for use. CGM users may benefit from wearing sensors on the arm during sustained bicycle rides.View largeDownload slideView largeDownload slide DisclosureM. Mueller-korbsch: Research Support; Self; Dexcom, Inc., Menarini Group, Novo Nordisk Inc. L. Fruehwald: None. M. Heer: None. G. Rega-kaun: None. M. Fangmeyer-binder: None. P. Fasching: None.

A New Calibration Estimator of Population Mean for Small Area with Nonresponse

This paper considered the challenges of population mean estimation in small area that is characterized by small or no sample size in the presence of unit nonresponse and presents a calibration estimator that produces reliable estimates under stratified random sampling from a class of synthetic estimators using calibration approach with alternative distance measure. Examining the proposed estimator relatively with existing ones under three distributional assumptions: normal, gamma, and exponential distributions with percent average absolute relative bias, percent average coefficient of variation, and average mean squared error as evaluation criteria using simulation analysis technique, the new estimator exhibited a more reliable estimate of the mean with less bias and greater gain in efficiency. Further evaluation using coefficient of variation under varying nonresponse rates to validate the results of variations suggests that the estimator is a suitable alternative for small area estimation. This finding has therefore contributed to the development of an ultimate estimator for small area estimation in the presence of unit nonresponse.

Ranked set sampling with application of modified Kies exponential distribution

This paper is concerned with estimating the parameters of the modified Kies exponential (MKEx) distribution using the classical estimation method, based on ranked set sampling (RSS), Likelihood estimation method is used for estimating the MKEx parameters. The maximum likelihood estimators (MLEs) are then investigated and compared to the corresponding ones based on simple random sampling (SRS) and RSS designs. A Monte Carlo simulation is used to obtain the absolute relative biases, mean square errors for the MKEx distribution. Efficiencies are compared for the different designs. The relative efficiency of RSS design was found to increase with increasing the number of cycles, compared with other designs for the MKEx distribution.

Estimation of the Exponential Pareto Distribution’s Parameters under Ranked and Double Ranked Set Sampling Designs

In this paper, the derivation of the likelihood function for parameter estimation based on double ranked set sampling (DRSS) designs used by Sabry el.al.; (2019) for the estimation of the parameters of the power generalized Weibull distribution is considered. The developed likelihood function is then used for the estimation of the exponential Pareto distribution parameters. The maximum likelihood estimators (MLEs) are then investigated and compared to the corresponding ones based on simple random sampling (SRS) and ranked set sampling (RSS) designs. A Monte Carlo simulation is conducted and the absolute relative biases, mean square errors, and efficiencies are compared for the different designs. The relative efficiency of the DRSS estimates with respect to other designs was found to be higher in case of the exponential Pareto distribution (EP).

Inference on a New Lifetime Distribution under Progressive Type II Censoring for a Parallel-Series Structure

A new lifetime distribution, called exponential doubly Poisson distribution, is proposed with decreasing, increasing, and upside-down bathtub-shaped hazard rates. One of the reasons for introducing the new distribution is that it can describe the failure time of a system connected in the form of a parallel-series structure. Some properties of the proposed distribution are addressed. Four methods of estimation for the involved parameters are considered based on progressively type II censored data. These methods are maximum likelihood, moments, least squares, and weighted least squares estimations. Through an extensive numerical simulation, the performance of the estimation methods is compared based on the average of mean squared errors and the average of absolute relative biases of the estimates. Two real datasets are used to compare the proposed distribution with some other well-known distributions. The comparison indicates that the proposed distribution is better than the other distributions to match the data provided.

Bayesian Spatial and Trend Analysis on Ozone Extreme Data in South Korea: 1991–2015

Background. Extreme events like flooding, extreme temperature, and ozone depletion are happening in every corner of the world. Thus, the need to model such rare events having enormous damage has been getting priorities in most countries of the world. Methods. The dataset contains the ozone data from 29 representative air monitoring sites in South Korea collected from 1991 to 2015. Spatial generalized extreme value (GEV) using maximum likelihood estimation (MLE) and two max-stable and Bayesian kriging models are the statistical models used for analysis. Moreover, predictive performances of these statistical models are compared using measures like root-mean-squared error (RMSE), mean absolute error (MAE), relative bias (rBIAS), and relative mean separation (rMSEP) have been utilized. Results. From the time plot of ozone data, extreme ozone concentration is increasing linearly within the specified period. The return level of ozone concentration after 10, 25, 50, and 100 years have been forecasted and showed that there was an increasing trend in ozone extremes. High spatial variability of ozone extreme was observed, and those areas around the territories were having extreme ozone concentration than the centers. Moreover, Bayesian Kriging brought about relatively the minimum RMSE compared to the other models. Conclusion. The extreme ozone concentration has clearly showed a positive trend and spatial variation. Moreover, among the models considered in the paper, the Bayesian Kriging has been chosen as the better model.

Evaluation of TRMM 3B42V7 and CHIRPS Satellite Precipitation Products as an Input for Hydrological Model over Eastern Nile Basin

Nowadays, precipitation estimations based on satellite products (PESPs) have become an alternative source of sparse rainfall gauge data for various hydrologic applications, especially in scarce data regions like Africa which suffer from a lack of surface monitoring resources. Hence, their accuracy and performances must be evaluated by climate variance, complex topography, and geographical position due to their variation from one region to another. The Blue Nile is considered the crucial tributary of the Nile River which provides the utmost share of the river flow. So, this study aims to evaluate high-resolution PESPs [Tropical Rainfall Measuring Mission product 3B42V7 (TRMM 3B42V7) and Climate Hazards Group InfraRed Precipitation with Station data (CHIRPS)] over the Blue Nile basin (BNB) using categorical metrics [probability of detection (POD), and false alarm ratio (FAR)] and continuous statistical indicators [root mean square error (RMSE), mean absolute error (MAE), relative bias (RE), and correlation coefficient (R)] to assess its capability of rainfall amount detection and event occurrence. Hydrological river basin environmental assessment model (Hydro-BEAM) distributed model is also employed to investigate their capabilities to predict streamflow over the BNB. The hydrological daily and monthly simulations were calibrated and validated at Khartoum and Eldeim station for the period 1998–2007. Further, a hydrological monthly simulation was performed at various stations in the Eastern Nile basin (ENB) within the period 2001–2007 using Hydro-BEAM to appraise the ability of both precipitation products to predict streamflow. Moreover, a trial is made to adopt Hydro-BEAM to consider into the runoff simulation the influence of exiting dams during the simulation periods along the ENB to avoid the uncertainness and inaccuracies in simulation results.

A laboratory investigation on the potential of computational intelligence approaches to estimate the discharge coefficient of piano key weir

The piano key weir (PKW) is a type of nonlinear control structure that can be used to increase unit discharge over linear overflow weir geometries, particularly when the weir footprint area is restricted To predict the outflow passing over a piano key weir, the discharge coefficient in the general equation of weir needs to be known. This paper presents the results of laboratory model testing of a piano key weir located on the straight open channel flume in the hydraulic laboratory of Bu-Ali Sina University. The discharge coefficient of piano key weir is estimated by using four computational intelligence approaches, namely, feed forward back-propagation neural network (FFBPN), an extension of genetic programming namely gene-expression programming (GEP), least square support vector machine (LSSVM) and extreme learning machine (ELM). For this purpose, 70 laboratory test results were used for determining discharge coefficient of piano key weir for a wide range of discharge values. Coefficient of determination (R2), Nash-Sutcliffe efficiency coefficient (NS), root mean square error (RMSE), mean absolute relative error (MARE), scatter index (SI) and BIAS are used for measuring the models’ performance. Overall performance of the models shows that, all the studied models are able to estimate discharge coefficient of piano key weir satisfactorily. Comparison of results showed that the ELM (R2=0.997 and NS= 0.986) and LSSVM (RMSE=0.016 and MARE=0.027) models were able to produce better results than the other models investigated and could be employed successfully in modeling discharge coefficient from the available experimental data.

An assessment of sampling designs using SCR analyses to estimate abundance of boreal caribou.

Accurately estimating abundance is a critical component of monitoring and recovery of rare and elusive species. Spatial capture–recapture (SCR) models are an increasingly popular method for robust estimation of ecological parameters. We provide an analytical framework to assess results from empirical studies to inform SCR sampling design, using both simulated and empirical data from noninvasive genetic sampling of seven boreal caribou populations (Rangifer tarandus caribou), which varied in range size and estimated population density. We use simulated population data with varying levels of clustered distributions to quantify the impact of nonindependence of detections on density estimates, and empirical datasets to explore the influence of varied sampling intensity on the relative bias and precision of density estimates. Simulations revealed that clustered distributions of detections did not significantly impact relative bias or precision of density estimates. The genotyping success rate of our empirical dataset (n = 7,210 samples) was 95.1%, and 1,755 unique individuals were identified. Analysis of the empirical data indicated that reduced sampling intensity had a greater impact on density estimates in smaller ranges. The number of captures and spatial recaptures was strongly correlated with precision, but not absolute relative bias. The best sampling designs did not differ with estimated population density but differed between large and small ranges. We provide an efficient framework implemented in R to estimate the detection parameters required when designing SCR studies. The framework can be used when designing a monitoring program to minimize effort and cost while maximizing effectiveness, which is critical for informing wildlife management and conservation.

Efficiency of Domain Mean Estimators in the Presence of Non-response Using Two-Stage Sampling with Non-linear and Linear Cost Function

This study compares the efficiency of the estimators of the domain population mean computed using double sampling for ratio estimation design with linear, non-linear or logarithmic cost functions. In the estimation of the domain mean, information of the study and auxiliary variables which suffers from non-response at the second phase sampling has been used. Optimal stratum sample sizes for a given set of unit costs have been computed using Lagrangian multiplier partial differential equations and Taylor’s linearization series. The relative precision of the domain population mean estimate obtained has been compared using mean square error, relative efficiency, Bias and absolute relative bias. From the results obtained, the estimator of the domain population mean computed using auxiliary information had better efficiency on average compared to those computed without auxiliary information. It is also noted that of the three cost functions used in the computation of estimators, logarithmic cost function produced superior estimator compared to that computed using linear or non-linear (quadratic) cost function. This method of estimation can be used in estimating efficiently, infected population incidence rate by a given pandemic using optimal sample size at a minimum survey cost.