Unbiasedness Research Articles

Improved exponential type mean estimators for non-response case using two concomitant variables in simple random sampling

This paper addresses new exponential estimators for population mean in case of non-response on both the study and the concomitant variables using simple random sampling. The expressions for theoretical bias and mean square error of new estimators are derived up to first-order approximation and comparisons are made with the existing estimators. The proposed estimators are observed more efficient as compared to the considered estimators in the literature. For instance, the classical [4] unbiased estimator, the estimator of [9], and other existing estimators under the explained conditions. The theoretical results are supported numerically by using real-life data sets, under the criteria of bias, mean square error, percent relative efficiency and mathematical conditions. It is also clear from the numerical results that the suggested exponential estimators performed better than the estimators in the literature.

What contributes more to BRI economic growth, renewable or non-renewable energy consumption: A third generation panel data analysis.

Given the increasing investment by Belt and Road Initiative (BRI) participants in the renewable energy industry, it is imperative to ascertain how much this investment contributes to economic growth. The objective of this study is to ascertain the extent to which renewable energy contributes to economic growth within the Belt and Road Initiative compared to non-renewable energy sources. Prior studies have yet to incorporate oil prices as a variable in the production function, among other output aspects. This study integrates the inclusion of real oil prices as a variable within the production function alongside capital, labor, renewable energy consumption, and non-renewable energy consumption. A cohort including 49 Belt and Road Initiative participants was formed, encompassing data from 1990 to 2019. The data has undergone an initial examination to assess cross-sectional dependence, slope heterogeneity, and structural break(s), and are verified. Hence, third-generation panel data analysis has been utilized. The continuously updated fully modified estimator and continuously updated biased corrected estimator provide evidence supporting the notion that renewable energy plays a substantial role in fostering economic growth within nations participating in the Belt and Road Initiative. Furthermore, this contribution is found to be more pronounced when compared to the impact of non-renewable energy sources. The study's findings inform policy recommendations at both the BRI and nationallevel.

Confidence intervals for intentionally biased estimators

. We propose and study three confidence intervals (CIs) centered at an estimator that is intentionally biased to reduce mean squared error. The first CI simply uses an unbiased estimator’s standard error; compared to centering at the unbiased estimator, this CI has higher coverage probability for confidence levels above 91. 7%, even if the biased and unbiased estimators have equal mean squared error. The second CI trades some of this “excess” coverage for shorter length. The third CI is centered at a convex combination of the two estimators to further reduce length. Practically, these CIs apply broadly and are simple to compute.

Finite-Sample Bias of the Linear Excess Relative Risk in Cohort Studies of Computed Tomography-Related Radiation Exposure and Cancer.

The linear excess relative risk (ERR) is the most commonly reported measure of association in radiation epidemiological studies, when individual dose estimates are available. While the asymptotic properties of the ERR estimator are well understood, there is evidence of small sample bias in case-control studies of treatment-related radiation exposure and second cancer risk. Cohort studies of cancer risk after exposure to low doses of radiation from diagnostic procedures, e.g., computed tomography (CT) examinations, typically have small numbers of cases and risks are small. Therefore, understanding the properties of the estimated ERR is essential for interpretation and analysis of such studies. We present results of a simulation study that evaluates the finite-sample bias of the ERR estimated by time-to-event analyses and its confidence interval using simulated data, resembling a retrospective cohort study of radiation-related leukemia risk after CT examinations in childhood and adolescence. Furthermore, we evaluate how the Firth-corrected estimator reduces the finite-sample bias of the classical estimator. We show that the ERR is overestimated by about 30% for a cohort of about 150,000 individuals, with 42 leukemia cases observed on average. The bias is reduced for higher baseline incidence rates and for higher values of the true ERR. As the number of cases increases, the ERR is approximately unbiased. The Firth correction reduces the bias for all cohort sizes to generally around or under 5%. Epidemiological studies showing an association between radiation exposure from pediatric CT and cancer risk, unless very large, may overestimate the magnitude of the relationship, while there is no evidence of an increased chance for false-positive results. Conducting large studies, perhaps by pooling individual studies to increase the number of cases, should be a priority. If this is not possible, Firth correction should be applied to reduce small-sample bias.

Most-likely DCF Estimates of Magnetic Field Strength

The Davis–Chandrasekhar–Fermi (DCF) method is widely used to evaluate magnetic fields in star-forming regions. Yet it remains unclear how well DCF equations estimate the mean plane-of-the-sky field strength in a map region. To address this question, five DCF equations are applied to an idealized cloud map. Its polarization angles have a normal distribution with dispersion σ θ , and its density and velocity dispersion have negligible variation. Each DCF equation specifies a global field strength B DCF and a distribution of local DCF estimates. The “most-likely” DCF field strength B ml is the distribution mode, for which a correction factor β ml ≡ B ml/B DCF is calculated analytically. For each equation, β ml < 1, indicating that B DCF is a biased estimator of B ml. The values of β ml are β ml ≈ 0.7 when BDCF∝σθ−1 due to turbulent excitation of Alfvénic MHD waves, and β ml ≈ 0.9 when BDCF∝σθ−1/2 due to non-Alfvénic MHD waves. These statistical correction factors β ml have partial agreement with correction factors βsim obtained from MHD simulations. The relative importance of the statistical correction is estimated by assuming that each simulation correction has both a statistical and a physical component. Then the standard, structure function, and original DCF equations appear most accurate because they require the least physical correction. Their relative physical correction factors are 0.1, 0.3, and 0.4 on a scale from 0 to 1. In contrast, the large-angle and parallel-δ B equations have physical correction factors 0.6 and 0.7. These results may be useful in selecting DCF equations, within model limitations.

Mill and Landbase Attributes Condition Response Rates to Timber Product Output Surveys in the Western United States

Abstract Since the 1940s, the USDA Forest Service has surveyed roundwood receiving facilities to report on timber products output (TPO). The TPO program provides information on forest removals, processing capacity, and wood product markets, complementing inventory estimates of status and change. The program adopted an annual state-level probability sampling design in 2019 and this research evaluates rates of unit nonresponse (UN) in surveys of eleven western states over reference years 2019–2021. The overall response rate for this region and period was 43.7%, which appears low relative to prior western surveys. Response rates also differed significantly by state, facility type, and facility size class. Furthermore, distributions of forestland ownership and harvest levels over potential facility feedstock areas differed significantly between respondents and nonrespondents for an important class of large sawmills. Taken together, these results suggest UN is substantially degrading the precision of western TPO surveys and may be inducing appreciable bias in current estimators. At the same time, response rates were significantly higher where responses were obtained in previous years, suggesting a positive facilitation effect. The implications of these rates and patterns in UN for TPO survey design and estimation are discussed. Study Implications: The USDA Forest Service estimates timber products output (TPO) from US forests using sample surveys of roundwood receiving facilities. In TPO samples of western states for the period 2019–2021, the average response rate was only 43.7%. The level of unit nonresponse will substantially degrade the precision of TPO estimates at state and regional levels, while the observed patterns may induce bias. Further research is needed to identify the bias and precision of current and alternative estimators and to investigate survey implementation factors or design enhancements that would allow more intensive follow-up efforts to focus on a smaller number of nonrespondents.

Testing temporal transferability of remote sensing models for large area monitoring

Applying remote sensing models outside the temporal range of their training data, referred to as temporal model transfer, has become common practice for large area monitoring projects that extrapolate models for hindcasting or forecasting to time periods lacking reference data. However, the development of appropriate validation methods for temporal transfer has lagged behind its rapid adoption. Breaking temporal transfer's assumption of temporal consistency in both remote sensing and reference data and their relationship to each other could lead to biased pixel-level predictions and small area estimators, compromising the operational validity of large area monitoring products. Few studies using temporal transfer have evaluated its effects on model accuracy at the pixel/plot level, and the propensity for biased small area estimators and trends resulting from temporal transfer remains unexplored. We present a framework for evaluating temporal transferability by combining temporal cross-validation with a multiscale map assessment to aid in identifying where and when biased model predictions could scale to small area estimates and affect predicted trends.This validation framework is demonstrated in a case study of annual percent tree canopy cover mapping in Michigan. We tested and compared temporal transferability of random forest models of canopy cover derived from 2010 to 2016 systematic dot-grid photo-interpretations at Forest Inventory and Analysis plots with Landsat spectral indices fit with the LandTrendr temporal segmentation algorithm serving as the primary predictor variables. The temporal cross-validation error (mean RMSE = 13.9% cover) was higher than the common validation approach of considering all time periods of testing data together (RMSE = 13.6% cover) and lower than models trained and tested within the same year (mean RMSE = 14.2% cover). However, the bias of model predictions and small area estimators for individual years was higher with temporal transfer models than when applying models within the same year as their training data. We also evaluated how training models using different temporal subsets and with and without LandTrendr fitting affected predictions of Michigan's 1984–2020 predicted annual mean cover. The mean cover from LandTrendr-based models followed expected and consistent trends and had less difference between models trained with different temporal subsets (max difference = 5.8% cover). While those from Landsat had high interannual variations and greater difference between temporal models (max difference = 11.2% cover). The results of this case study demonstrate that evaluation of temporal transferability is necessary for establishing the operational validity of large area monitoring products, even when using time series algorithms that improve temporal consistency.

The proposed model for analyzing off-street parking Dynamics: A case study of Taipei City

To reduce traffic congestion, air pollution, and lost revenue due to wasted driving around looking for parking spaces, effective parking management has become a crucial issue in urban areas. Previous studies have shown that parking demand is related to the location of parking spaces/lots, parking fees, time spent looking for spaces, and various driver and environmental characteristics. However, there have been more studies of on-street rather than off-street parking. Also, the spatio-temporal variance between variables and turnover rate (such as the hours of operation for various types of Points of Interest (POIs) as well as the causes of bias estimators has been largely overlooked.To solve the above problems, the Geographical and Temporal Weighted Regression (GTWR) model was utilized in this study to predict the hourly parking turnover rate in off-street parking lots. The flexible coefficient setting of this model can be used to capture the spatial and temporal variance. In addition to this model, the Geographically Weighted Regression (GWR) and the Ordinary Least Squares (OLS) models were used as a basis for comparison. The study included 346 public off-street parking lots in Taipei and 10 types of nearby POIs. The study period was for 24 h on August 31, 2021. Due to the dissimilar trend of the turnover rate, the researchers separated all parking lots into three groups for regression analysis: those that experience a daytime decrease, remain stable, and those with an increase during the day.Our results show the following: (1) For the types of parking lots that experienced increases and decreases, the GTWR model performed best for the prediction of hourly turnover rate, while all models performed similarly for the prediction of the stable type parking lot. (2) With regard to related factors (the type 1 parking lot for example), parking lots in areas with more traditional markets, MRT stations, and with fewer schools, supermarkets, hotel bus stops, and lower parking fees tended to have higher turnover rates. (3) Incorporating a more precise POI dataset (the number and types of POIs as well as their business hours) and applying a suitable spatial temporal model improved the parking demand model’s performance. However, the GTWR model’s limitations may hamper its performance, especially with regard to analysis of the time-stable parking lots or variables. Future studies might include other datasets, such as nearby private parking lots or holiday data to improve the model fit.

Adjusted variance estimators based on minimizing mean squared error for stratified random samples

In the realm of survey data analysis, encountering substantial variance relative to bias is a common occurrence. In this study, we present an innovative strategy to tackle this issue by introducing slightly biased variance estimators. These estimators incorporate a constant c within the range of 0 to 1, which is determined through the minimization of Mean Squared Error (MSE) for c × ( variance estimator ) . This research builds upon the foundation laid by Kourouklis (2012, A new estimator of the variance based on minimizing mean squared error. The American Statistician, 66(4), 234–236) and extends their work into the domain of survey sampling. Extensive simulation studies are conducted to illustrate the superior performance of the adjusted variance estimators when compared to standard variance estimators, particularly in terms of MSE. These findings underscore the efficacy of our proposed approach in enhancing the precision of variance estimation within the context of survey data analysis.

A two-parameter estimator for correlated regressors in gamma regression model

Gamma Modified Two Parameter (GMTP) is a novel biased two-parameter estimator proposed to address the effects of multicollinearity in Generalized Linear Models (GLMs). An expansion of the linear regression model's Modified Two Parameters (MTP) is the newly suggested estimator. The performance of the GMTP estimator over the maximum likelihood estimator (MLE), gamma ridge estimator (GRE), gamma Liu estimator (GLE), and gamma Liu-type estimator (GLTE) reviewed in this article are theoretically compared, and the estimator's properties is discussed. A simulation study that examine the effects of the dispersion parameter, sample size, explanatory variables, and degree of correlation are used to examine the superiority of the GMTP with four different biasing parameters over the MLE, GRE, GLE, and GLTE with regard to the estimated MSE criterion. The GMTP estimator with biasing parameters and outperforms the MLE, GRE, GLE, and GLTE, according to simulation research. More research can be done to see how well the GMTP estimator performs in comparison to other estimators that were not examined in this study. 2 k 4 k

Identification and responses to positivity violations in longitudinal studies: an illustration based on invasively mechanically ventilated ICU patients

Identification and estimation of causal effects relies on the positivity assumption, which states that there should be some positive probability of having each treatment level of interest, regardless of covariate levels. Violations of positivity can lead to both non-identified target causal parameters, estimator bias and inflated variance. We discuss reasons for and responses to positivity violations when the causal effect of interest involves treatments or exposures at multiple time points. For illustration, we use a data example involving the cumulative effect of controlling arterial oxygen tension over time on death among ICU patients receiving invasive mechanical ventilation. We distinguish between practical (by chance) violations that relate to sample size and structural violations in which certain treatment levels occur with zero probability for certain covariate levels. We focus on responses that either redefines the target population, e.g. via trimming or redefines the intervention making it more dynamic or more stochastic. Supported by a simulation study, we illustrate how these responses help restore needed positivity but also modify the target causal parameter. We further introduce an inability to intervene variable and show how such a variable will often be a time-dependent confounder and essential when addressing structural positivity violations in longitudinal settings.

Performance of Alternative Estimators in the Poisson-Inverse Gaussian Regression Model: Simulation and Application

Abstract The study proposed and compared the biased estimators for the Poisson-Inverse Gaussian regression model to deal with correlated regressors. The limitations of each biased estimator are also discussed. Additionally, some biasing parameters for the Stein estimator are proposed. The performance of estimators is evaluated with the help of a simulation study and a real-life application based on the minimum mean squared error criterion. The simulation and application findings favor the ridge estimator with specific biasing parameters because it provides less variation than others.

Optimal Photometry of Point Sources: Joint Source Flux and Background Determination on Array Detectors—from Theory to Practical Implementation

In this paper we study the joint determination of source and background flux for point sources as observed by digital array detectors. We explicitly compute the two-dimensional Cramér–Rao absolute lower bound (CRLB) as well as the performance bounds for high-dimensional implicit estimators from a generalized Taylor expansion. This later approach allows us to obtain computable prescriptions for the bias and variance of the joint estimators. We compare these prescriptions with empirical results from numerical simulations in the case of the weighted least squares estimator (introducing an improved version, denoted stochastic weighted least-squares) as well as with the maximum likelihood estimator, finding excellent agreement. We demonstrate that these estimators provide quasi-unbiased joint estimations of the flux and background, with a variance that approaches the CRLB very tightly and are, hence, optimal, unlike the case of sequential estimation used commonly in astronomical photometry which is sub-optimal. We compare our predictions with numerical simulations of realistic observations, as well as with observations of a bona fide non-variable stellar source observed with TESS, and compare it to the results from the sequential estimation of background and flux, confirming our theoretical expectations. Our practical estimators can be used as benchmarks for general photometric pipelines, or for applications that require maximum precision and accuracy in absolute photometry.

On the bias in the AUC variance estimate

The area under the Receiver Operating Characteristic (ROC) curve (AUC) is a standard metric for quantifying and comparing binary classifiers. A popular approach to estimating the AUCs and the associated variabilities – the variance of the AUC or the full covariance matrix of multiple correlated AUCs – is the one proposed by DeLong et al. (1988), which is based on the Mann Whitney two-sample U-statistics. The bias of a variance estimator is an important factor in applications such as hypothesis testing and construction of confidence intervals – a negatively biased variance estimator may lead to incorrect conclusions, and a positive bias is conservative hence preferable. In this work, we show that the (co-)variance estimate in DeLong’s approach is always positively biased. More specifically, the difference matrix between the expectation of the estimated covariance and the true covariance is a positive semi-definite matrix. This bias is non-negligible when the sample size is small, and quickly diminishes as the sample size increases. Our method relies on constructing, from the AUC kernel, a random variable whose (co-)variance matrix coincides with the bias, thereby establishing the claim. We also discuss alternative approaches to AUC variance estimation that may potentially reduce the bias.

A New biased estimator and variations based on the Kibria Lukman Estimator

A New biased estimator and variations based on the Kibria Lukman Estimator

Kibria–Lukman estimator for the zero inflated negative binomial regression model: theory, simulation and applications

The zero inflated negative binomial model is an appropriate choice to model count response variables with excessive zeros and over-dispersion simultaneously. This article addresses the parameter estimation for the zero-inflated negative binomial model when there are many predictors and the problems of multicollinearity are present. Since, under multicollinearity, the widely used maximum likelihood estimator becomes unstable, this article proposes an alternative estimator, called Kibria–Lukman estimator for the zero inflated negative binomial model and provided some new biasing parameters. Then compared the performance of Kibria–Lukman estimator with some of the traditional biased estimators, that is, ridge and Liu estimators. The superiority of the proposed estimator is systematically scrutinized both theoretically and numerically. For numerical assessment, we conduct a Monte Carlo simulation study under different controlled factors. A numerical example is also applied to appraise the performance of proposed estimator. Based on the simulation and example results, we observed that the performance of the proposed estimator under different biasing parameters was better than that of the maximum likelihood estimator and other involved biased estimation methods when there exists a high but imperfect multicollinearity.

BETA-BINOMIAL MODEL IN SMALL AREA ESTIMATION USING HIERARCHICAL LIKELIHOOD APPROACH

Small Area Estimation is a statistical method used to estimate parameters in sub-populations with small or even no sample sizes. This research aims to evaluate the Beta-Binomial model's performance for estimating small areas at the area level. The estimation method used is Hierarchical Likelihood (HL). The data used are simulation data and empirical data. Simulation studies were used to investigate the proposed model. The estimator's Mean Squared Error of Prediction (MSEP) and Absolute Bias (AB) estimator values determine the best estimation criteria. An empirical study using data on the illiteracy rate at the sub-district level in Bengkulu Province. The results of the simulation study show that, in general, the parameter estimators are nearly unbiased. Proportion prediction has the same tendency as parameters. Finally, the HL estimator has a small MSEP estimator. The results of an empirical study show that the average illiteracy rate in Bengkulu province is quite diverse. Kepahiang District has the highest average illiteracy rate in Bengkulu Province in 2021.

Bias reduction for semi-competing risks frailty model with rare events: application to a chronic kidney disease cohort study in South Korea.

In a semi-competing risks model in which a terminal event censors a non-terminal event but not vice versa, the conventional method can predict clinical outcomes by maximizing likelihood estimation. However, this method can produce unreliable or biased estimators when the number of events in the datasets is small. Specifically, parameter estimates may converge to infinity, or their standard errors can be very large. Moreover, terminal and non-terminal event times may be correlated, which can account for the frailty term. Here, we adapt the penalized likelihood with Firth's correction method for gamma frailty models with semi-competing risks data to reduce the bias caused by rare events. The proposed method is evaluated in terms of relative bias, mean squared error, standard error, and standard deviation compared to the conventional methods through simulation studies. The results of the proposed method are stable and robust even when data contain only a few events with the misspecification of the baseline hazard function. We also illustrate a real example with a multi-centre, patient-based cohort study to identify risk factors for chronic kidney disease progression or adverse clinical outcomes. This study will provide a better understanding of semi-competing risk data in which the number of specific diseases or events of interest is rare.

The odd log- logistic Power Inverse Lindley distribution: Model, Properties and Applications

In this article, we introduce a new three-parameter odd log-logistic power inverse Lindley distribution and discuss some of its properties. These include the shapes of the density and hazard rate functions, mixture representation, the moments, the quantile function, and order statistics. Maximum likelihood estimation of the parameters and their estimated asymptotic standard errors are derived. Three algorithms are proposed for generating random data from the proposed distribution. A simulation study is carried out to examine the bias and root mean square error of the maximum likelihood estimators of the parameters. An application of the model to three real data sets is presented finally and compared with the fit attained by some other well-known two and three-parameter distributions for illustrative purposes. It is observed that the proposed model has some advantages in analyzing lifetime data as compared to other popular models in the sense that it exhibits varying shapes and shows more flexibility than many currently available distributions.

Magnification bias estimators for realistic surveys: an application to the BOSS survey

ABSTRACT In addition to the intrinsic clustering of galaxies themselves, the spatial distribution of galaxies observed in surveys is modulated by the presence of weak lensing due to matter in the foreground. This effect, known as magnification bias, is a significant contaminant to analyses of galaxy-lensing cross-correlations and must be carefully modelled. We present a method to estimate the magnification bias in spectroscopically confirmed galaxy samples based on finite differences of galaxy catalogues while marginalizing over errors due to finite step size. We use our estimator to measure the magnification biases of the CMASS and LOWZ samples in the SDSS BOSS galaxy survey, analytically taking into account the dependence on galaxy shape for fibre and PSF magnitudes, finding αCMASS = 2.71 ± 0.02 and αLOWZ = 2.45 ± 0.02 and quantify modelling uncertainties in these measurements. Finally, we quantify the redshift evolution of the magnification bias within the CMASS and LOWZ samples, finding a difference of up to a factor of three between the lower and upper redshift bounds for the former. We discuss how to account for this evolution in modelling and its interaction with commonly applied redshift-dependent weights. Our method should be readily applicable to upcoming surveys and we make our code publicly available as part of this work.