Unbiasedness Research Articles

Estimation of heterogeneity variance based on a generalized Q statistic in meta-analysis of log-odds-ratio.

For estimation of heterogeneity variance in meta-analysis of log-odds-ratio, we derive new mean- and median-unbiased point estimators and new interval estimators based on a generalized statistic, , in which the weights depend on only the studies' effective sample sizes. We compare them with familiar estimators based on the inverse-variance-weights version of , In an extensive simulation, we studied the bias (including median bias) of the point estimators and the coverage (including left and right coverage error) of the confidence intervals. Most estimators add to each cell of the table when one cell contains a zero count; we include a version that always adds . The results show that: two of the new point estimators and two of the familiar point estimators are almost unbiased when the total sample size and the probability in the Control arm ( ) is 0.1, and when and is 0.2 or 0.5; for , all estimators have negative bias for small to medium sample sizes, but for larger sample sizes some of the new median-unbiased estimators are almost median-unbiased; choices of interval estimators depend on values of parameters, but one of the new estimators is reasonable when and another, when or ; and lack of balance between left and right coverage errors for small and/or implies that the available approximations for the distributions of and are accurate only for larger sample sizes.

Random noise test of analog-to-digital converters

The random noise test of analog to digital converters recommended by the IEEE 1057 Standard for digitizing waveform recorders is studied. The heuristically derived expression presented for the estimation of the random noise standard deviation is experimentally validated. The standard suggests a triangular stimulus signal. Here we will show how to use a sinusoidal stimulus signal to carry out the test. The influence of stimulus signal offset and amplitude on the estimation error is also analyzed and an expression is presented to compute the minimum amplitude value that guarantees an upper bound on the estimator bias.

Fitting and Testing Log-Linear Subpopulation Models with Known Support.

In this paper, the support of the joint probability distribution of categorical variables in the total population is treated as unknown. From a general total population model with unknown support, a general subpopulation model with its support equal to the set of all observed score patterns is derived. In maximum likelihood estimation of the parameters of any such subpopulation model, the evaluation of the log-likelihood function only requires the summation over a number of terms equal to at most the sample size. It is made clear that the parameters of a hypothesized total population model are consistently and asymptotically efficiently estimated by the values that maximize the log-likelihood function of the corresponding subpopulation model. Next, new likelihood ratio goodness-of-fit tests are proposed as alternatives to the Pearson chi-square goodness-of-fit test and the likelihood ratio test against the saturated model. In a simulation study, the asymptotic bias and efficiency of maximum likelihood estimators and the asymptotic performance of the goodness-of-fit tests are investigated.

Robust Liu‐type estimator based on GM estimator

Ordinary Least Squares Estimator (OLSE) is widely used to estimate parameters in regression analysis. In practice, the assumptions of regression analysis are often not met. The most common problems that break these assumptions are outliers and multicollinearity problems. As a result of these problems, OLSE loses efficiency. Therefore, alternative estimators to OLSE have been proposed to solve these problems. Robust estimators are often used to solve the outlier problem, and biased estimators are often used to solve the multicollinearity problem. These problems do not always occur individually in the real‐world dataset. Therefore, robust biased estimators are proposed for simultaneous solutions to these problems. The aim of this study is to propose Liu‐type Generalized M Estimator as an alternative to the robust biased estimators available in the literature to obtain more efficient results. This estimator gives effective results in the case of outlier and multicollinearity in both dependent and independent variables. The proposed estimator is theoretically compared with other estimators available in the literature. In addition, Monte Carlo simulation and real dataset example are performed to compare the performance of the estimator with existing estimators.

State-of-Charge Estimation of Batteries for Hybrid Urban Air Mobility

This paper proposes a framework for accurately estimating the state-of-charge (SOC) and current sensor bias, with the aim of integrating it into urban air mobility (UAM) with hybrid propulsion. Considering the heightened safety concerns in an airborne environment, more reliable state estimation is required, particularly for the UAM that uses a battery as its primary power source. To ensure the suitability of the framework for the UAM, a two-pronged approach is taken. First, realistic test profiles, reflecting actual operational scenarios for the UAM, are used to model the battery and validate its state estimator. These profiles incorporate variations in battery power flow, namely, charge-depleting and charge-sustaining modes, during the different phases of the UAM’s flight, including take-off, cruise, and landing. Moreover, the current sensor bias is estimated and corrected concurrently with the SOC. An extended Kalman filter-based bias estimator is developed and experimentally validated using actual current measurements from a Hall sensor, which is prone to noise. With this correction, a SOC estimation error is consistently maintained at 2% or lower, even during transitions between operational modes.

A new Liu-type estimator for the gamma regression model

In many real-world problems, there are situations where the dependent variable may have a Gamma distribution. The Gamma Regression Models (GRMs) are preferred when the response variable assumes a Gamma distribution with a given set of independent variables. The Maximum Likelihood Estimator (MLE) is used to estimate the unknown parameters. In the presence of multicollinearity, the variance of the MLE becomes inflated and the inference based on the MLE may not be reasonable. In this article, we propose a new biased estimator called the new Liu-type estimator in the GRMs to combat multicollinearity. The proposed estimator is a general estimator which includes other biased estimators, such as the Gamma ridge estimator, Gamma Liu estimator, and the estimators with two biasing parameters as special cases. Furthermore, several methods are proposed to determine the biasing parameters in the estimators. Also, a Monte Carlo simulation study has been conducted to assess the performance of the proposed biased estimator where the Estimated Mean Squared Error (EMSE) is considered as a performance criterion. Finally, two numerical examples are given to investigate the performance of the proposed estimator over existing estimators.

Adjusting for Selection Bias in Nonprobability Samples by Empirical Likelihood Approach

Abstract Large amount of data are today available, that are easier and faster to collect than survey data, bringing new challenges. One of them is the nonprobability nature of these big data that may not represent the target population properly and hence result in highly biased estimators. In this article two approaches for dealing with selection bias when the selection process is nonignorable are discussed. The first one, based on the empirical likelihood, does not require parametric specification of the population model but the probability of being in the nonprobability sample needed to be modeled. Auxiliary information known for the population or estimable from a probability sample can be incorporated as calibration constraints, thus enhancing the precision of the estimators. The second one is a mixed approach based on mass imputation and propensity score adjustment requiring that the big data membership is known throughout a probability sample. Finally, two simulation experiments and an application to income data are performed to evaluate the performance of the proposed estimators in terms of robustness and efficiency.

The beta Liu-type estimator: simulation and application

The Beta Regression Model (BRM) is commonly used while analyzing data where the dependent variable is restricted to the interval $[0,1]$ for example proportion or probability. The Maximum Likelihood Estimator (MLE) is used to estimate the regression coefficients of BRMs. But in the presence of multicollinearity, MLE is very sensitive to high correlation among the explanatory variables. For this reason, we introduce a new biased estimator called the Beta Liu-Type Estimator (BLTE) to overcome the multicollinearity problem in the case that dependent variable follows a Beta distribution. The proposed estimator is a general estimator which includes other biased estimators, such as the Ridge Estimator, Liu Estimator, and the estimators with two biasing parameters as special cases in BRM. The performance of the proposed new estimator is compared to the MLE and other biased estimators in terms of the Estimated Mean Squared Error (EMSE) criterion by conducting a simulation study. Finally, a numerical example is given to show the benefit of the proposed estimator over existing estimators.

An Almost Unbiased Ridge Estimator for the Conway–Maxwell–Poisson Regression Model

The Poisson model is the most widely used model for counts type response variables. It has a limitation of equal mean and variance, which undermines its application as compared to the Conway–Maxwell–Poisson–regression model (COMPRM). In general, the maximum likelihood estimator (MLE) is used to estimate the COMPRM, but when there is a high correlation among the explanatory variables, the MLE may not provides efficient estimates. In this situation, the ridge estimation technique provides a better alternative to the MLE but with a larger bias. In this work, we propose an almost unbiased ridge estimator for the estimation of COMPRM coefficients and derive its theoretical properties. The proposed estimator is compared with the available biased estimator as well as the MLE based on the mean squared error (MSE) and bias criteria. A Monte Carlo simulation analysis is performed for comparisons under various controlled conditions. A real application is considered to study the significance of the proposed estimator using MSE and cross-validation criteria. The simulation and real-world application results show that the proposed estimator outperforms the classical MLE and ridge estimators in terms of the minimum MSE and bias.

Bivariate Discrete Odd Generalized Exponential Generator of Distributions for Count Data: Copula Technique, Mathematical Theory, and Applications

In this article, a new family of bivariate discrete distributions is proposed based on the copula concept, in the so-called bivariate discrete odd generalized exponential-G family. Some distributional properties, including the joint probability mass function, joint survival function, joint failure rate function, median correlation coefficient, and conditional expectation, are derived. After proposing the general class, one special model of the new bivariate family is discussed in detail. The maximum likelihood approach is utilized to estimate the family parameters. A detailed simulation study is carried out to examine the bias and mean square error of maximum likelihood estimators. Finally, the importance of the new bivariate family is explained by means of two distinctive real data sets in various fields.

A mixed distribution approach for low-flow frequency analysis – Part 2: Comparative assessment of a mixed probability vs. copula-based dependence framework

Abstract. In climates with a warm and a cold season, low flows are generated by different processes, which violates the homogeneity assumption of extreme value statistics. In this second part of a two-part series, we extend the mixed probability estimator of the companion paper (Laaha, 2023) to deal with dependency of seasonal events. We formulate a copula-based estimator for seasonal minima series and examine it in a hydrological context. The estimator is a valid generalization of the annual probability estimator and provides a consistent framework for estimating return periods of summer, winter, and annual events. Using archetypal examples we show that differences in the mixed estimator are always observed in the upper part of the distribution, which is less relevant for low-flow frequency analysis. The differences decrease as the return period increases so that both models coincide for the severest events. In a quantitative evaluation, we test the performance of the copula estimator on a pan-European data set. We find a large gain of both mixed distribution approaches over the annual estimator, making these approaches highly relevant for Europe as a whole. We then examine the relative performance gain of the mixed copula versus the mixed distribution approach in more detail. The analysis shows that the differences in the 100-year event are actually minimal. However, the differences in 2-year events are considerable in some of the catchments, with a relative deviation of −15 % to −25 % in the most affected regions. This points to a prediction bias of the mixed probability estimator that can be corrected using the copula approach. Using multiple regression models, we show that the performance gain can be well explained on hydrological grounds, with weak seasonality leading to a high potential for corrections and strong seasonal correlation reinforcing the need to take this potential into account. Accordingly, the greatest differences can be observed in mid-mountain regions in cold and temperate climates, where rivers have a strongly mixed low-flow regime. This finding is of particular relevance for event mapping, where regional severity can be misinterpreted when the seasonal correlation is neglected. We conclude that the two mixed probability estimators are quite similar, and both are conceptually more adequate than the annual minima approach for mixed summer and winter low-flow regimes. In regions with strong seasonal correlation the mixed copula estimator appears most appropriate and should be preferred over the mixed distribution approach.

Exploring and Correcting the Bias in the Estimation of the Gini Measure of Inequality

The Gini index is probably the most commonly used indicator to measure inequality. For continuous distributions, the Gini index can be computed using several equivalent formulations. However, this is not the case with discrete distributions, where controversy remains regarding the expression to be used to estimate the Gini index. We attempt to bring a better understanding of the underlying problem by regrouping and classifying the most common estimators of the Gini index proposed in both infinite and finite populations, and focusing on the biases. We use Monte Carlo simulation studies to analyse the bias of the various estimators under a wide range of scenarios. Extremely large biases are observed in heavy-tailed distributions with high Gini indices, and bias corrections are recommended in this situation. We propose the use of some (new and traditional) bootstrap-based and jackknife-based strategies to mitigate this bias problem. Results are based on continuous distributions often used in the modelling of income distributions. We describe a simulation-based criterion for deciding when to use bias corrections. Various real data sets are used to illustrate the practical application of the suggested bias corrected procedures.

Unbiased prediction errors for partial least squares regression models: Choosing a representative error estimator for process monitoring

Partial least squares (PLS) regression is widely used to predict chemical analytes from spectroscopic data, thus reducing the need for expensive and time-consuming wet chemical reference analysis in industrial process monitoring. However, predictions via PLS by definition carry sample-specific errors, and estimation of these errors is essential for correct interpretation of results. To increase trust in PLS regression-based predictions, reliable prediction error estimates must be reported. This can be achieved by determining realistic sample-specific prediction errors using an unbiased mean squared prediction error estimate. This work provides a guide for estimating sample-specific prediction errors, showing the importance of choosing an appropriate error estimator prior to deploying PLS models for industrial applications. We reviewed recent and established methods for estimating the sample-specific prediction error and test them through simulation studies. The methods were subsequently applied for estimating prediction errors in two real-life datasets from the food ingredients industry, where near-infrared spectroscopy was used to quantify i) urea in process water and ii) individual protein concentrations in ultrafiltration retentates from a protein fractionation process. Both the simulations and real data examples showed that the mean squared error of calibration is always a downward biased estimator. Although leave-one-out-cross-validation performed surprisingly well in the data analysed in this work, this paper demonstrated that the appropriate choice of error estimator requires the user to make an informed, data-centered decision.

Efficient peer effects estimators with group effects

We study linear peer effect models where peers interact in groups and individual’s outcomes are linear in the group mean outcome and characteristics. We allow for unobserved random group effects as well as observed fixed group effects. The specification is in part motivated by the moment conditions imposed in Graham (2008). We show that these moment conditions can be cast in terms of a linear random group effects model and that they lead to a class of GMM estimators with parameters generally identified as long as there is sufficient variation in group size or group types. We also show that our class of GMM estimators contains a Quasi Maximum Likelihood estimator (QMLE) for the random group effects model, as well as the Wald estimator of Graham (2008) and the within estimator of Lee (2007) as special cases. Our identification results extend insights in Graham (2008) that show how assumptions about random group effects, variation in group size and certain forms of heteroscedasticity can be used to overcome the reflection problem in identifying peer effects. Our QMLE and GMM estimators accommodate additional covariates and are valid in situations with a large but finite number of different group sizes or types. Because our estimators are general moment based procedures, using instruments other than binary group indicators in estimation is straight forward. Our QMLE estimator accommodates group level covariates in the spirit of Mundlak and Chamberlain and offers an alternative to fixed effects specifications. This model feature significantly extends the applicability of Graham’s identification strategy to situations where group assignment may not be random but correlation of group level effects with peer effects can be controlled for with observable group level characteristics. Monte-Carlo simulations show that the bias of the QMLE estimator decreases with the number of groups and the variation in group size, and increases with group size. We also prove the consistency and asymptotic normality of the estimator under reasonable assumptions.

Stochastic zeroth-order gradient and Hessian estimators: variance reduction and refined bias bounds

Abstract We study stochastic zeroth-order gradient and Hessian estimators for real-valued functions in $\mathbb{R}^n$. We show that, via taking finite difference along random orthogonal directions, the variance of the stochastic finite difference estimators can be significantly reduced. In particular, we design estimators for smooth functions such that, if one uses $ \varTheta \left ( k \right ) $ random directions sampled from the Stiefel manifold $ \text{St} (n,k) $ and finite-difference granularity $\delta $, the variance of the gradient estimator is bounded by $ \mathscr{O} \left ( \left ( \frac{n}{k} - 1 \right ) + \left ( \frac{n^2}{k} - n \right ) \delta ^2 + \frac{ n^2 \delta ^4} { k } \right ) $, and the variance of the Hessian estimator is bounded by $\mathscr{O} \left ( \left ( \frac{n^2}{k^2} - 1 \right ) + \left ( \frac{n^4}{k^2} - n^2 \right ) \delta ^2 + \frac{n^4 \delta ^4 }{k^2} \right ) $. When $k = n$, the variances become negligibly small. In addition, we provide improved bias bounds for the estimators. The bias of both gradient and Hessian estimators for smooth function $f$ is of order $\mathscr{O} \big( \delta ^2 \varGamma \big )$, where $\delta $ is the finite-difference granularity, and $ \varGamma $ depends on high-order derivatives of $f$. Our results are evidenced by empirical observations.

Modeling and maximum likelihood based inference ofinterval-censored data with unknown upper limits andtime-dependent covariates.

Due to the nature of study design or other reasons, the upper limits of the interval-censored data with multiple visits are unknown. A naïve approach is to treat the last observed time as the exact event time, which may induce biased estimators of the model parameters. In this paper, we first develop a Cox model with time-dependent covariates for the event time and a proportional hazards model with frailty for the gap time. We then construct the upper limits using the latent gap times to resolve the issue of interval-censored event time data with unknown upper limits. A data-augmentation technique and a Monte Carlo EM (MCEM) algorithm are developed to facilitate computation. Theoretical properties of the computational algorithm are also investigated. Additionally, new model comparison criteria are developed to assess the fit of the gap time data as well as the fit of the event time data conditional on the gap time data. Our proposed method compares favorably with competing methods in both simulation study and real data analysis.

Misclassification Error, Binary Regression Bias, and Reliability in Multidimensional Poverty Measurement: An Estimation Approach Based on Bayesian Modelling

ABSTRACT Measurement error affects the quality of population orderings of an index and, hence, increases the misclassification of the poor and the non-poor groups and affects statistical inferences from binary regression models. Hence, the conclusions about the extent, profile, and distribution of poverty are likely to be misleading. However, the size and type (false positive/negatives) of classification error have remained untraceable in poverty research. This paper draws upon previous theoretical literature to develop a Bayesian-based estimator of population misclassification and binary-regression coefficient bias. The study uses the reliability values of existing poverty indices to set up a Monte Carlo study based on factor mixture models to illustrate the connections between measurement error, misclassification, and bias and evaluate the procedure and discusses its importance for real-world applications.

Methodological problems in studies on the Taylor rule

This paper raises concerns about the methodological approaches commonly adopted in typical Taylor rule studies. We find that many empirical studies on the Taylor rule do not follow the required econometric procedures. These studies ignore the presence of unit roots, cointegration, and serial correlation in their tests and estimation. The Taylor rule equation is typically estimated in levels. We show that the Taylor rule can be an unbalanced regression that involves a mixture of I(0) and I(1) variables. Spurious regressions may occur if the variables are not cointegrated and the Taylor rule equation is estimated using variables in levels. In addition, empirical models of the Taylor rule commonly include lags of the dependent variable, and equation residuals are serially correlated. The presence of lagged dependent variables and serially correlated residuals will cause biased and inconsistent least squares estimators. To illustrate our arguments, we re-examine two recent papers to point out the econometric problems that are general in typical Taylor rule studies. We show that an inadequate analysis of the time series properties of the individual series and diagnostic checks of the estimated equations can often lead to invalid conclusions about the empirical validity of the Taylor rule. We demonstrate how autoregressive distributed lag methods can overcome these issues and how the equation can be estimated efficiently.

Efficient item count techniques with one or two lists

If the direct questioning on sensitive variables leads to non-ignorable item-nonresponse and untruthful answering, a considerably biased estimator might be the consequence. In such cases, indirect questioning designs, which protect the respondents’ privacy by masking the sensitive information, could pay off in terms of accuracy through an increased willingness to cooperate. To achieve this goal, such a design has to be simple in its implementation for the users and easy to understand for the respondents. In this article, it is shown for one of the indirect questioning designs, the item count technique, how the usage of specific oftentimes available prior information can substantially improve the estimation accuracy and at the same time reduce the respondents’ task. This can make the method a stronger and more serious competitor of the direct questioning on sensitive attributes, which is commonly used in empirical research.

Improved family of estimators for the population mean using supplementary variables under PPS sampling.

In this article, we suggest an enhanced family of estimators for estimation of population mean employing the supplementary variables under probability proportional to size sampling. Up to the first order of approximation, numerical formulations of the bias and mean square error of estimators are obtained. From our suggested improved family of estimators, we give sixteen different members. The recommended family of estimators has specifically been used to derive the characteristics of sixteen estimators based on the known population parameters of the study as well as auxiliary variables. The performances of the suggested estimators have been assessed using three actual data. Furthermore, a simulation investigation is also accompanied to evaluate the effectiveness of estimators. The proposed estimators have a smaller MSE and an advanced PRE when linked to existing estimators, which are based on actual data sets and simulation studies. Theoretically and empirically studies also reveal that the suggested estimators accomplish well than the usual estimators.