Bias Reduction Method Research Articles

Jive for Panel Dynamic Simultaneous Equations Models

We consider the method of moments estimation of a structural equation in a panel dynamic simultaneous equations model under different sample size combinations of cross-sectional dimension, N, and time series dimension, T. Two types of linear transformation to remove the individual-specific effects from the model, first difference and forward orthogonal demeaning, are considered. We show that the Alvarez and Arellano (2003) type GMM estimator under both transformations is consistent only if T/N → 0 as (N, T) → ∞. However, it is asymptotically biased if T^3/N → κ ≠ 0 < ∞. Since the validity of statistical inference depends critically on whether an estimator is asymptotically unbiased, we suggest a jackknife bias reduction method and derive its limiting distribution. Monte Carlo studies are conducted to demonstrate the importance of using an asymptotically unbiased estimator to obtain valid statistical inference.

Adherence to continuous positive airway pressure improves attention/psychomotor function and sleepiness: a bias-reduction method with further assessment of APPLES

Objective/backgroundVariable adherence to prescribed therapies for sleep disorders is commonplace. This study was designed to integrate three available statistical technologies (instrumental variables, residual inclusion, and shrinkage) to allow sleep investigators to employ data on variable adherence in the estimation of the causal effect of treatment as received on clinical outcomes. Patients/methodsUsing data from the Apnea Positive Pressure Long-term Efficacy Study (APPLES), regression adjustment for observed and unobserved confounders was applied to two primary neurocognitive outcomes, plus two measures of sleepiness. We demonstrate how to obtain estimates of reduced uncertainty for the causal effect of treatment as received for continuous positive airway pressure (CPAP) within clinical subpopulations (defined by baseline disease severity) of sleep apnea patients. Results and conclusionsFollowing six months of treatment, statistically significant improvements caused by device adherence were detected for subjective sleepiness in mild, moderate, and severe disease, objective sleepiness in severe disease, and attention and psychomotor function in moderate disease. Some evidence for worsening of learning and memory due to increased adherence in moderate disease was also detected. Application to APPLES illustrates that this method can yield bias corrections for unobserved confounders that are substantial—revealing new clinical findings. Use of this fully general method throughout sleep research could sharpen understanding of the true efficacy of pharmacotherapies, medical devices, and behavioral interventions. Extensive technical appendices are provided to facilitate application of this general method.Clinicaltrials.gov identifier NCT00051363.

Many IVs estimation of dynamic panel regression models with measurement error

In this paper, we investigate a dynamic linear panel regression model with measurement error. We consider the panel data estimation whose time dimension (T) is not small and comparable to the cross sectional dimension (N). First, we show that the 2SLS estimator suffers from the bias problem due to many instrumental variables. Using the alternative asymptotics where T3N goes to a constant as N,T→∞, we characterize its asymptotic bias due to many IVs. As a bias reduction method, we investigate the JIVE and derive its limiting distribution under the alternative asymptotics.

Adjustment for survey non-representativeness using record-linkage: refined estimates of alcohol consumption by deprivation in Scotland.

Background and aimsAnalytical approaches to addressing survey non‐participation bias typically use only demographic information to improve estimates. We applied a novel methodology which uses health information from data linkage to adjust for non‐representativeness. We illustrate the method by presenting adjusted alcohol consumption estimates for Scotland.DesignData on consenting respondents to the Scottish Health Surveys (SHeSs) 1995–2010 were linked confidentially to routinely collected hospital admission and mortality records. Synthetic observations representing non‐respondents were created using general population data. Multiple imputation was performed to compute adjusted alcohol estimates given a range of assumptions about the missing data. Adjusted estimates of mean weekly consumption were additionally calibrated to per‐capita alcohol sales data.SettingScotland.Participants13 936 male and 18 021 female respondents to the SHeSs 1995–2010, aged 20–64 years.MeasurementsWeekly alcohol consumption, non‐, binge‐ and problem‐drinking.FindingsInitial adjustment for non‐response resulted in estimates of mean weekly consumption that were elevated by up to 17.8% [26.5 units (18.6–34.4)] compared with corrections based solely on socio‐demographic data [22.5 (17.7–27.3)]; other drinking behaviour estimates were little changed. Under more extreme assumptions the overall difference was up to 53%, and calibrating to sales estimates resulted in up to 88% difference. Increases were especially pronounced among males in deprived areas.ConclusionsThe use of routinely collected health data to reduce bias arising from survey non‐response resulted in higher alcohol consumption estimates among working‐age males in Scotland, with less impact for females. This new method of bias reduction can be generalized to other surveys to improve estimates of alternative harmful behaviours.

Distributed pseudolinear estimation and UAV path optimization for 3D AOA target tracking

We address the problem of angle-of-arrival (AOA) target tracking using multiple unmanned aerial vehicles (UAVs) in three-dimensional (3D) space. A distributed 3D AOA target tracking method is proposed consisting of a distributed estimator and path optimization algorithm for multiple UAVs. First a novel 3D distributed pseudolinear Kalman filter (DPLKF) is developed to improve the stability of an extended Kalman filter solution. The DPLKF consists of two coupled filters; viz., an xy-DPLKF and a z-DPLKF. The bias problem of the 3D DPLKF is analyzed and a bias reduction method is proposed. A distributed path optimization algorithm is developed subject to communication range constraints and no-fly zones. This algorithm computes UAV waypoints using gradient-descent optimization on the xy-plane and grid search along the z-axis. To improve the tracking performance, the trace of the error covariance matrix is minimized. The properties and effectiveness of the proposed strategy are discussed and validated with simulation examples.

A new polarization amplitude bias reduction method

Polarisation amplitude estimation is affected by a positive noise bias, particularly important in regions with low signal-to-noise ratio (SNR). We present a new approach to correct for this bias in the case there is additional information about the polarisation angle. We develop the 'known-angle estimator' that works in the special case when there is an independent and high signal-to-noise ratio ($\gtrsim 2\sigma$) measurement of the polarisation angle. It is derived for the general case where the uncertainties in the Q,U Stokes parameters are not symmetric. This estimator completely corrects for the polarisation bias if the polarisation angle is perfectly known. In the realistic case, where the angle template has uncertainties, a small residual bias remains, but that is shown to be much smaller that the one left by other classical estimators. We also test our method with more realistic data, using the noise properties of the three lower frequency maps of WMAP. In this case, the known-angle estimator also produces better results than methods that do not include the angle information. This estimator is therefore useful in the case where the polarisation angle is expected to be constant over different data sets with different SNR.

Bias-reduced maximum likelihood estimation of the zero-inflated Poisson distribution

We investigate the small-sample quality of the maximum likelihood estimators (MLE) of the parameters of a zero-inflated Poisson distribution (ZIP). The finite-sample bias of the MLE is determined to O(n−1) using an analytic bias-reduction methodology based on the work of Cox and Snell (1968) and Cordeiro and Klein (1994). Monte Carlo simulations show that the MLEs have very small percentage biases for this distribution, but the analytic bias-reduction methods essentially eliminate the bias without adversely affecting the mean-squared errors of the estimators. The analytic adjustment compares favorably with the parametric bootstrap bias-corrected estimator, in terms of bias reduction itself, as well as with respect to mean-squared error and Pitman’s nearness measure.

Global Polynomial Kernel Hazard Estimation

&lt;p&gt;This paper introduces a new bias reducing method for kernel hazard estimation. The method is called global polynomial adjustment (GPA). It is a global correction which is applicable to any kernel hazard estimator. The estimator works well from a theoretical point of view as it asymptotically reduces bias with unchanged variance. A simulation study investigates the finite-sample properties of GPA. The method is tested on local constant and local linear estimators. From the simulation experiment we conclude that the global estimator improves the goodness-of-fit. An especially encouraging result is that the bias-correction works well for small samples, where traditional bias reduction methods have a tendency to fail.&lt;/p&gt;

Penalization, bias reduction, and default priors in logistic and related categorical and survival regressions.

Penalization is a very general method of stabilizing or regularizing estimates, which has both frequentist and Bayesian rationales. We consider some questions that arise when considering alternative penalties for logistic regression and related models. The most widely programmed penalty appears to be the Firth small-sample bias-reduction method (albeit with small differences among implementations and the results they provide), which corresponds to using the log density of the Jeffreys invariant prior distribution as a penalty function. The latter representation raises some serious contextual objections to the Firth reduction, which also apply to alternative penalties based on t-distributions (including Cauchy priors). Taking simplicity of implementation and interpretation as our chief criteria, we propose that the log-F(1,1) prior provides a better default penalty than other proposals. Penalization based on more general log-F priors is trivial to implement and facilitates mean-squared error reduction and sensitivity analyses of penalty strength by varying the number of prior degrees of freedom. We caution however against penalization of intercepts, which are unduly sensitive to covariate coding and design idiosyncrasies.

Localization Bias Reduction in Wireless Sensor Networks

In this paper, a novel bias-reduction method is proposed to analytically express and reduce the bias arising in sensor network localization problems, thereby improving the localization accuracy. The proposed bias-reduction method mixes Taylor series and a maximum-likelihood estimate and leads to an easily calculated analytical bias expression in terms of a known maximum-likelihood cost function. In contrast to existing contributions, this paper considers a sensor network as a whole when the bias is investigated by introducing the geometric structure of the sensor network into the proposed bias-reduction method via the rigidity matrix, a concept drawn from graph theory. The maximum-likelihood cost function is related to the rigidity matrix resulting in the final analytical expression of localization bias in terms of the rigidity matrix. Another important contribution of this paper is that, in addition to the presented simulation results, experimental results obtained by using a wireless localization system, which is developed based on reconfigurable software-defined radios (SDRs), are also provided to verify the performance of the proposed bias-reduction method. Both the simulation and experimental results demonstrate that the proposed method can reduce the bias, thereby improving the localization accuracy in different scenarios.

Controlling Time-Dependent Confounding by Health Status and Frailty: Restriction Versus Statistical Adjustment.

Nonexperimental studies of preventive interventions are often biased because of the healthy-user effect and, in frail populations, because of confounding by functional status. Bias is evident when estimating influenza vaccine effectiveness, even after adjustment for claims-based indicators of illness. We explored bias reduction methods while estimating vaccine effectiveness in a cohort of adult hemodialysis patients. Using the United States Renal Data System and linked data from a commercial dialysis provider, we estimated vaccine effectiveness using a Cox proportional hazards marginal structural model of all-cause mortality before and during 3 influenza seasons in 2005/2006 through 2007/2008. To improve confounding control, we added frailty indicators to the model, measured time-varying confounders at different time intervals, and restricted the sample in multiple ways. Crude and baseline-adjusted marginal structural models remained strongly biased. Restricting to a healthier population removed some unmeasured confounding; however, this reduced the sample size, resulting in wide confidence intervals. We estimated an influenza vaccine effectiveness of 9% (hazard ratio = 0.91, 95% confidence interval: 0.72, 1.15) when bias was minimized through cohort restriction. In this study, the healthy-user bias could not be controlled through statistical adjustment; however, sample restriction reduced much of the bias.

Classical Laplace estimation for [formula omitted]-consistent estimators: Improved convergence rates and rate-adaptive inference

We propose a classical Laplace estimator alternative for a large class of n3-consistent estimators, including isotonic regression, monotone hazard, and maximum score estimators. The proposed alternative provides a unified method of smoothing; easier computation is a byproduct in the maximum score case. Depending on input parameter choice and smoothness, the convergence rate of our estimator varies between n3 and (almost) n and its limit distribution varies from Chernoff to normal. We provide a bias reduction method and an inference procedure which automatically adapts to the correct convergence rate and limit distribution.

Bias reduction when data are rounded

Analytical bias reduction methods are developed for univariate rounded data for the first time. Extensions are given to rounding of multivariate data, and to smooth functionals of several distributions. As a by‐product, we give for the first time the relation between rounded and unrounded multivariate cumulants. Estimators obtained by analytical bias reduction are compared with bootstrap and jackknife estimators by simulation.

Research Based Recommendations for Child Custody Evaluation Practices and Policies in Cases of Intimate Partner Violence

This article reviews recent research on child custody evaluations in intimate partner violence (IPV) cases. Specifically, it covers assessment methods, evaluator selection, evaluator education, guidelines, differential assessment, and state policies. Special attention is given to new methods of bias reduction, the need to focus on coercive and controlling abuse, and the need to interpret psychological tests within a trauma framework. Recommendations are made in each area reviewed.

Futures Prices in Supply Analysis: Are Instrumental Variables Necessary?

AbstractCrop yield shocks are partially predictable—high planting‐time futures prices have tended to indicate that yield would be below trend. As a result, regressions of total caloric production on futures prices produce estimates of the supply elasticity that are biased downwards by up to 75%. Regressions of the world's growing area on futures prices have a much smaller bias of about 20% because although yield shocks are partially predictable, this predictability has a relatively small effect on land allocation. We argue that the preferred method for estimating the crop supply elasticity is to use regressions of growing area on futures prices and to include the realized yield shock as a control variable. An alternative method for bias reduction is to use instrumental variables (IVs). We show that the marginal contribution of an IV to bias reduction is small—IVs are not necessary for futures prices in supply analysis.

Time-of-Flight Estimation in the Presence of Outliers. Part II—Multiple Echo Processing

The mean squared error of the classical maximum likelihood time-of-flight (ToF) estimator increases dramatically when the signal-to-noise ratio falls below a certain threshold. For narrow-band signals, this well-known threshold effect occurs largely due to the biased outliers which are induced by the local maxima of the source signal autocorrelation function. In our previous work (Part I), we have described a machine learning biosonar-inspired method for reducing the effect of the outlier bias on the accuracy of a single-echo estimate. In this paper, we extend this approach by introducing a method for combining multiple echo signals into a robust ToF estimator which is resilient to outliers. The individual bias-corrected estimates are combined together using the optimal weighted averaging (OWA) scheme which takes into account the uncertainties associated with inlier and outlier measurements. As in the single-echo case, a weak classifier and a bank of phase-shifted unmatched filters are used for estimating the probabilities of appearance of a specific outlier class in a single-echo estimate. Combined with the previously introduced single-echo bias-reduction method, the OWA scheme results in significant improvement in the ToF estimation accuracy.

Nonnegative bias reduction methods for density estimation using asymmetric kernels

Two classes of multiplicative bias correction (“MBC”) methods are applied to density estimation with support on [0,∞). It is demonstrated that under sufficient smoothness of the true density, each MBC technique reduces the order of magnitude in bias, whereas the order of magnitude in variance remains unchanged. Accordingly, the mean integrated squared error of each MBC estimator achieves a faster convergence rate of O(n−8/9) when best implemented, where n is the sample size. Furthermore, MBC estimators always generate nonnegative estimates by construction. Plug-in smoothing parameter choice rules for the estimators are proposed, and their finite sample performance is examined via Monte Carlo simulations.

Nonlinear Granger Causality: Guidelines for Multivariate Analysis

In this paper we propose an extension of the nonparametric Granger causality test, originally introduced by Diks and Panchenko [2006. A new statistic and practical guidelines for nonparametric Granger causality testing. Journal of Economic Dynamics & Control 30, 1647-1669]. We show that the basic test statistics lacks consistency in the multivariate setting. The problem is the result of the kernel density estimator bias, which does not converge to zero at a sufficiently fast rate when the number of conditioning variables is larger than one. In order to overcome this difficulty we apply the data-sharpening method for bias reduction. We then derive the asymptotic properties of the 'sharpened' test statistics and we investigate its performance numerically. We conclude with an empirical application to the US grain market.

Risk Factors Associated with Breast Lymphedema

The development of breast lymphedema (BLE) after breast/axillary surgery is poorly characterized. We prospectively evaluated clinical and surgical factors associated with development of BLE. Patients undergoing unilateral breast-conserving surgery were prospectively enrolled preoperatively and followed for development of BLE. To augment the number of patients with BLE for evaluation of risk factors, postoperative patients identified in the clinic with signs and symptoms of BLE were also enrolled. Logistic regression with Firth's penalized likelihood bias-reduction method was used for univariate and multivariate analysis. Of 144 women, 124 were enrolled preoperatively (38 of whom developed BLE), and 20 women with BLE were enrolled postoperatively. Any type of axillary surgery was the strongest factor associated with BLE (odds ratio, 134; 95 % confidence interval, 18 to >1,000). All 58 BLE events occurred in women with axillary surgery as compared with no events in the 46 patients without axillary surgery (p < 0.0001). Among 98 women who underwent axillary surgery, BLE did not occur more often after axillary lymph node dissection versus sentinel lymph node biopsy (p = 0.38) and was not associated with total number of nodes removed (p = 0.52). In multivariate analysis, factors associated with the development of BLE in the axillary surgery subgroup included baseline BMI (p = 0.004), incision location (p = 0.009), and prior surgical biopsy (p = 0.01). Risk of BLE is primarily related to performance of any axillary surgery but not the extent of axillary surgery or number of lymph nodes removed. Other factors associated with BLE were increased body mass index, incision location, and prior surgical excisional biopsy.

Effective bias reduction methods for passive source localization using TDOA and GROA

For passive source localization based on both TDOA and GROA, this paper proposes two bias reduction methods for the well-known Weighted-Least-Squares (WLS) estimator. We first derive the passive source localization bias from the two-step algebraic closed-form solution. This bias is found to be considerably larger than the Maximum Likelihood Estimator (MLE) and limits the WLS estimator’s practical applications. In this paper, We develop two methods to reduce the bias. The first one called Bias-Subtraction-Method (BSM) directly subtracts the expected bias from the solution of the WLS estimator, and the second one called Bias-Reduction-Method (BRM) imposes a constraint to the equation error formulation to improve the source location estimate. The noise covariance matrix must be known exactly in calculating the expected bias in BSM, and we only need to know the structure of it in BRM. For far-field sources localization when the noise is Gaussian and not too large, both of the two proposed methods can reduce the localization bias effectively and achieve the Cramer-Rao Lower Bound (CRLB) performance very well, and the BRM almost has the same performance as the MLE estimator. Simulations corroborate the performance of the two proposed methods.