Bias Estimation Method Research Articles

Comparison of Ridge Regression and Least Squares Methods in the Presence of Multicollinearity for Body Measurements in Saanen Kids

Least square (LS) method is a common method used to estimate the coefficients in multiple regression models. The least square multiple regression models produce biased regression coefficients when the multicollinearity is encountered in the studied data sets. Multicollinearity problem can be solved by using some methods. As one of the methods, Ridge Regression (RR) is a biased estimation method that enables to obtain models having more reliable coefficient of determination (R2). This study was conducted on 40 Saanen kids in order to determine some morphological measurements (withers height, rump height, body length, chest width, chest girth and chest depth) affecting body weight. In this study, usability of ridge regression method in the presence of multicollinearity was evaluated. Variance Inflation Factor (VIF) values higher than 10 were detected for withers height and rump height. Coefficient of determination (R2) was obtained as 0.88 from LS method and R2 was obtained 0.875 with k=0.0136 from RR method. As a result, the model obtained from RR is more reliable than that obtained from LS.

Identifying and estimating bias in overlap-sampling free-energy calculations

ABSTRACT We examine several methods for detecting or quantifying bias in free energy calculations performed using Bennett's acceptance ratio (BAR) method for combining data from molecular simulations of two systems. The metrics for bias detection studied here are one based on the emergence, at the BAR estimate, of a zero-slope inflection of the free energy with respect to its optimisation parameter, and another that makes use of calculation of the dissipated work. Bias estimation methods studied here are two approaches based on consideration of the maximum possible contribution from a configuration that may be rarely sampled, and another that appeared recently in the literature that is derived explicitly using the neglected-tail ansatz. All approaches are tested as a function of sampling amount in application to a model multiharmonic system. The dissipated-work method provides the more reliable indicator of the presence of bias, and the maximal sample techniques yield the tightest bounds on the bias, among the methods tested.

Latitude Determination and Error Analysis for Stationary SINS in Unknow-Position Condition.

The initial geographic latitude information is the key to the self-alignment of the strapdown inertial navigation system (SINS), but how to determine the latitude when the latitude cannot be obtained directly or in a short time? The latitude determination (LD) methods are introduced, including magnitude method, geometric method, and analytical methods 1 and 2, to solve this situation only by the output of the SINS itself. Simulation and experimental test results validate the efficiency of these LD methods. In order to improve the accuracy of the LD, the error of the LD method is derived through comparative analysis. Based on the relationship between LD error and inertial measurement unit (IMU) bias. Partial bias estimation method is introduced and executed during latitude determination. After compensating the estimated IMU bias, the accuracy of the LD will be further improved. Latitude errors are also affected by the latitude where SINS is located. Comprehensive simulation and experimental tests verify the effectiveness of the method. The IMU determined latitude can not only be used to achieve the self-alignment of the SINS, but also to correct the navigation latitude of the long-term SINS, thereby improving the autonomy and positioning accuracy of the navigation system.

Orthogonal iteration process of determining K value on estimator of Jackknife ridge regression parameter

Jackknife is re-sampling bias estimation method, in predict standard deviations. The principle of the Jackknife method in regression parameters estimation is to eliminate one data and repeat it as much as the number of existing data samples. The step in estimating regression parameter of Jackknife Ridge (JR) was the first to transform data through cantering and scaling process and orthogonalization on independent variables. The second determines initial value k0 and perform the iteration process. The third by transform initial estimator JR and finally by testing the feasibility of the resulting model of Jackknife ridge regression. Results obtained, iteration process is conducted until obtained a value of and iteration stops at 5th iteration, so obtain estimator value of generalized ridge coefficient of orthogonal independent variable value of generalized ridge coefficient of orthogonal independent variable .

RBFN 과 강화학습을 활용한 관성항법장치의 자이로 바이어스 추정 기법

In this paper, a new gyro bias estimation method is proposed by using reinforcement learning and RBFN (Radial Basis Function Network). A set of lattices for better navigation performance is investigated using reinforcement learning. A function of estimating gyro bias is constructed by connecting the set lattices using RBFN. The performance of the proposed method is evaluated by comparing with various methods such as 3rd order function method, 3rd order function with a temperature rate method (TRM), classic RBFN method, and MLR (Multiple Linear Regression) method. The results of experiment show that the proposed gyro bias estimation method has better navigation performance than other methods.

A new biased estimation method based on Neumann series for solving ill-posed problems

The ill-posed least squares problems often arise in many engineering applications such as machine learning, intelligent navigation algorithms, surveying and mapping adjustment model, and linear regression model. A new biased estimation (BE) method based on Neumann series is proposed in this article to solve the ill-posed problems more effectively. Using Neumann series expansion, the unbiased estimate can be expressed as the sum of infinite items. When all the high-order items are omitted, the proposed method degenerates into the ridge estimation or generalized ridge estimation method, whereas a series of new biased estimates can be acquired by including some high-order items. Using the comparative analysis, the optimal biased estimate can be found out with less computation. The developed theory establishes the essential relationship between BE and unbiased estimation and can unify the existing unbiased and biased estimate formulas. Moreover, the proposed algorithm suits for not only ill-conditioned equations but also rank-defect equations. Numerical results show that the proposed BE method has improved accuracy over the existing robust estimation methods to a certain extent.

Bias CRLB in Sine Space for a Three-Dimensional Sensor

As bias estimation methods are developed, it becomes necessary to obtain the bound on bias estimation for more complex bias and sensor models. Three-dimensional (3-D) sensors, such as radars commonly used in applications, contain both scale and additive biases in sine space which result in a nonlinear estimation problem that may have poor observability and accuracy depending on the geometry of the sensors. By converting the sine space and range measurements to Cartesian using an unbiased conversion, it is possible, via creation of pseudomeasurements, to eliminate the need to estimate the target's state thereby reducing the sensor bias estimator complexity. The present paper evaluates the Cramer–Rao lower bound (CRLB) for estimating scale and additive biases in sine space for 3-D sensors and compares it with a maximum likelihood formulation implemented via iterated least squares, which is thereby shown to be statistically efficient. Additionally, the importance of measurement diversity is investigated with respect to the CRLB.

Improve the precision and accuracy of retrieval of particle size-distribution based the unconstrained linear regression

In this paper, we try to find a way to take into account both of the precision and accuracy of particle sizing that based on Mie scattering. It is known that in the retrieval of particle size distribution one of the most important issues is to solve the ill-conditioned problem. Due to the ill-conditioned problem, the retrieval is very imprecision usually. The biased estimation methods can improve the precision effectively, which, therefore, is widely used. But the price is the decrease of the retrieval accuracy, because such method, after all, is of bias. It is known that the unconstrained linear regression (ULR) is unbiased, therefore, based on this ULR, both of the retrieval precision and accuracy can be taken into account.

A deep learning approach to estimation of subject-level bias and variance in high angular resolution diffusion imaging

The ability to evaluate empirical diffusion MRI acquisitions for quality and to correct the resulting imaging metrics allows for improved inference and increased replicability. Previous work has shown promise for estimation of bias and variance of generalized fractional anisotropy (GFA) but comes at the price of computational complexity. This paper aims to provide methods for estimating GFA, bias of GFA and standard deviation of GFA quickly and accurately. In order to provide a method for bias and variance estimation that can return results faster than the previously studied statistical techniques, three deep, fully-connected neural networks are developed for GFA, bias of GFA, and standard deviation of GFA. The results of these networks are compared to the observed values of the metrics as well as those fit from the statistical techniques (i.e. Simulation Extrapolation (SIMEX) for bias estimation and wild bootstrap for variance estimation). Our GFA network provides predictions that are closer to the true GFA values than a Q-ball fit of the observed data (root-mean-square error (RMSE) 0.0077 vs 0.0082, p < .001). The bias network also shows statistically significant improvement in comparison to the SIMEX-estimated error of GFA (RMSE 0.0071 vs. 0.01, p < .001).

An improved and efficient biased estimation technique in logistic regression model

In this article, we propose a new improved and efficient biased estimation method which is a modified restricted Liu-type estimator satisfying some sub-space linear restrictions in the binary logistic regression model. We study the properties of the new estimator under the mean squared error matrix criterion and our results show that under certain conditions the new estimator is superior to some other estimators. Moreover, a Monte Carlo simulation study is conducted to show the performance of the new estimator in the simulated mean squared error and predictive median squared errors sense. Finally, a real application is considered.

Evaluation of Two Stage Modified Ridge Estimator and Its Performance

Biased estimation methods are more desirable than two stage least squares estimation for simultaneous equations models suffering from the problem of multicollinearity. This problem is also handled by using some prior information. Taking account of this knowledge, we recommend two stage modified ridge estimator. The new estimator can also be evaluated as an alternative to the previously proposed two stage ridge estimator. The widespread performance criterion, mean square error, is taken into consideration to compare the two stage modified ridge, two stage ridge and two stage least squares estimators. A real life data analysis is investigated to prove the theoretical results in practice. In addition, the intervals of the biasing parameter which provide the superiority of the two stage modified ridge estimator are determined with the help of figures. The researchers who deal with simultaneous systems with multicollinearity can opt for the two stage modified ridge estimator.

Gaming the System: An Agent-Based Model of Estimation Strategies and their Effects on System Performance

Parameter estimates in large-scale complex engineered systems (LaCES) affect system evolution, yet can be difficult and expensive to test. Systems engineering uses analytical methods to reduce uncertainty, but a growing body of work from other disciplines indicates that cognitive heuristics also affect decision-making. Results from interviews with expert aerospace practitioners suggest that engineers bias estimation strategies. Practitioners reaffirmed known system features and posited that engineers may bias estimation methods as a negotiation and resource conservation strategy. Specifically, participants reported that some systems engineers “game the system” by biasing requirements to counteract subsystem estimation biases. An agent-based model (ABM) simulation which recreates these characteristics is presented. Model results suggest that system-level estimate accuracy and uncertainty depend on subsystem behavior and are not significantly affected by systems engineers' “gaming” strategy.

Two-Parameter Ridge Estimation for the Coefficients of Almon Distributed Lag Model

This paper resolves the difficulty in using Almon’s technique in the estimation of distributed lag coefficients when the researchers run into the problem of multicollinearity. Multicollinearity arising in the analysis leads us to the biased estimation methods, one of which is Almon ridge estimator. In consideration of two-parameter ridge solution of Lipovetsky and Conklin (Appl Stoch Mod Bus Ind 21:525–540, 2005), we offer Almon two-parameter ridge estimator, which has advantage over Almon estimator as well as Almon ridge estimator with regard to mean square error criterion. Besides, an improvement in coefficient of multiple determination is observed for the new estimator relative to the Almon ridge estimator. An illustrative application of the mentioned estimators is examined by widely used Almon data to support the theoretical results. Additionally, a Monte Carlo experiment is performed to investigate the performance of the estimators in detail.

Investigating the two parameter analysis of Lipovetsky for simultaneous systems

Two stage least squares regression analysis is the most practical statistical technique that is used in the analysis of structural equations. This study demonstrates the utility of some biased estimation methods when there is inherent multicollinearity among exogenous variables of a simultaneous system. Two stage ridge estimator is one of the biased estimators encountered in this model. In the light of the two parameter ridge estimator of Lipovetsky and Conklin (Appl Stoch Mod Bus Ind 21:525–540, 2005) in linear regression model, we propose two stage two parameter ridge estimator in the simultaneous equations model. Due to the fact that Lipovetsky and Conklin’s two parameter ridge estimator is superior to the ridge and ordinary least squares estimators, we expect the superiority of our new two stage two parameter ridge estimator to the two stage ridge estimator and the two stage least squares estimator. This superiority is proved theoretically. A data analysis involved with Klein Model I is examined to illustrate the mastery of the two stage two parameter ridge estimator in the sense of mean square error. In addition, an extensive Monte Carlo experiment is conducted. It is recommended that investigators who develop simultaneous equations models may perform the new estimator to eliminate the effect of multicollinearity on parameter estimates.

Multicollinearity in simultaneous equations system: evaluation of estimation performance of two-parameter estimator

In simultaneous equations model, two-stage least squares estimator is easy to apply and commonly preferred. When multicollinearity exists, two-stage least squares estimator has some drawbacks and it is no longer favorable. In this context, biased estimation methods are recommended. Two-parameter estimator of Ozkale and Kaciranlar (Commun Stat Theory Methods 36(15):2707–2725, 2007) had been established to be superior to the ordinary least squares estimator under some conditions in linear regression model suffering from multicollinearity. In this paper, the idea of two-parameter estimation in linear regression model is carried out to the simultaneous equations model. For this model, two-stage two-parameter estimator is proposed to remedy the problem of multicollinearity. Estimation performance of this new estimator is evaluated by means of two real-life data analyses. In addition to the numerical example, an extensive Monte Carlo experiment is conducted.

A Fast In-Field Coarse Alignment and Bias Estimation Method for Stationary Intermediate-Grade IMUs

This paper presents an innovative in-field coarse bias estimation (CBE) method for stationary intermediate-grade inertial measurement units (IMUs), which is based on the existence of normality and orthogonality errors in the attitude matrix supplied by the traditional three-axis attitude determination stationary coarse alignment (CA) stage. Differently from the currently existing in-field bias estimation formulations, the proposed CBE method is conceived to be conducted in stationary conditions, jointly with the CA, and it allows the down accelerometer bias and the north and down angular rate sensor biases to be adequately estimated. As a main contribution of this paper, we demonstrate that the proposed CBE method is able to greatly accelerate the estimation process of the aforementioned biases, contributing, hence, to shorten the IMU setup time. A comprehensive error analysis is presented, and the conclusions are twofold: 1) the proposed CBE method is valid regardless of the IMU orientation and 2) its estimation accuracy is mainly constrained by the north accelerometer bias and the position location uncertainty, which are, in general, very reduced. Results from simulated and experimental test confirm the adequacy of the outlined verifications, also attesting the superiority of the proposed CBE method in situations where, due to time constraints, stationary fine alignment procedures are not allowed to be carried out.

Optimal Linear Biased Estimation Based on Generalized Contraction Mapping

Estimation methods are generalized in this paper by the idea of “scalar-vector-matrix”. A generalized contraction mapping (GCM) framework is proposed for searching the optimal linear biased estimation. First, based on the latent model and the mean square error criterion, four different biased estimation methods are analyzed. They are the improved principal component estimation (PCE), the improved principal component estimation (IPCE), the ridge estimation (RE), and the generalized ridge estimation (GRE). A suboptimal ridge parameter for the RE is given. Four estimation performance theorems for the four methods are obtained using the traditional contraction mapping (CM) framework. The theoretical results can ease the difficulty of choosing methods for application. Second, we generalize the CM framework into the generalized contraction mapping (GCM) framework, and the optimal linear biased estimation method based GCM is given theoretically by the geometric tools of rotation, contraction, and reflection. Therefore, the GCM framework further improves the estimation performance. Finally, a numerical experiment is designed to validate the correctness of the theorems in the paper.

Causal inference with measurement error in outcomes: Bias analysis and estimation methods.

Inverse probability weighting estimation has been popularly used to consistently estimate the average treatment effect. Its validity, however, is challenged by the presence of error-prone variables. In this paper, we explore the inverse probability weighting estimation with mismeasured outcome variables. We study the impact of measurement error for both continuous and discrete outcome variables and reveal interesting consequences of the naive analysis which ignores measurement error. When a continuous outcome variable is mismeasured under an additive measurement error model, the naive analysis may still yield a consistent estimator; when the outcome is binary, we derive the asymptotic bias in a closed-form. Furthermore, we develop consistent estimation procedures for practical scenarios where either validation data or replicates are available. With validation data, we propose an efficient method for estimation of average treatment effect; the efficiency gain is substantial relative to usual methods of using validation data. To provide protection against model misspecification, we further propose a doubly robust estimator which is consistent even when either the treatment model or the outcome model is misspecified. Simulation studies are reported to assess the performance of the proposed methods. An application to a smoking cessation dataset is presented.

Performance of some ridge estimators for the gamma regression model

In this study, we proposed some ridge estimators by considering the work of Mansson (Econ Model 29(2):178–184, 2012), Dorugade (J Assoc Arab Univ Basic Appl Sci 15:94–99, 2014) and some others for the gamma regression model (GRM). The GRM is a special form of the generalized linear model (GLM), where the response variable is positively skewed and well fitted to the gamma distribution. The commonly used method for estimation of the GRM coefficients is the maximum likelihood (ML) estimation method. The ML estimation method perform better, if the explanatory variables are uncorrelated. There are the situations, where the explanatory variables are correlated, then the ML estimation method is incapable to estimate the GRM coefficients. In this situation, some biased estimation methods are proposed and the most popular one is the ridge estimation method. The ridge estimators for the GRM are proposed and compared on the basis of mean squared error (MSE). Moreover, the outperforms of proposed ridge estimators are also calculated. The comparison has done using a Monte Carlo simulation study and two real data sets. Results show that Kibria’s and Mansson and Shukur’s methods are preferred over the ML method.

A Map-based Lateral and Longitudinal DGPS/DR Bias Estimation Method for Autonomous Driving

A Map-based Lateral and Longitudinal DGPS/DR Bias Estimation Method for Autonomous Driving