Robust Estimation Procedure Research Articles

Smoothing combined generalized estimating equations in quantile partially linear additive models with longitudinal data

This paper develops a robust and efficient estimation procedure for quantile partially linear additive models with longitudinal data, where the nonparametric components are approximated by B spline basis functions. The proposed approach can incorporate the correlation structure between repeated measures to improve estimation efficiency. Moreover, the new method is empirically shown to be much more efficient and robust than the popular generalized estimating equations method for non-normal correlated random errors. However, the proposed estimating functions are non-smooth and non-convex. In order to reduce computational burdens, we apply the induced smoothing method for fast and accurate computation of the parameter estimates and its asymptotic covariance. Under some regularity conditions, we establish the asymptotically normal distribution of the estimators for the parametric components and the convergence rate of the estimators for the nonparametric functions. Furthermore, a variable selection procedure based on smooth-threshold estimating equations is developed to simultaneously identify non-zero parametric and nonparametric components. Finally, simulation studies have been conducted to evaluate the finite sample performance of the proposed method, and a real data example is analyzed to illustrate the application of the proposed method.

Robust estimation for varying index coefficient models

Varying index coefficient models (VICMs) proposed by Ma and Song (J Am Stat Assoc, 2014. doi:10.1080/01621459.2014.903185) are a new class of semiparametric models, which encompass most of the existing semiparametric models. So far, only the profile least squares method and local linear fitting were developed for the VICM, which are very sensitive to the outliers and will lose efficiency for the heavy tailed error distributions. In this paper, we propose an efficient and robust estimation procedure for the VICM based on modal regression which depends on a bandwidth. We establish the consistency and asymptotic normality of proposed estimators for index coefficients by utilizing profile spline modal regression method. The oracle property of estimators for the nonparametric functions is also established by utilizing a two-step spline backfitted local linear modal regression approach. In addition, we discuss the bandwidth selection for achieving better robustness and efficiency and propose a modified expectation---maximization-type algorithm for the proposed estimation procedure. Finally, simulation studies and a real data analysis are carried out to assess the finite sample performance of the proposed method.

Robust estimation in generalized linear models: the density power divergence approach

The generalised linear model (GLM) is a very important tool for analysing real data in biology, sociology, agriculture, engineering and many other application domain where the relationship between the response and explanatory variables may not be linear or the distributions may not be normal in all the cases. However, quite often such real data contain a significant number of outliers in relation to the standard parametric model used in the analysis; in such cases the classical maximum likelihood estimator may fail to produce reasonable estimators and related inference could be unreliable. In this paper, we develop a robust estimation procedure for the generalised linear models that can generate robust estimators with little loss in efficiency. We will also explore two particular cases of the generalised linear model in details -- Poisson regression for count data and logistic regression for binary data -- which are widely applied in real life experiments. We will also illustrate the performance of the proposed estimators through several interesting data examples

Solid‐state fermentation process model reparametrization procedure for parameters estimation using particle swarm optimization

AbstractBACKGROUNDSolid‐state fermentation is a well‐known bioprocess. The development of a solid‐state fermentation reactor faces difficulties in controlling temperature gradients inside the bed. To understand this behavior, a good phenomenological model must be used. Furthermore, the model parameters must be obtained by a reliable and robust parameters estimation procedure, since often the model parameters are not available in the literature.RESULTSThe heuristic particle swarm optimization (PSO) method was used to estimate the parameters of the reparametrized model through the minimization of a nonlinear‐square objective function, since it is less sensitive to initial guesses than derivative based methods. Statistical analyses were made to evaluate the parameter estimation quality. Also, simulations with the reparametrized model were performed. All the analyses have revealed the great accuracy of the proposed model, predicting with very small residuals (errors) several experimental data sets of a solid‐state fermentation process.CONCLUSIONParameter models reparametrization procedure can be a very useful mathematical tool to obtain accurate and reliable models with fewer parameters to be estimated, providing less parameters correlation and increasing the degrees of freedom to perform the statistical analysis. In addition, the particle swarm optimization was found to be a very robust and efficient parameter estimation method. © 2015 Society of Chemical Industry

Improved deep-etched multilayer grating reconstruction by considering etching anisotropy and abnormal errors in optical scatterometry.

Accurate, fast, and nondestructive reconstruction of the etched nanostructures is important for etching process control to achieve good fidelity, as well as high manufacturing yield. In this work, we have demonstrated the improved deep-etched multilayer grating reconstruction by simultaneously considering the model error of nonuniform side-wall angle (SWA) because of different etching anisotropies of various materials and by suppressing the abnormally distributed measurement errors using a robust statistics based method in optical scatterometry. More specifically, we introduce an additional parameter to perfect the profile model under measurement, and use a robust estimation procedure at the end of each iteration of the Gauss-Newton (GN) method to obtain the more accurate parameter departure vector. By applying the proposed methods, more accurate reconstructed results can be achieved.

Robust ridge regression estimators for nonlinear models with applications to high throughput screening assay data.

Nonlinear regression is often used to evaluate the toxicity of a chemical or a drug by fitting data from a dose-response study. Toxicologists and pharmacologists may draw a conclusion about whether a chemical is toxic by testing the significance of the estimated parameters. However, sometimes the null hypothesis cannot be rejected even though the fit is quite good. One possible reason for such cases is that the estimated standard errors of the parameter estimates are extremely large. In this paper, we propose robust ridge regression estimation procedures for nonlinear models to solve this problem. The asymptotic properties of the proposed estimators are investigated; in particular, their mean squared errors are derived. The performances of the proposed estimators are compared with several standard estimators using simulation studies. The proposed methodology is also illustrated using high throughput screening assay data obtained from the National Toxicology Program.

Robust smooth-threshold estimating equations for generalized varying-coefficient partially linear models based on exponential score function

In this paper, we present a new efficient and robust estimation procedure for generalized varying coefficient partially linear models (GVCPLMs), where the nonparametric coefficients are approximated by polynomial splines. A bounded exponential score function with a tuning parameter γ and leverage based weights are applied to the estimating equations for achieving robustness against outliers in both the response and covariates directions. Our motivation for the new estimation procedure is that it enables us to achieve better robustness and efficiency by selecting automatically the tuning parameter γ using the observed data. The proposed estimator is as asymptotically efficient as the common quasi-likelihood estimator when there are no outliers. Moreover, an automatic variable selection procedure is developed to select significant parametric components for the GVCPLM based on robust smooth-threshold estimating equations. Simulations and a real data example are used to demonstrate the finite sample behavior of the proposed estimator.

Optimize Preview Model Parameters Evaluation of RANSAC

The Random Sample Consensus (RANSAC) algorithm is a popular tool for robust estimation problems in computer vision, primarily due to its ability to tolerate a tremendous fraction of outliers. In this paper, we propose an approach for optimizing the preview model parameters evaluation of RANSAC that has the benefit of offering fast and accurate RANSAC. With guaranteeing the same confidence of the solution as RANSAC, a very large number of erroneous model parameters obtained from the contaminated samples are discarded in the preview evaluation selection. And use local optimization step apply to selected models. The combination of these two strategies results in a robust estimation procedure that provides a significant speed and accuracy RANSAC techniques, while requiring no prior information to guide the sampling process.

Moving beyond the hazard ratio in quantifying the between-group difference in survival analysis.

In a longitudinal clinical study to compare two groups, the primary end point is often the time to a specific event (eg, disease progression, death). The hazard ratio estimate is routinely used to empirically quantify the between-group difference under the assumption that the ratio of the two hazard functions is approximately constant over time. When this assumption is plausible, such a ratio estimate may capture the relative difference between two survival curves. However, the clinical meaning of such a ratio estimate is difficult, if not impossible, to interpret when the underlying proportional hazards assumption is violated (ie, the hazard ratio is not constant over time). Although this issue has been studied extensively and various alternatives to the hazard ratio estimator have been discussed in the statistical literature, such crucial information does not seem to have reached the broader community of health science researchers. In this article, we summarize several critical concerns regarding this conventional practice and discuss various well-known alternatives for quantifying the underlying differences between groups with respect to a time-to-event end point. The data from three recent cancer clinical trials, which reflect a variety of scenarios, are used throughout to illustrate our discussions. When there is not sufficient information about the profile of the between-group difference at the design stage of the study, we encourage practitioners to consider a prespecified, clinically meaningful, model-free measure for quantifying the difference and to use robust estimation procedures to draw primary inferences.

Reciprocal social influence on investment decisions: behavioral evidence from a group of mutual fund managers

In this paper, I analyze reciprocal social influence on investment decisions in an international group of roughly 2,000 mutual fund managers who invested in companies in the DAX30. Using a robust estimation procedure, I provide empirical evidence that the average fund manager puts 0.69 % more portfolio weight on a particular stock if his or her peers, on average, assign a weight to the corresponding position that is 1 % higher compared to other stocks in the portfolio. The dynamics of this influence on choice of portfolio weights suggest that fund managers adjust their behavior based on the prevailing market situation and are more strongly influenced by others in times of an economic downturn. Analyzing the working locations of the fund managers, I conclude that more than 90 % of the magnitude of influence stems from social learning. Although this form of influence varies a great deal over time, the magnitude of influence resulting from the exchange of opinions is more or less constant.

Estimating the characteristics of randomized dynamic data models (the Entropy-Robust Approach)

We propose a new approach to finding dependencies between small volumes of input and output data based on randomized dynamic models and density estimation for the distributions of their parameters. Randomized dynamic models are defined by functional Volterra polynomials. To construct robust nonparametric estimation procedures, we develop an entropybased approach that employs functionals of generalized informational Boltzmann and Fermi entropies.

Impact of Critical Care Nursing on 30-Day Mortality of Mechanically Ventilated Older Adults*

The mortality rate for mechanically ventilated older adults in ICUs is high. A robust research literature shows a significant association between nurse staffing, nurses' education, and the quality of nurse work environments and mortality following common surgical procedures. A distinguishing feature of ICUs is greater investment in nursing care. The objective of this study is to determine the extent to which variation in ICU nursing characteristics-staffing, work environment, education, and experience-is associated with mortality, thus potentially illuminating strategies for improving patient outcomes. Multistate, cross-sectional study of hospitals linking nurse survey data from 2006 to 2008 with hospital administrative data and Medicare claims data from the same period. Logistic regression models with robust estimation procedures to account for clustering were used to assess the effect of critical care nursing on 30-day mortality before and after adjusting for patient, hospital, and physician characteristics. Three hundred and three adult acute care hospitals in California, Florida, New Jersey, and Pennsylvania. The patient sample included 55,159 older adults on mechanical ventilation admitted to a study hospital. None. Patients in critical care units with better nurse work environments experienced 11% lower odds of 30-day mortality than those in worse nurse work environments. Additionally, each 10% point increase in the proportion of ICU nurses with a bachelor's degree in nursing was associated with a 2% reduction in the odds of 30-day mortality, which implies that the odds on patient deaths in hospitals with 75% nurses with a bachelor's degree in nursing would be 10% lower than in hospitals with 25% nurses with a bachelor's degree in nursing. Critical care nurse staffing did not vary substantially across hospitals. Staffing and nurse experience were not associated with mortality after accounting for these other nurse characteristics. Patients in hospitals with better critical care nurse work environments and higher proportions of critical care nurses with a bachelor's degree in nursing experienced significantly lower odds of death.

REKINDLE: Robust extraction of kurtosis INDices with linear estimation

Recent literature shows that diffusion tensor properties can be estimated more accurately with diffusion kurtosis imaging (DKI) than with diffusion tensor imaging (DTI). Furthermore, the additional non-Gaussian diffusion features from DKI can be sensitive markers for tissue characterization. Despite these benefits, DKI is more susceptible to data artifacts than DTI due to its increased model complexity, higher acquisition demands, and longer scanning times. To increase the reliability of diffusion tensor and kurtosis estimates, we propose a robust estimation procedure for DKI. We have developed a robust and linear estimation framework, coined REKINDLE (Robust Extraction of Kurtosis INDices with Linear Estimation), consisting of an iteratively reweighted linear least squares approach. Simulations are performed, in which REKINDLE is evaluated and compared with the widely used RESTORE (Robust EStimation of Tensors by Outlier REjection) method. Simulations demonstrate that in the presence of outliers, REKINDLE can estimate diffusion and kurtosis indices reliably and with a 10-fold reduction in computation time compared with RESTORE. We have presented and evaluated REKINDLE, a linear and robust estimation framework for DKI. While REKINDLE has been developed for DKI, it is by design also applicable to DTI and other diffusion models that can be linearized.

Robust mixture regression model fitting by Laplace distribution

A robust estimation procedure for mixture linear regression models is proposed by assuming that the error terms follow a Laplace distribution. Using the fact that the Laplace distribution can be wr...

A Genome-Scale Integration and Analysis of Lactococcus lactis Translation Data

Protein synthesis is a template polymerization process composed by three main steps: initiation, elongation, and termination. During translation, ribosomes are engaged into polysomes whose size is used for the quantitative characterization of translatome. However, simultaneous transcription and translation in the bacterial cytosol complicates the analysis of translatome data. We established a procedure for robust estimation of the ribosomal density in hundreds of genes from Lactococcus lactis polysome size measurements. We used a mechanistic model of translation to integrate the information about the ribosomal density and for the first time we estimated the protein synthesis rate for each gene and identified the rate limiting steps. Contrary to conventional considerations, we find significant number of genes to be elongation limited. This number increases during stress conditions compared to optimal growth and proteins synthesized at maximum rate are predominantly elongation limited. Consistent with bacterial physiology, we found proteins with similar rate and control characteristics belonging to the same functional categories. Under stress conditions, we found that synthesis rate of regulatory proteins is becoming comparable to proteins favored under optimal growth. These findings suggest that the coupling of metabolic states and protein synthesis is more important than previously thought.

Robust errors-in-variables linear regression via Laplace distribution

Robust estimation procedures for linear and mixture linear errors-in-variables regression models are proposed based on the relationship between the least absolute deviation criterion and maximum likelihood estimation in a Laplace distribution. The finite sample performance of the proposed procedures is evaluated by simulation studies.

Item-Level RFID Tag Location Sensing Utilizing Reader Antenna Spatial Diversity

A robust estimation procedure for sensing the locations of passive UHF radio frequency identification (RFID) tags is introduced based on spatial deployment of the reader antennas for maximum signal diversity. A signal model is developed for the received signal strength indicator seen by each reader antenna and incorporated into a mean-square error testing function. The error function is minimized at each test point in the interrogation zone to find the point with the minimum mean-square error. The minimization is independent of the tag type and orientation, making the proposed method very robust compared with other methods that are based on reference tags and radio maps. Experimental results are presented for a realistic retail scenario with multiple tagged items achieving an estimation accuracy of 35 cm. The location sensing system uses conventional UHF RFID readers, antennas, and passive tags, providing additional capability to existing item-level RFID systems. This added value will help to offset the high cost of large-scale RFID infrastructure development.

Local rank estimation and related test for varying-coefficient partially linear models

This paper develops a robust estimation procedure for the varying-coefficient partially linear model via local rank technique. The new procedure provides a highly efficient and robust alternative to the local linear least-squares method. In other words, the proposed method is highly efficient across a wide class of non-normal error distributions and it only loses a small amount of efficiency for normal error. Moreover, a test for the hypothesis of constancy for the nonparametric component is proposed. The test statistic is simple and thus the test procedure can be easily implemented. We conduct Monte Carlo simulation to examine the finite sample performance of the proposed procedures and apply them to analyse the environment data set. Both the theoretical and the numerical results demonstrate that the performance of our approach is at least comparable to those existing competitors.

Estimate the Performance of Multi-Model Estimation Algorithms

A robust estimation procedure is necessary to estimate the true model parameters in computer vision. Evaluating the multiple-model in the presence of outliers-robust is a fundamentally different task than the single-model problem.Despite there are many diversity multi-model estimation algorithms, it is difficult to pick an effective and advisably approach.So we present a novel quantitative evaluation of multi-model estimation algorithms, efficiency may be evaluated by either examining the asymptotic efficiency of the algorithms or by running them for a series of data sets of increasing size.Thus we create a specifical testing dataset,and introduce a performance metric, Strongest-Intersection.and using the model-aware correctness criterion. Finally, well show the validity of estimation strategy by the Experimention of line-fitting.

Robust estimation for partially linear models with large-dimensional covariates.

We are concerned with robust estimation procedures to estimate the parameters in partially linear models with large-dimensional covariates. To enhance the interpretability, we suggest implementing a noncon-cave regularization method in the robust estimation procedure to select important covariates from the linear component. We establish the consistency for both the linear and the nonlinear components when the covariate dimension diverges at the rate of [Formula: see text], where n is the sample size. We show that the robust estimate of linear component performs asymptotically as well as its oracle counterpart which assumes the baseline function and the unimportant covariates were known a priori. With a consistent estimator of the linear component, we estimate the nonparametric component by a robust local linear regression. It is proved that the robust estimate of nonlinear component performs asymptotically as well as if the linear component were known in advance. Comprehensive simulation studies are carried out and an application is presented to examine the finite-sample performance of the proposed procedures.