Presence Of Influential Observations Research Articles

Proportional hazard‐based robust monitoring schemes using logistic distribution

AbstractIn the manufacturing industry, process surveillance plays an important role in improving product reliability. Many monitoring procedures have been devised to improve the reliability of a product in the literature. Due to cascading nature of multistage processes, the quality variable of the final stage can be influenced by the quality variable in the previous stages. Furthermore, the ordinary least squares method produces biased estimates if there are outliers in the historical data. The existence of cascade property in the multistage process and the presence of influential observations (outliers) in the historical data make the analysis of control schemes more challenging. Therefore, it is essential to take into account the impact of effective covariates and outliers in the historical dataset. In this paper, a cumulative sum (CUSUM) and two exponentially weighted moving average (EWMA) charts have been developed to monitor a two‐stage‐dependent process. The proportional hazard (PH) model has been applied to model the relationship among the incoming and outgoing variables of the two stage process. To deal with the deleterious effects of outliers on the results, a robust regression technique known as the M‐estimation has been implemented and the performance of the proposed monitoring procedures has been analyzed through Monte Carlo simulations. Lastly, two real‐life applications of the proposed control schemes are presented.

Empirical Bayes Model Averaging with Influential Observations: Tuning Zellner’s [formula omitted] Prior for Predictive Robustness

The behavior of Bayesian model averaging (BMA) for the normal linear regression model in the presence of influential observations that contribute to model misfit is investigated. Remedies to attenuate the potential negative impacts of such observations on inference and prediction are proposed. The methodology is motivated by the view that well-behaved residuals and good predictive performance often go hand-in-hand. Focus is placed on regression models that use variants on Zellner's g prior. Studying the impact of various forms of model misfit on BMA predictions in simple situations points to prescriptive guidelines for “tuning” Zellner's g prior to obtain optimal predictions. The tuning of the prior distribution is obtained by considering theoretical properties that should be enjoyed by the optimal fits of the various models in the BMA ensemble. The methodology can be thought of as an “empirical Bayes” approach to modeling, as the data help to inform the specification of the prior in an attempt to attenuate the negative impact of influential cases.

Influence diagnostics for censored regression models with autoregressive errors

SummaryObservations collected over time are often autocorrelated rather than independent, and sometimes include observations below or above detection limits (i.e. censored values reported as less or more than a level of detection) and/or missing data. Practitioners commonly disregard censored data cases or replace these observations with some function of the limit of detection, which often results in biased estimates. Moreover, parameter estimation can be greatly affected by the presence of influential observations in the data. In this paper we derive local influence diagnostic measures for censored regression models with autoregressive errors of order p (hereafter, AR(p)‐CR models) on the basis of the Q‐function under three useful perturbation schemes. In order to account for censoring in a likelihood‐based estimation procedure for AR(p)‐CR models, we used a stochastic approximation version of the expectation‐maximisation algorithm. The accuracy of the local influence diagnostic measure in detecting influential observations is explored through the analysis of empirical studies. The proposed methods are illustrated using data, from a study of total phosphorus concentration, that contain left‐censored observations. These methods are implemented in the R package ARCensReg.

Spatial Variability in Slash Linear Modeling with Finite Second Moment

This article studies the dependence of spatial linear models using a slash distribution with a finite second moment. The parameters of the model are estimated with maximum likelihood by using the EM algorithm. To avoid identifiability problems, the cross-validation, the Trace and the maximum log-likelihood value are used to choose the parameter for adjusting the kurtosis of the slash distribution and the selection of the model to explain the spatial dependence. We present diagnostic techniques of global and local influences for exploring the sensibility of estimators and the presence of possible influential observations. A simulation study is developed to determine the performance of the methodology. The results showed the effectiveness of the choice criteria of the parameter for adjusting the kurtosis and for the selection of the spatial dependence model. It has also showed that the slash distribution provides an increased robustness to the presence of influential observations. As an illustration, the proposed model and its diagnostics are used to analyze an aquifer data. The spatial prediction with and without the influential observations were compared. The results show that the contours of the interpolation maps and prediction standard error maps showed low changes when we removed the influential observations. Thus, this model is a robust alternative in the spatial linear modeling for dependent random variables. Supplementary materials accompanying this paper appear online.

A multiple-case deletion approach for detecting influential points in high-dimensional regression

ABSTRACTIn high-dimensional regression, the presence of influential observations may lead to inaccurate analysis results so that it is a prime and important issue to detect these unusual points before statistical regression analysis. Most of the traditional approaches are, however, based on single-case diagnostics, and they may fail due to the presence of multiple influential observations that suffer from masking effects. In this paper, an adaptive multiple-case deletion approach is proposed for detecting multiple influential observations in the presence of masking effects in high-dimensional regression. The procedure contains two stages. Firstly, we propose a multiple-case deletion technique, and obtain an approximate clean subset of the data that is presumably free of influential observations. To enhance efficiency, in the second stage, we refine the detection rule. Monte Carlo simulation studies and a real-life data analysis investigate the effective performance of the proposed procedure.

Robust Adaptive Lasso method for parameter's estimation and variable selection in high-dimensional sparse models.

High dimensional data are commonly encountered in various scientific fields and pose great challenges to modern statistical analysis. To address this issue different penalized regression procedures have been introduced in the litrature, but these methods cannot cope with the problem of outliers and leverage points in the heavy tailed high dimensional data. For this purppose, a new Robust Adaptive Lasso (RAL) method is proposed which is based on pearson residuals weighting scheme. The weight function determines the compatibility of each observations and downweight it if they are inconsistent with the assumed model. It is observed that RAL estimator can correctly select the covariates with non-zero coefficients and can estimate parameters, simultaneously, not only in the presence of influential observations, but also in the presence of high multicolliearity. We also discuss the model selection oracle property and the asymptotic normality of the RAL. Simulations findings and real data examples also demonstrate the better performance of the proposed penalized regression approach.

A robust variable screening method for high-dimensional data

ABSTRACTIn practice, the presence of influential observations may lead to misleading results in variable screening problems. We, therefore, propose a robust variable screening procedure for high-dimensional data analysis in this paper. Our method consists of two steps. The first step is to define a new high-dimensional influence measure and propose a novel influence diagnostic procedure to remove those unusual observations. The second step is to utilize the sure independence screening procedure based on distance correlation to select important variables in high-dimensional regression analysis. The new influence measure and diagnostic procedure that we developed are model free. To confirm the effectiveness of the proposed method, we conduct simulation studies and a real-life data analysis to illustrate the merits of the proposed approach over some competing methods. Both the simulation results and the real-life data analysis demonstrate that the proposed method can greatly control the adverse effect after detecting and removing those unusual observations, and performs better than the competing methods.

High-dimensional influence measure

Influence diagnosis is important since presence of influential observations could lead to distorted analysis and misleading interpretations. For high-dimensional data, it is particularly so, as the increased dimensionality and complexity may amplify both the chance of an observation being influential, and its potential impact on the analysis. In this article, we propose a novel high-dimensional influence measure for regressions with the number of predictors far exceeding the sample size. Our proposal can be viewed as a high-dimensional counterpart to the classical Cook's distance. However, whereas the Cook's distance quantifies the individual observation's influence on the least squares regression coefficient estimate, our new diagnosis measure captures the influence on the marginal correlations, which in turn exerts serious influence on downstream analysis including coefficient estimation, variable selection and screening. Moreover, we establish the asymptotic distribution of the proposed influence measure by letting the predictor dimension go to infinity. Availability of this asymptotic distribution leads to a principled rule to determine the critical value for influential observation detection. Both simulations and real data analysis demonstrate usefulness of the new influence diagnosis measure.

Detecting influential observations in Liu and modified Liu estimators

In regression, detecting anomalous observations is a significant step for model-building process. Various influence measures based on different motivational arguments are designed to measure the influence of observations through different aspects of various regression models. The presence of influential observations in the data is complicated by the existence of multicollinearity. The purpose of this paper is to assess the influence of observations in the Liu [9] and modified Liu [15] estimators by using the method of approximate case deletion formulas suggested by Walker and Birch [14]. A numerical example using a real data set used by Longley [10] and a Monte Carlo simulation are given to illustrate the theoretical results.

Detecting Global Influential Observations in Liu Regression Model

In linear regression analysis, detecting anomalous observations is an important step for model building process. Various influential measures based on different motivational arguments and designed to measure the influence of observations on different aspects of various regression results are elucidated and critiqued. The presence of influential observations in the data is complicated by the presence of multicollinearity. In this paper, when Liu estimator is used to mitigate the effects of multicollinearity the influence of some observations can be drastically modified. Approximate deletion formulas for the detection of influential points are proposed for Liu estimator. Two real macroeconomic data sets are used to illustrate the methodologies proposed in this paper.

A simulation study of predictive ability measures in a survival model II: explained randomness and predictive accuracy

Several R(2) -type measures have been proposed to evaluate the predictive ability of a survival model. In Part I, we classified the measures into four categories and studied the measures in the explained variation category. In this paper, we study the remaining measures in a similar fashion, discussing their strengths and shortcomings. Simulation studies are used to examine the performance of the measures with respect to the criteria we set out in Part I. Our simulation studies showed that among the measures studied in this paper, the measures proposed by Kent and O'Quigley ρ(W)(2) (and its approximation ρ(W,A)(2)) and Schemper and Kaider R(SK)(2) perform better with respect to our criteria. However, our investigations showed that ρ(W)(2) is adversely affected by the distribution of covariate and the presence of influential observations. The results show that the other measures perform poorly, primarily because they are affected either by the degree of censoring or the follow-up period.

Restricted methods in symmetrical linear regression models

In this paper we discuss the problem of testing equality and inequality constraints in symmetrical linear regression models. This class of models includes all symmetric continuous distributions, such as normal, Student- t, Pearson VII, power exponential and logistic, among others. It is commonly used for the analysis of data containing influential or outlying observations with responses supposedly normal. Iterative processes for evaluating the parameters under equality and inequality constraints are presented. The asymptotic null distribution of three asymptotically equivalent one-sided tests is showed to be invariant with the symmetrical error. A sensitivity study to investigate the robustness of the maximum likelihood estimates from some symmetrical models against high leverage and influential observations is presented. An illustrative example with presence of influential observations on the decisions from the statistical tests of different symmetrical models is given. The robustness aspects of such models are also discussed.

Hydrologic process simulation of a semiarid, endoreic catchment in Sahelian West Niger. 2. Model calibration and uncertainty characterization

The Wankama endoreic system in the region of Niamey (Niger), monitored over the period 1992–2000, is studied with r.water.fea, a physically-based, spatially-distributed rainfall–runoff model. Catchment characteristics and data, together with model principles and construction, are described in Peugeot et al. [J. Hydrol., 2003], who used the uncalibrated model as one of several investigation tools for the screening of rainfall–runoff observations. This second paper focuses on model calibration and verification, namely the methods and criteria used to that end followed by the results thereby obtained. Based on a diagnostic function that combines errors in runoff volumes and in peak discharges, calibration is performed by exploring a 3D parameter space. A resampling-based cross-validation technique is used to investigate calibration stability with respect to data sample fluctuations, and to assess the predictive capabilities of the calibrated model. The issues of parameter uncertainty, sample representativeness, and presence of influential observations, are discussed. An empirical, non-parametric method is devised to characterize parameter uncertainty and to assign intervals to volume predictions. Model verification is performed against the data from the last two seasons. Internal catchment behavior, as produced by the model, appears qualitatively consistent with field information, including a weak upper-area contribution to catchment outflow due to large runoff abstraction by the conveying hydrographic network.