Showing papers on "Outlier published in 1992"

Methods for Dealing With Reaction Time Outliers

Abstract: The effect of outliers on reaction time analyses is evaluated. The first section assesses the power of different methods of minimizing the effect of outliers on analysis of variance (ANOVA) and makes recommendations about the use of transformations and cutoffs. The second section examines the effect of outliers and cutoffs on different measures of location, spread, and shape and concludes using quantitative examples that robust measures are much less affected by outliers and cutoffs than measures based on moments. The third section examines fitting explicit distribution functions as a way of recovering means and standard deviations and concludes that unless fitting the distribution function is used as a model of distribution shape, the method is probably not worth routine use.

Accommodating Outliers and Nonlinearity in Decision Models

Abstract: This paper describes and compares six procedures that can be used in a regression model to adjust for outliers in the data and nonlinearities in the relationship between the dependent and independe...

A note on the sampling variance of the mean uncorrected correlation in meta-analysis and validity generalization.

Abstract: This article compares the accuracy of several formulas for the standard error of the mean uncorrected correlation in meta-analytic and validity generalization studies. The effect of computing the mean correlation by weighting the correlation in each study by its sample size is also studied. On the basis of formal analysis and simulation studies, it is concluded that the common formula for the sampling variance of the mean correlation, V r =V/ r /K where K is the number of studies in the meta-analysis, gives reasonably accurate results. This formula gives accurate results even when sample sizes and ps are unequal and regardless of whether or not the statistical artifacts vary from study to study. It is also shown that using sample-size weighting may result in underestimation of the standard error of the mean uncorrected correlation when there are outlier sample sizes

Looking at large data sets using binned data plots

Abstract: This report addresses the monumental challenge of developing exploratory analysis methods for large data sets. The goals of the report are to increase awareness of large data sets problems and to contribute simple graphical methods that address some of the problems. The graphical methods focus on two- and three-dimensional data and common task such as finding outliers and tail structure, assessing central structure and comparing central structures. The methods handle large sample size problems through binning, incorporate information from statistical models and adapt image processing algorithms. Examples demonstrate the application of methods to a variety of publicly available large data sets. The most novel application addresses the too many plots to examine'' problem by using cognostics, computer guiding diagnostics, to prioritize plots. The particular application prioritizes views of computational fluid dynamics solution sets on the fly. That is, as each time step of a solution set is generated on a parallel processor the cognostics algorithms assess virtual plots based on the previous time step. Work in such areas is in its infancy and the examples suggest numerous challenges that remain. 35 refs., 15 figs.

Sequential Application of Wilks's Multivariate Outlier Test

Abstract: A generalization of Wilks's single‐outlier test suitable for application to the many‐outlier problem of detecting from 1 to k outliers in a multivariate data set is proposed and appropriate critical values determined. The method used follows that suggested by Rosner employing sequential application of the generalized extreme Studentized deviate to univariate samples of reducing size, in which the type I error is controlled both under the hypothesis of no outliers and under the alternative hypothesis of 1, 2,. . ., k outliers. It is shown that critical values for the sequential application of Wilks's test to detect many outliers depend only on those for a single outlier test which may be approximated by percentage points from the F‐distributions as tabulated by Wilks. Relationships between Wilks's test statistic, the Mahalanobis distance between the ‘outlier’ and the mean vector, and Hotelling's T2‐test between the outlier and the rest of the data, are used to reduce the amount of computation involved in applying the sequential procedure. Simulations are used to show that the method behaves well in detecting multiple outliers in samples larger than about 25. Finally, an example with three dimensions is used to illustrate how the method is applied.

A generalized estreme Studentized residual multiple-outlier-detetection procedure in linear regression

Abstract: This article is concerned with procedures for detecting multiple y outhers in linear regression. A generalized extreme studentized residual (GESR) procedure, which controls type I error rate, is developed. An approximate formula to calculate the percentiles is given for large samples and more accurate percentiles for n ≤ 25 are tabulated. The performance of this procedure is compared with others by Monte Carlo techniques and found to be superior. The procedure. however, fails in detecting y outliers that are on high-leverage cases. For this. a two-phase procedure is suggested. In phase 1, a set of suspect observations is identified by GESR and one of the diagnostics applied sequentially. In phase 2, a backward testing is conducted using the GESR procedure to see which of the suspect cases are outlicrs. Several examples are analyzed.

A note on time series model specification in the presence of outliers

Abstract: We investigate the usefulness of sample autocorrelations and partial autocorrelations as model specification tools when the observed time series is contaminated by an outlier. The results indicate that the specification power of these statistics could be significantly jeopardized by an additive outlier. On the other hand, an innovational outlier seems to cause no harm to them.

Bayes Factors for Outlier Models Using the Device of Imaginary Observations

Abstract: Suppose we think that most observations in a sample have been generated from a distribution with density f(x) but we fear that a few outliers from a distribution with density g(x) may have contaminated our sample. In many situations, we might assume that f(x) is a density depending on a parameter θ and that g(x) is of the same form as f but with parameter θ + δ or θδ. A number of Bayesian models for this problem when f is normal have been discussed by Freeman. He points out that with a vague improper prior for contaminating parameters, most posterior weight is put on the model allowing for the largest number of outliers. He therefore confines attention to proper priors when trying to answer the question of “how many outliers?” However, in many situations we do not have very certain information on the contaminating parameters and would like to make inferences about outliers when using improper priors for the parameters of the model. In this article, we apply the ideas of Spiegelhalter and Smith to...

An excel macro for transformed and weighted averaging

Abstract: An Excel macro is presented for averaging spreadsheet data. The macro has several special features: (1) The data are weighted by the inverse variance of each datum to decrease the contribution-of noisy outliers. (2) There is a provision for a power or a log transform of the data before averaging. The rationale for transforming the data before averaging is discussed (3) The output includes the average value, its standard error, and the reduced chi-square that measures the goodness of fit (4) The standard error is corrected by a heterogeneity factor based on the reduced chi-square The averaging of data is rarely done properly, and the intent of this article is to clarify the issues and provide a tool that allows researchers to improve their averaging techniques.

Algorithms for least median of squares state estimation of power systems

Abstract: The least median of squares (LMS) estimator minimizes the vth ordered squared residual. The authors derived a general expression of the optimal v for which the breakdown point of the LMS attains the highest possible fraction of outliers that any regression equivariant estimator can handle. This fraction is equal to half of the minimum surplus divided by the number of measurements in the network. The surplus of a fundamental set is defined as the smallest number of measurements whose removal from that fundamental set turns at least one measurement in the network into a critical one. Based on the surplus concept, a system decomposition scheme that significantly increases the number of outliers that can be identified by the LMS is developed. In addition, it dramatically reduces the computing time of the LMS, opening the door to real-time applications of that estimator to large-scale systems. Finally, outlier diagnostics based on robust Mahalanobis distances are proposed. >

Comparing one-step m-estimators of location corresponding to two independent groups

Abstract: Experience with real data indicates that psychometric measures often have heavy-tailed distributions. This is known to be a serious problem when comparing the means of two independent groups because heavy-tailed distributions can have a serious effect on power. Another problem that is common in some areas is outliers. This paper suggests an approach to these problems based on the one-step M-estimator of location. Simulations indicate that the new procedure provides very good control over the probability of a Type I error even when distributions are skewed, have different shapes, and the variances are unequal. Moreover, the new procedure has considerably more power than Welch's method when distributions have heavy tails, and it compares well to Yuen's method for comparing trimmed means. Wilcox's median procedure has about the same power as the proposed procedure, but Wilcox's method is based on a statistic that has a finite sample breakdown point of only 1/n, wheren is the sample size. Comments on other methods for comparing groups are also included.

Robust estimation of AR parameters and its application for speech enhancement

Abstract: There are two major problems in estimating vocal tract characteristics by conventional linear prediction: estimation accuracy being subject to the characteristics of the excitation source, and the output quality and the estimation accuracy deteriorating with additive background noise. The authors solved these problems as follows: first, estimate the parameters of a robust AR model where the driving noise is a mixture of a Gaussian and an outlier process; then, propose an iterative procedure that involves parameter estimation for uncorrupted speech and data cleaning based on the robust Kalman filter; lastly, the above results are used to enhance speech corrupted by white noise. The results are more efficient and less biased for uncorrupted speech, and superior at low SNR for noisy speech. >

Missing observations and additive outliers in time series models

Abstract: The paper deals with estimation of missing observations in possible nonstationary ARIMA models. First, the model is assumed known, and the structure of the interpolation filter is analyzed. Using the inverse or dual autocorrelation function it is seen how estimation of a missing observation is analogous to the removal of an outlier effect; both problems are closely related with the signal plus noise decomposition of the series. The results are extended to cover, first, the case of a missing observation near the two extremes of the series; then to the case of a sequence of missing observations, and finally to the general case of any number of sequences of any length of missing observations. The optimal estimator can always be expressed, in a compact way, in terms of the dual autocorrelation function or a truncation thereof; is mean squared error is equal to the inverse of the (appropriately chosen) dual autocovariance matrix. The last part of the paper illustrates a point of applied interest: When the model is unknown, the additive outlier approach may provide a convenient and efficient alternative to the standard Kalman filter-fixed point smoother approach for missing observations estimation.

Monitoring for outliers and level shifts in kalman filter implementations of exponential smoothing

Abstract: This paper presents a new application of a Kalman filter implementation of exponential smoothing with monitoring for outliers and level shifts. The assumption is that each observation comes from one of three models: steady, outlier, or level shift. This concept was introduced as a multiprocess model by Harrison and Stevens (1976). However, their handling of the models is different. In this paper four different model-selection criteria are introduced and compared by applying them to data. The new features of the application include the four model-selection criteria and the estimation of the required parameters by maximum likelihood.

Computing missing values in time series

Abstract: This work presents two algorithms to estimate missing values in time series. The first is the Kaiman Filter, as developed by Kohn and Ansley (1986) and others. The second is the additive outlier approach, developed by Pena, Ljung and Maravall. Both are exact and lead to the same results. However, the first is, in general, faster and the second more flexible.

Performance evaluation of a class of M-estimators for surface parameter estimation in noisy range data

Abstract: Depth maps are frequently analyzed as if, to an adequate approximation, the errors are normally, identically, and independently distributed. This noise model does not consider at least two types of anomalies encountered in sampling: A few large deviations in the data, often thought of as outliers; and a uniformly distributed error component arising from rounding and quantization. The theory of robust statistics formally addresses these problems and is efficiently used in a robust sequential estimator (RSE) of our own design. The specific implementation was based on a t-distribution error model, and this work extends this concept to several well known M-estimators. We evaluate the performance of these estimators under different noise conditions and highlight the effects of tuning constants and the necessity of simultaneous scale and parameter estimation.

An information theoretic robust sequential procedure for surface model order selection in noisy range data

Abstract: Modeling of the unknown surface, a key first step in the perception of surfaces in range images using the function approximation approach, is considered. Akaike's entropy-based information criterion (AIC) is a simple but powerful tool for choosing the best fitting model among several competing models. However, the AIC presupposes a fixed data set and a normality assumption on the error's distribution. The AIC is extended to a t-distribution noise model, which more realistically represents anomalies in the data such as outliers and quantization errors. This criterion is modified to be used with a robust sequential algorithm to accommodate the variable data size resulting from fitting different models. The modified criterion is applied to real range data, and its performance is compared with that of AIC and Consistent AIC. >

Self-Organizing Rules for Robust Principal Component Analysis

Abstract: In the presence of outliers, the existing self-organizing rules for Principal Component Analysis (PCA) perform poorly. Using statistical physics techniques including the Gibbs distribution, binary decision fields and effective energies, we propose self-organizing PCA rules which are capable of resisting outliers while fulfilling various PCA-related tasks such as obtaining the first principal component vector, the first k principal component vectors, and directly finding the subspace spanned by the first k vector principal component vectors without solving for each vector individually. Comparative experiments have shown that the proposed robust rules improve the performances of the existing PCA algorithms significantly when outliers are present.

Outlier Detection and Adjustment An Empirical Analysis for Austrian Data

Abstract: Time series are often subject to the influence of non-repetitive events. Economic variables make here no exception. For example, the announcement and implementation of new regulations, major changes in economic policy or in the tax legislation, and similar events may cause substantial disturbances in economic time series. The presence of outliers may lead to wrongly identified models and inappropriately estimated model parameters giving rise to poor forecasts and erroneous conclusions. In the past, these problems had mostly to be ignored, because simple yet efficient techniques for the treatment of outliers did not exist. The situation improved slightly whenBox-Tiao (1975) proposed intervention analysis. However, the fact that a detailed knowledge of the structure of the series to be analysed is required for a successful application of this technique, is a severe restriction for its use in practical work. But, in the meantime, there exist already techniques which solve the outlier problem more or less automatically. For a detailed discussion of these techniques and their computer implementation seeChen-Liu-Hudak (1990). It is the aim of this paper to gain information on the reliability of these methods in practical situations. For this purpose, we apply them in the analysis of three Austrian economic time series, namely retail sales, purchases of durables, and car purchases. We believe that these series are well suited for our objective. They are strongly contaminated by outliers and, additionally, there already exist sophisticated intervention models which can serve as benchmarks in the comparison.

Detection of the numbers of outliers present in a data set using an information theoretic criterion

Abstract: We use an information theoretic criterion proposed by Zhao, Krishnaiah and Bai (1986) to detect the number of outliers in a data set. We consider univariable mean-slippage and dispersion-slippage outlier structure of the observations. Multivariate generalizations and the consistency of the estimates are also considered. Numerical examples are presented in tables.

A robust off-line output error method for system identification

Abstract: The model reference technique and Huber's minimax principle have been successfully used to develop an offline output error method for robust identification of systems. This method is named the robust iterative output error method with modified residuals. A convergence analysis of the proposed method has been included as well as some simulation results. In the presence of a small number of large errors (called outliers) in the input-output data, the presented method has demonstrated its distinctive advantages over not only the nonrobust methods but also previously developed robust methods. The main advantages are a fast convergence speed and satisfactory robustness. It is concluded that the method developed here is much superior to the other methods and therefore can be widely used in many real-time applications. >

Estimation of Radioimmunoassay Data Using Robust Nonlinear Regression Methods

Abstract: The paper discusses several nonlinear regression methods estimating contaminated radioimmunoassay data. The underlying model is an overdispersed Poisson process with four regression line parameters and one parameter related to the overdispersion of the variance. A generalized least-squares (GLS) algorithm can be used for parameter estimation of noncontaminated data. In the presence of outliers different methods are discussed such as L p -norm or nonlinear generalizations of Huber’s M-estimator. The best estimation results we get by a winsorized version of the GLS algorithm.