Problem Of Outliers Research Articles

Primary Schooling, Cognitive Skills and Wages in South Africa

Using a fairly rich data set from South Africa, the paper finds that, despite the sobriquet ‘gutter education’, the African schooling systems help to create cognitive skills, and these skills are a determinant of wage levels. Various robust estimators are used but the influential outlier problem does not turn out to be serious. Computational skills appear to be more important than comprehension skills in influencing wages. The African primary schooling system was an extremely poor generator of computational skill, the seven‐year course raising the computational test score by 13%, if that. A policy implication is that productivity could be raised by certain near‐costless reallocations of resources in favour of mathematical learning.

Productivity Gains from Farmer Education in China

Regression results for five Chinese provinces provide stronger empirical support than hitherto for the role of farmer education in productivity gains. However, these results are largely due to the inclusion of two small groups of outliers: one consists of very poor households whose heads have no education and the other, relatively well‐off households whose heads have only three years of education. This article illustrates the need for a cautious interpretation of the regression results of earlier studies, because they could be affected by problems of outliers, multicollinearity and omitted variable bias.

Gibbs Sampling Will Fail in Outlier Problems with Strong Masking

Abstract This article discusses the convergence of the Gibbs sampling algorithm when it is applied to the problem of outlier detection in regression models. Given any vector of initial conditions, theoretically, the algorithm converges to the true posterior distribution. However, the speed of convergence may slow down in a high-dimensional parameter space where the parameters are highly correlated. We show that the effect of the leverage in regression models makes very difficult the convergence of the Gibbs sampling algorithm in sets of data with strong masking. The problem is illustrated with examples.

Gibbs Sampling Will Fail in Outlier Problems with Strong Masking

This paper discusses the convergence of the Gibbs sampling algorithm when it is applied to the problem of outlier detection in regression models. Given any vector of initial conditions, theoretically, the algorithm converges to the true posterior distribution. However, the speed of convergence may slow down in a high dimensional parameter space where the parameters are highly correlated. We show that the effect of the leverage in regression models makes very difficult the convergence of the Gibbs sampling algorithm in sets of data with strong masking. The problem is illustrated in several examples.

A scaling growth model for bubbles in basaltic lava flows

Pahoehoe, an and massive lavas from Mount Etna show common statistical properties from one sample to another which are independent of scale/size over certain ranges. The gas vesicle distribution shows two scale-invariant regimes with number density n(V) α V −B−1 where V is the volume and empirically B ≈ 0 for small bubbles and B ≈ 1 for medium to large bubbles. We introduce a bubble growth model which explains the B > 1 range by a strongly non-linear cascading growth regime dominated by a quasi-steady-state coalescence process. The small bubble region is dominated by diffusion; its role is to supply small bubbles to the coalescence regime. The presence of measured dissolved gas in the matrix glass is consistent with the notion that bubbles generally grow in quasi-steady-state conditions. The basic model assumptions are quite robust with respect to the action of a wide variety of processes, since we only require that the dynamics are scaled over the relevant range of scales, and that during the coalescence process, bubble volumes are (approximately) conserved. The model also predicts a decaying coalescence regime (with B > 1) associated with a depletion of the gas source or, alternatively, a loss of large vesicles through the surface of the flow. Our model thus explains the empirical evidence pointing to the coexistence of two different growth mechanisms in subsurface lava flows, but acting over distinct ranges of scale, with non-linear coalescence as the primary growth process. The total vesicularity of each sample can then be well estimated from the partial vesicularity of each growth regime without any outlier problems.

Dynamic credibility with outliers and missing observations

In actuarial practice the credibility models must face the problem of outliers and missing observations. If using the $M$-estimation principle from robust statistics in combination with Kalman filtering one obtains the solution of this problem that is acceptable in the numerical framework of the practical actuarial credibility. The credibility models are classified as static and dynamic in this paper and the shrinkage is used for the final ratemaking.

Bayesian analysis of outlier problems using divergence measures

AbstractA Bayesian approach is presented for detecting influential observations using general divergence measures on the posterior distributions. A sampling‐based approach using a Gibbs or Metropolis‐within‐Gibbs method is used to compute the posterior divergence measures. Four specific measures are proposed, which convey the effects of a single observation or covariate on the posterior. The technique is applied to a generalized linear model with binary response data, an overdispersed model and a nonlinear model. An asymptotic approximation using Laplace method to obtain the posterior divergence is also briefly discussed.

Robust Dual Scaling with Tukey's Biweight

Use of the method of reciprocal biweighted means (MBM) for dealing with the outlier problem in dual scal ing compared favorably with other robust estimation procedures, such as the method of trimmed reciprocal averages (MTA). Like the MTA, the MBM was easy to implement and it converged to a stable point when a two-step estimation procedure was used. One advantage of the MBM over the MTA was that it afforded greater control in fine tuning the final solution. Empirical re sults for four datasets, some containing multiple outli ers, are presented. Index terms: biweight, dual scaling, outliers, reciprocal averages, robust estimation, Tukey 's biweight.

Summarizing a Set of Radiocarbon Determinations: A Robust Approach

A general (Bayesian) method for summarizing sets of radiocarbon determinations is presented, combining archaeological a priori considerations with the radiocarbon determinations to obtain dates on the calendar scale. The problems of outliers (which are common in radiocarbon dating) and robustness are addressed. Outliers are defined within this context and an extended model to cope with outliers is also presented. Two examples are presented to illustrate the techniques proposed.

Bayesian Analysis of Linear and Non-Linear Population Models by Using the Gibbs Sampler

Abstract : A fully Bayesian analysis of linear and nonlinear population models has previously been unavailable, as a consequence of the seeming impossibility of performing the necessary numerical Integrations in the complex multi- parameter structures typically arising in such models. It is demonstrated that, for a variety of linear and nonlinear population models, a fully Bayesian analysis can be implemented in a straightforward manner using the Gibbs sampler. The approach is illustrated with examples involving challenging problems of outliers and mean-variance relationships in population modelling.

Contract and Fiduciary Duty

During the last two centuries, courts have been adapting this duty of loyalty and its remedy to other agency relations, under the title "fiduciary" duty.1 That is adaptation, not extension. The many agency relations that fall under the "fiduciary" banner are so diverse that a single rule could not cover all without wreaking havoc. Courts have applied the term to relations as diverse as guardian-ward, attorney-client, and bank-borrower. Does anything other than the word "fiduciary" and an appeal to a duty of loyalty (in its strong form, a duty that the agent work for the "exclusive benefit" of the principal) unite these situations? Principles of ethics? Is the fiduciary morally bound to act in a particular way, perhaps? Or are the different situations wholly distinct, so that a union's fiduciary "duty of fair representation" in labor law is unrelated to a corporate manager's fiduciary obligations to investors?

Tutorial review—Outliers in experimental data and their treatment

This review summarizes critically the approaches available to the treatment of suspect outlying results in sets of experimental measurements. It covers the use of parametric methods such as the Dixon test (with comments on the problems of multiple outliers); the application of non-parametric statistics based on the median to by-pass outlier problems; and the application of robust statistical methods, which down-weight the importance of outliers. The extension of these approaches to outliers occurring in regression problems is also surveyed.

Comparing probabilistic methods for outlier detection in linear models

SUMMARY This paper compares the use of two posterior probability methods to deal with outliers in linear models. We show that putting together diagnostics that come from the mean-shift and variance-shift models yields a procedure that seems to be more effective than the use of probabilities computed from the posterior distributions of actual realized residuals. The relation of the suggested procedure to the use of a certain predictive distribution for diagnostics is derived. Two main procedures for outlier detection have emerged when using the Bayesian approach. The first of these confines itself to postulating a null model for the generation of the data and then seeks identification methods for outliers with no alternative model to the null entertained. Examples of work in the category are (i) use of the predictive distribution for detection, (ii) using the posterior probabilities of various unobserved perturbations, and (iii) looking at the change in a posterior of interest when some observations are deleted. These methods will be discussed in ? 3 of this paper, after the basic model is set out in ? 2. The second procedure takes into account an alternative model for the generation of a subset of the sample. As examples, various authors have proposed and utilized the mean-shift model and the variance-inflation model. These methods are discussed in ? 4 of this paper. We show in this paper that these procedures can be classified as those which identify outliers by looking at some functions of the predictive density ordinate, and those that look at the posterior probabilities of the unobserved residuals. The first seems to be effective in overcoming the problem of high leverage outliers, in contrast to the latter, where outliers are masked by high leverage. These results are illustrated by examples in ? 5.

Long term influence of fertilization in a Nardetum

This part refers to the previous article ‘The management of great quantities of data from permanent plots’, where the techniques of data management and analysis are described. From the plots of Dr. W. Ludi, the average indicator values were calculated for moisture, soil reaction, nutrients supply, humus and dispersion, according to Landolt (1977). Significant correlations between the average N-(nutrient) and R-(soil reaction) indicator values are discussed. For some selected species, the long-time reaction to different fertilizers is presented. The problem of outliers is discussed due to the average indicator values and groups of species.

Outlier detection and adjustment

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.

Bayesian analysis of outlier problems using the Gibbs sampler

We consider the Bayesian analysis of outlier models. We show that the Gibbs sampler brings considerable conceptual and computational simplicity to the problem of calculating posterior marginals. Although other techniques for finding posterior marginals are available, the Gibbs sampling approach is notable for its ease of implementation. Allowing the probability of an outlier to be unknown introduces an extra parameter into the model but this turns out to involve only minor modification to the algorithm. We illustrate these ideas using a contaminated Gaussian distribution, at-distribution, a contaminated binomial model and logistic regression.

A bayesian solution to the multiple outlier problem in time series

In this paper, Bayesian solutions for the multiple outlier problems are proposed for the case in which the undisturbed observations are assumed to be generated by an autoregressive process. The procedures require that the observations considered suspected outliers are previously determined. The tests are based on the marginal or conditional posterior distributions, depending on the particular way in which the disturbances affect the behavior of the series.

Outliers in a multivariate autoregressive moving-average process

In this paper we deal with the problem of outliers in a multivariate ARMA-process. The location of the suspicious values is assumed to be known. In order to estimate the parameters, the maximum likelihood method is applied. The estimators are shown to be strong consistent, if the degree of contamination is not too big. Furthermore a test of discordancy for the general linear hypothesis is introduced. On condition that the white noise is multivariate normally distributed, the asymptotic distribution of the test statistic is calculated. Simultaneous treatment of the time series shows some advantages. It is possible to detect outliers, which cannot be determined by a separate investigation of the components.

Automatic time series modeling,intervention analysis, and effective forecasting

The purpose of this study is to investigate the forecasting efficiency of an expert system, an automatic time series modeling system, when applied to a quarterly earnings per share series. The Bethlehem steel quarterly earnings series has a severe outlier problem and the intervention analysis which specifically models the outlier may enhance forecasting efficiency. The purpose of this study is to re-examine the intervention analysis of Bethlehem Steel's quarterly earnings per share series behaviour previously analyzed in Hopwood and McKeown (1986). The very large $1 billion loss of Bethlehm Steel in 1982 created an outlier in the quartely earnings series that may distort the autocorrelation and partial autocorrelation function estimates such that traditional time series models may not be appropriate [Box and Tiao (1975)]. The intervention analysis model reported in Hopwood and McKeown is substantiated in this analysis; however, the intervention modeling effort is expanded by using the intervention model i...

Detection of multivariate outliers with location slippage or scale inflation in left orthogonally invariant or elliptically contoured distributions

This paper is concerned with two kinds of multiple outlier problems in multivariate regression. One is a multiple location-slippage problem and the other is a multiple scale-inflation problem. A multi-decision rule is proposed. Its optimality is shown for the first problem in a class of left orthogonally invariant distributions and is also shown for the second problem in a class of elliptically contoured distributions. Thus the decision rule is robust against departures from normality. Further the null robustness of the decision statistic which the rule is based on is pointed out in each problem.