Assessment Of Local Influence Research Articles

On diagnostics in conditionally heteroskedastic time series models under elliptical distributions

In statistical diagnostics and sensitivity analysis, the local influence method plays an important rôle. In the present paper, we use this method to study financial time series data and conditionally heteroskedastic models under elliptical distributions. We start with a likelihood displacement, and consider data- and model-perturbation schemes. We obtain corresponding matrices of derivatives, and measures of slope and normal curvature, and then discuss the assessment of local influence.

On influence diagnostic in univariate elliptical linear regression models

We discuss in this paper the assessment of local influence in univariate elliptical linear regression models. This class includes all symmetric continuous distributions, such as normal, Student-t, Pearson VII, exponential power and logistic, among others. We derive the appropriate matrices for assessing the local influence on the parameter estimates and on predictions by considering as influence measures the likelihood displacement and a distance based on the Pearson residual. Two examples with real data are given for illustration.

Local influence in multivariate elliptical linear regression models

Local influence is a method of sensitivity analysis for assessing the influence of small perturbations in a general statistical model. In the present paper, this popular method is applied to multivariate elliptical linear regression models. Several schemes of perturbation, including perturbations in case-weights, explanatory variables and response variables are considered. The observed information matrix under the postulated model and Delta matrices under the corresponding perturbed models are derived. Assessment of local influence is made.

Local influence on bandwidth estimation for kernel smoothing

This paper examines the problem of assessing local influence on the optimal bandwidth estimation in kernel smoothing based on cross validation. The bandwidth for kernel smoothing plays an important role in the model fitting and is often estimated using the cross-validation criterion. Following the argument of the second-order approach to local influence suggested by Wu and Luo (1993), we develop a new diagnostic statistic to examine the local influence of the observations on the estimation of the optimal bandwidth, where the perturbation may belong to one of three schemes. These are the response perturbation, the perturbation in the explanatory variable, and the case-weight perturbation. The proposed diagnostic is nonparametric and is capable of identifying influential observations with strong influence on the bandwidth estimation. An example is presented to illustrate the application of the proposed diagnostic, and the usefulness of the nonparametric approach is illustrated in comparison with some other approaches to the assessment of local influence

On local influence for elliptical linear models

The local influence method plays an important role in regression diagnostics and sensitivity analysis. To implement it, we need the Delta matrix for the underlying scheme of perturbations, in addition to the observed information matrix under the postulated model. Galea, Paula and Bolfarine (1997) has recently given the observed information matrix and the Delta matrix for a scheme of scale perturbations and has assessed of local influence for elliptical linear regression models. In the present paper, we consider the same elliptical linear regression models. We study the schemes of scale, predictor and response perturbations, and obtain their corresponding Delta matrices, respectively. To illustrate the methodology for assessment of local influence for these schemes and the implementation of the obtained results, we give an example.

Local influence assessment in canonical correlation analysis

The local influence method is adapted to canonical correlation analysis for the purpose of investigating the influence of observations. We consider a perturbation based on the empirical distribution function. An illustrative example is given to show the effectiveness of the local influence method for the identification of influential observations.

Conformal Normal Curvature and Assessment of Local Influence

Summary In 1986, R. D. Cook proposed differential geometry to assess local influence of minor perturbations of statistical models. We construct a conformally invariant curvature, the conformal normal curvature, for the same purpose. This curvature provides a measure of local influence ranging from 0 to 1, with objective bench-marks to judge largeness. We study various approaches to using the conformal normal curvature and the relationships between these approaches.

Assessment of local influence on Cox’s proportional hazards model

The second order approach of local influence (see [15]) is developed and applied to Cox’s proportional hazards model, and compared with Cook's local influence approach (see [6] and [13]) which was used in this model. To study local influence, we perturb not only all cases simultaneously, but also cases individually to obtain “direction curvature” in directionl and “curvature” for single case. Some examples are used to illustrate these methods.

Theory and Methods: Influence Diagnostics for Simultaneous Equations Models

This paper presents influence diagnostics for simultaneous equations models. It proposes residuals, leverage and other influence measures. A missing data method is adopted to minimize the masking effect due to case deletions. The assessment of local influence is also considered. The paper shows how to evaluate the effects that perturbations to the endogenous variables, predetermined variables and case weights may have on the parameter estimates. The diagnostics are illustrated with two examples.

Local influence assessment in the growth curve model with unstructured covariance

In this paper, a local influence approach is employed to assess adequacy of the growth curve model with an unstructured covariance, based on likelihood displacement. The Hessian matrix of the model is investigated in detail under an abstract perturbation scheme. For illustration, covariance-weighted perturbation is discussed and used to analyze two real-life biological data sets, which show that the criteria presented in this article are useful in practice.

Assessment of local influence in multivariate regression analysis

Different schemes of perturbation can be adopted in the method of local influence on multiple regression analysis such as perturbation in case-weights, explanatory variables and response variables. These are generalized to multivariate regression analysis. Sometimes a subset of parameters is also of interest in local influence analysis. Kim (1995) has considered only the case-weights perturbation with full parameters of interest in multivariate regression, but his formulation is complicated. The proof of the equivalence of his result and one of our formulae is given. In this paper, all results derived are comparable to those obtained for multiple regression. An illustrative example is shown for the application of local influence in multivariate regression.

Local influence assessment based on local divergence in stochastic regression model

This paper describes the local influence assessment for parameter inference of a statistical model by using curvatures associated with local divergence under a generic perturbation scheme. The results are applied to examine the local influence in stochastic regression model under two perturbation schemes. An economic example is analyzed to illustrate results here.

Assessing Local Influence in Measurement Error Models

AbstractWe consider the assessment of local influence for generalized linear models when the covariates are measured with errors. We show how to evaluate the effect that perturbations to the data, case weights, and model assumptions may have on the parameter estimates. Based on the likelihood displacement functions, some useful influence diagnostics are derived. Two examples illustrate application of the proposed diagnostics and assessment of the measurement error assumptions.

Residual sum of squares and multiple potential, diagnostics by a second order local approach

Inspired by Cook's (1986) assessment of local influence by studying the curvature of a surface associated with the overall discrepancy measure, this paper assesses the local influence through the curvature of the perturbation-formed surface of residual sum of squares (RSS) and multiple potential respectively. Two examples demonstrate the effectiveness of this method on identification of influential points.

Discussion of the Paper by Bruce and Martin

Discussion of the Paper by Bruce and Martin

Discussion of the Paper by Copas

Journal of the Royal Statistical Society: Series B (Methodological)Volume 50, Issue 2 p. 254-265 DiscussionFree Access Discussion of the Paper by Copas First published: 1988 https://doi.org/10.1111/j.2517-6161.1988.tb01724.xAboutPDF ToolsExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat REFERENCES IN THE DISCUSSION Box, G. E. P. and Tiao, G. C. (1968) A Bayesian approach to some outlier problems. Biometrika, 55, 119– 129. Chhikara, R. S. and McKeon, J. (1984) Linear discriminant analysis with misallocation in training samples. J. Amer. Statist. Ass., 79, 899– 906. Cook, D. (1986) Assessment of local influence. J. R. Statist. Soc. B, 48, 133– 169. Daniels, H. E. (1958) Discussion on Cox. J. R. Statist. Soc. 20, 236– 238. Dawid, A. P. (1976) Properties of diagnostic data distributions. Biometrics, 32, 647– 658. Ekholm, A., Green, M. and Palmgren, J. (1986) Fitting exponential family nonlinear models in GLIM 3.77. GLIM Newslett., 13, 4– 13. Ekholm, A. and Palmgren, J. (1987) Correction for misclassification using doubly sampled data. J. Off. Statist., 3, 419– 429. Fisher, R. A. and Yates, F. (1962) Statistical Tables in Agricultural, Biological and Medical Research, 6th edn. London: Longman. Fowlkes, E. B. (1987) Some diagnostics for binary logistic regression via smoothing. Biometrika, 74, 503– 516. Kay, R. and Little, S. (1987) Transformations of the explanatory variables in the logistic regression model for binary data. Biometrika, 74, 495– 502. Landwehr, J. M., Pregibon, D. and Shoemaker, A. C. (1984) Graphical methods for assessing logistic regression models. J. Amer. Statist. Ass., 79, 61– 83. Lemeshow, S. and Hosmer, D. W. (1982) A review of goodness of fit statistics for use in the development of logistic regression models. Amer. J. Epidemiol., 115, 92– 106. Lenth, R. V. and Green, P. J. (1987) Consistency of deviance-based M estimators. J. R. Statist. Soc. B, 49, 326– 330. Lindsey, J. K. (1975) Likelihood analysis and tests for binary data. Appl. Statist., 24, 1– 16 Mandel, J. and Stiehler, R. D. (1954) Sensitivity — a criterion for the comparison of methods of test. J. Res. Natl Bur. Stand., 53, 155– 159. McCullagh, P. and Nelder, J. A. (1983) Generalized Linear Models, ch.10. London: Chapman and Hall. Nelder, J. A. (1985) Quasi-likelihood and GLIM. Proc. GLIM 85 (eds R. Gilchrist, B. Francis and J. Whittaker), pp. 120– 127. Heidelberg: Springer. Nelder, J. A. and Pregibon, D. (1987) An extended quasi-likelihood function. Biometrika, 74, 221– 232. O'Hagan, A. (1979) On outlier rejection phenomena in Bayes inference. J. R. Statist. Soc. B, 41, 358– 367. Palmgren, J. (1987) Precision of double sampling estimators for comparing two probabilities. Biometrika, 74, 687– 694. Palmgren, J. and Ekholm, A. (1987) Exponential family nonlinear models for categorical data with errors of observation. Appl. Stochast. Model Data Anal., 3, 111– 124. Pregibon, D. (1979) PhD Thesis, p. 134. University of Toronto. Pregibon, D. (1980) Goodness of link tests for generalized linear models. Appl. Statist., 29, 15– 24. Pregibon, D. (1981) Logistic regression diagnostics. Ann. Statist., 9, 705– 724. Pregibon, D. (1984) Review of “Generalized linear models” by McCullagh and Nelder. Ann. Statist., 12, 1589– 1596. Pregibon, D. (1985) Link tests. In Encyclopedia of Statistical Sciences (eds S. Kotz and N. L. Johnson), vol. 5, 82– 85. Scallan, A., Gilchrist, R. and Green, M. (1984) Fitting parametric link functions in generalized linear models. Comput. Statist. Data Anal., 1, 37– 19. Simpson, D. G., Carroll, R. J. and Ruppert, D. (1987) M-estimation for discrete data: Asymptotic distribution theory and implications. Ann. Statist., 15, 657– 669. Smith, A. F. M. and Pettit, L. I. (1983) Outliers and influential observations in linear models. In Bayesian Statistics 2 (eds J. M. Bernardo, M. H. DeGroot, D. V. Lindley and A. F. M. Smith), pp. 473– 490. Amsterdam: North-Holland. Tenenbein, A. (1970) A double sampling scheme for estimating from binomial data with misclassification. J. Amer. Statist. Ass., 65, 1350– 1361. West, M. (1985) Generalized linear models: scale parameters, outlier accommodation and prior distributions. In Bayesian Statistics 2 (eds J. M. Bernardo, M. H. DeGroot, D. V. Lindley and A. F. M. Smith), pp. 531– 558. Williams, B. A. (1987) Generalized linear model diagnostics using the deviance and single case deletions. Appl. Statist., 36, 181– 191. Volume50, Issue21988Pages 254-265 This article also appears in:Discussion Papers ReferencesRelatedInformation

Discussion of the Paper by Professors Cox and Reid

Discussion of the Paper by Professors Cox and Reid

Assessment of Local Influence

SUMMARY Statistical models usually involve some degree of approximation and therefore are nearly always wrong. Because of this inexactness, an assessment of the influence of minor perturbations of the model is important. We discuss a method for carrying out such an assessment. The method is not restricted to linear regression models, and it seems to provide a relatively simple, unified approach for handling a variety of problems.