The robustness of the systemwise breusch-godfrey autocorrelation test for non-normal distributed error terms

Using Monte Carlo methods, the properties of systemwise generalisations of the Breusch-Godfrey test for autocorrelated errors are studied in situations when the error terms follow either normal or non-normal distributions, and when these errors follow either AR(1) or MA(1) processes. Edgerton and Shukur (1999) studied the properties of the test using normally distributed error terms and when these errors follow an AR(1) process. When the errors follow a non-normal distribution, the performances of the tests deteriorate especially when the tails are very heavy. The performances of the tests become better (as in the case when the errors are generated by the normal distribution) when the errors are less heavy tailed.     

Crossover designs based on type I orthogonal arrays for a self and simple mixed carryover effects model with correlated errors

We investigate the performance of crossover designs based on type I orthogonal arrays for a self and simple mixed carryover effects model in the presence of correlated errors. Assuming that between-subject errors are independent while within-subject errors behave according to the stationary first-order autoregressive and moving average processes, analytical optimality results for 3-period designs are established and, as an illustration, numerical details for a number of 4-period cases are tabulated.     

A Note on Asymmetry and Robustness in Linear Regression

We discuss the assumption of symmetry in robust linear regression. It is important to distinguish between the intercept term and the slope parameters. Ordinary robust regression requires no assumption of symmetry when interest lies in slope parameters; computer programs, confidence intervals, standard errors, and so forth do not change because the errors are asymmetric. The situation is radically different for bounded-influence estimators. With the exception of the Mallows class, these estimators are inconsistent for slope when the errors are asymmetric.     

The robustness of response surface designs with errors in factor levels

ABSRTACT

Since errors in factor levels affect the traditional statistical properties of response surface designs, an important question to consider is robustness of design to errors. However, when the actual design could be observed in the experimental settings, its optimality and prediction are of interest. Various numerical and graphical methods are useful tools for understanding the behavior of the designs. The D- and G-efficiencies and the fraction of design space plot are adapted to assess second-order response surface designs where the predictor variables are disturbed by a random error. Our study shows that the D-efficiencies of the competing designs are considerably low for big variance of the error, while the G-efficiencies are quite good. Fraction of design space plots display the distribution of the scaled prediction variance through the design space with and without errors in factor levels. The robustness of experimental designs against factor errors is explored through comparative study. The construction and use of the D- and G-efficiencies and the fraction of design space plots are demonstrated with several examples of different designs with errors.     

Discrete M-robust designs for regression models

M-robust designs are defined and constructed for misspecified linear regression models with possibly autocorrelated errors on a discrete design space. These designs minimize the mean-squared errors if linear regression models are correct with uncorrelated errors, subject to two robust constraints which control the change of the bias and the change of variance under model departures. Simulated annealing algorithm is applied to construct M-robust designs. Examples are given to show M-robust designs and compare them with minimax robust designs.     

A comparison of estimators of the precision of two instruments

Three different estimators of the variance in errors of measurement, or the “imprecisions” of instruments, have been proposed (Hahn and Nelson, 1970; Maxwell, 1974; Hanumara: 1975) for the case where two measurements by one instrument and one measurement by a second instrument are available for each item. The estimators are compared by studying the probabilities of negative values, the biases, the variances, and the mean square errors. Based on these results, Hahn and Nelson's estimators for the variances in errors of measurement are recommended. Simultaneous confidence intervals of the imprecisions of instruments are also given.     

Asymptotic normality and strong consistency of LS estimators in the EV regression model with NA errors

In this article, the asymptotic normality and strong consistency of the least square estimators for the unknown parameters in the simple linear errors in variables model are established under the assumptions that the errors are stationary negatively associated sequences.     

Bias of S 2 in Linear Regressions with Dependent Errors

Bounds are given for the expected value of the estimator of the error variance in linear regressions, when the errors are dependent or heteroscedastic. The bounds are valid irrespective of the covariance structure between the errors. Necessary and sufficient conditions to attain the bounds are supplied.     

Variance components of the linear regression model with a random intercept

Several estimators for the variance components of the above model are derived. Biases and mean square errors of the estimators for small samples are examined. Results on the skewness and kurtosis coefficients and the large sample biases and mean square errors of these estimators are presented in detail.     

Cure Rate Model with Measurement Error

This simulation study focuses on the relative small sample properties of some widely applied predictors in regression with AR(1) errors where there errors are allowed to follow normal and non-normal distributions. The conclusions are: all predictors considered are significantly unbiased; the relative performances of predictors, from the efficiency point of view, seemed insensitive to the nature of the error distribution; and the standard errors of predictors computed from the asymptotic formulas are very useful for purposes of inference in small sample and under all assumed distributions.     

Evaluation of Response Surface Designs in Presence of Errors in Factor Levels

Experimenters are often confronted with the problem that errors in setting factor levels cannot be measured. In the robust design scenario, the goal is to determine the design that minimizes the variability transmitted to the response from the variables’ errors. The prediction variance performance of response surface designs with errors is investigated using design efficiency and the maximum and minimum scaled prediction variance. The evaluation and comparison of response surface designs with and without errors in variables are developed for second order designs on spherical regions. The prediction variance and design efficiency results and recommendations for their use are provided.     

Tests of heteroscedasticity and correlation in multivariate t regression models with AR and ARMA errors

Heteroscedasticity checking in regression analysis plays an important role in modelling. It is of great interest when random errors are correlated, including autocorrelated and partial autocorrelated errors. In this paper, we consider multivariate t linear regression models, and construct the score test for the case of AR(1) errors, and ARMA(s,d) errors. The asymptotic properties, including asymptotic chi-square and approximate powers under local alternatives of the score tests, are studied. Based on modified profile likelihood, the adjusted score test is also developed. The finite sample performance of the tests is investigated through Monte Carlo simulations, and also the tests are illustrated with two real data sets.     

Mixture of measurement errors and their impact on parameter inferences

A mixture measurement error model built upon skew normal distributions and normal distributions is developed to evaluate various impacts of measurement errors to parameter inferences in logistic regressions. Data generated from survey questionnaires are usually error contaminated. We consider two types of errors: person-specific bias and random errors. Person-specific bias is modelled using skew normal distribution, and the distribution of random errors is described by a normal distribution. Intensive simulations are conducted to evaluate the contribution of each component in the mixture to outcomes of interest. The proposed method is then applied to a questionnaire data set generated from a neural tube defect study. Simulation results and real data application indicate that ignoring measurement errors or misspecifying measurement error components can both produce misleading results, especially when measurement errors are actually skew distributed. The inferred parameters can be attenuated or inflated depending on how the measurement error components are specified. We expect the findings will self-explain the importance of adjusting measurement errors and thus benefit future data collection effort.     

Bivariate deconvolution with SIMEX: an application to mapping Alaska earthquake density

Constructing spatial density maps of seismic events, such as earthquake hypocentres, is complicated by the fact that events are not located precisely. In this paper, we present a method for estimating density maps from event locations that are measured with error. The estimator is based on the simulation–extrapolation method of estimation and is appropriate for location errors that are either homoscedastic or heteroscedastic. A simulation study shows that the estimator outperforms the standard estimator of density that ignores location errors in the data, even when location errors are spatially dependent. We apply our method to construct an estimated density map of earthquake hypocenters using data from the Alaska earthquake catalogue.     

Testing for autocorreiation in nested analysis of variance

This paper considers the problem in which repeated measures are taken on each subject in an experimental design and the model errors follow a first order autoregressive process. The appropriate form of the Durbin-Watson test statistic for autocorrelated errors is presented. Critical values for the test statistic are reported.     

Estimation in Second-Order Models with Errors in the Factor Levels

The impact of errors in the factor levels is examined on the estimation of parameters in second-order response models. Errors can occur in setting the factor levels for response surface and robust parameter design models. These errors can lead to heterogeneity of variances in model errors that make ordinary least squares estimation inappropriate. Weighted least squares and maximum likelihood estimation approaches are developed as viable alternatives where it is assumed the variances and covariances of the errors are known. Performance of these estimation techniques are examined in simulation studies for two examples. Another example is given that applies these results.     

Adjustment of provisional mortality series: the dynamic linear model with structured measurement errors

The authors "consider the problem of adjusting provisional time series using a bivariate structural model with correlated measurement errors. Maximum likelihood estimators and a minimum mean squared error adjustment procedure are derived for a provisional and final series containing common trend and seasonal components. The model also includes measurement errors common to both series and errors that are specific to the provisional series. [The authors] illustrate the technique by using provisional data to forecast ischemic heart disease mortality."     

A bound for codes correcting random and low-density closed-loop burst errors

This paper presents a lower bound on the number of parity-check digits required for a linear code that corrects random errors and errors which are in the form of closed-loop low-density bursts.     

Robust automatic methods for outlier and error detection

Summary.  Editing in surveys of economic populations is often complicated by the fact that outliers due to errors in the data are mixed in with correct, but extreme, data values. We describe and evaluate two automatic techniques for the identification of errors in such long-tailed data distributions. The first is a forward search procedure based on finding a sequence of error-free subsets of the error-contaminated data and then using regression modelling within these subsets to identify errors. The second uses a robust regression tree modelling procedure to identify errors. Both approaches can be implemented on a univariate basis or on a multivariate basis. An application to a business survey data set that contains a mix of extreme errors and true outliers is described.