Multivariate outliers and decompositions of mahalanobis distance

Two decompositions of the Mahalanobis distance are considered. These decompositions help to explain some reasons for the outlyingness of multivari- ate observations. They also provide a graphical tool for identifying outliers including those that have a large influence on the multiple correlation coefficient, Illustrative examples are given.     

ROBUST ESTIMATION UNDER TYPE II CENSORING

The properties of robust M-estimators with type II censored failure time data are considered. The optimal members within two classes of ψ-functions are characterized. The first optimality result is the censored data analogue of the optimality result described in Hampel et al. (1986); the estimators corresponding to the optimal members within this class are referred to as the optimal robust estimators. The second result pertains to a restricted class of ψ-functions which is the analogue of the class of ψ-functions considered in James (1986) for randomly censored data; the estimators corresponding to the optimal members within this restricted class are referred to as the optimal James-type estimators. We examine the usefulness of the two classes of ψ-functions and find that the breakdown point and efficiency of the optimal James-type estimators compare favourably with those of the corresponding optimal robust estimators. From the computational point of view, the optimal James-type ψ-functions are readily obtainable from the optimal ψ-functions in the uncensored case. The ψ-functions for the optimal robust estimators require a separate algorithm which is provided. A data set illustrates the optimal robust estimators for the parameters of the extreme value distribution.     

DESPERATE TIMES CALL FOR DESPERATE MEASURES: GOVERNMENT SPENDING MULTIPLIERS IN HARD TIMES

We investigate state-dependent effects of fiscal multipliers and allow for endogenous sample splitting to determine whether the U.S. economy is in a slack state. When the endogenized slack state is estimated as the period of the unemployment rate higher than about 12%, the estimated cumulative multipliers are significantly larger during slack periods than nonslack periods and are above unity. We also examine the possibility of time-varying regimes of slackness and find that our empirical results are robust under a more flexible framework. Our estimation results point out the importance of the heterogenous effects of fiscal policy and shed light on the prospect of fiscal policy in response to economic shocks from the current COVID-19 pandemic. (JEL C32, E62, H20, H62)     

Constrained Bayes and empirical Bayes estimation under random effects normal ANOVA model with balanced loss function

The paper develops constrained Bayes and empirical Bayes estimators in the random effects ANOVA model under balanced loss functions. In the balanced normal–normal model, estimators of the Bayes risks of the constrained Bayes and constrained empirical Bayes estimators are provided which are correct asymptotically up to O(m^-1)$\mathrm{O}(m^{-1})$, that is the remainder term is o(m^-1)$\mathrm{o}(m^{-1})$, m$m$ denoting the number of strata.     

Discriminating among probability weighting functions using adaptive design optimization

Probability weighting functions relate objective probabilities and their subjective weights, and play a central role in modeling choices under risk within cumulative prospect theory. While several different parametric forms have been proposed, their qualitative similarities make it challenging to discriminate among them empirically. In this paper, we use both simulation and choice experiments to investigate the extent to which different parametric forms of the probability weighting function can be discriminated using adaptive design optimization, a computer-based methodology that identifies and exploits model differences for the purpose of model discrimination. The simulation experiments show that the correct (data-generating) form can be conclusively discriminated from its competitors. The results of an empirical experiment reveal heterogeneity between participants in terms of the functional form, with two models (Prelec-2, Linear-in-Log-Odds) emerging as the most common best-fitting models. The findings shed light on assumptions underlying these models.     

Outliers and influential observations in the structural errors-in-variables model

The influence of observations on the parameter estimates for the simple structural errors-in-variables model with no equation error is investigated using the local influence method. Residuals themselves are not sufficient for detecting outliers. The likelihood displacement approach is useful for outlier detection especially when a masking phenomenon is present. An illustrative example is provided.     

Local influence in box-cox transformation for multivariate regression data

The Box-Cox power family of transformations for multivariate regression data is considered. The influence of cases on the maximum likelihood estimators of the transformation parameters is investigated using the local influence approach, An example is given to- illustrate the local influence method and to show the effectiveness of the method.     

Local influence in multivariate regression

The method of local influence is generalized to the multivariate regression. The scheme of perturbations adopted in multivariate regression is similar in spirit to the perturbation of case-weights in univariate regression case. The method developed here is useful for identifying influential observations in multivariate regression as an exploratory or confirmatory data analysis. An illustrative example is given for the effectiveness of the local influence approach in multivariate regression.     

Geometric aspects of deletion diagnostics in multivariate regression

In multivariate regression, a graphical diagnostic method of detecting observations that are influential in estimating regression coefficients is introduced. It is based on the principal components and their variances obtained from the covariance matrix of the probability distribution for the change in the estimator of the matrix of unknown regression coefficients due to a single-case deletion. As a result, each deletion statistic obtained in a form of matrix is transformed into a two-dimensional quantity. Its univariate version is also introduced in a little different way. No distributional form is assumed. For illustration, we provide a numerical example in which the graphical method introduced here is seen to be effective in getting information about influential observations.     

A family of test statistics for trend change in mean residual life with unknown turning point using censored data

In this paper, we develop a family of test statistics for testing exponentiality against increasing then decreasing mean residual life alternatives to accommodate the randomly censored data when neither the change point nor the proportion is known. We establish the asymptotic null distribution of test statistics. Monte Carlo simulations are conducted to investigate the speed of convergence of test statistics to the asymptotic null distribution and study the performance of test statistics by the power of tests.