While a variety of specification tests are routinely employed to test for misspecification in linear regression model, such tests and their applications to the truncated and censored regression models are uncommon. This paper develops a regression error specification test (RESET) for the truncated regression model as an extension of the popular RESET for the linear regression model (Ramsey (1969)). The two proposed extensions TRESET1 and TRESET2 developed in the paper are applied to labor force participation data from Mroz (1987). The paper studies the empirical size and power properties of the proposed tests via Monte Carlo experiments. Our simulation results suggest that both TRESET tests have reasonably good size and power properties for the truncated regression model in medium to large samples. However, TRESET2 consistently outperforms TRESET1 both in terms of empirical size and power in our experiments.  

The maximum likelihood estimator for the Probit model can be substantially biased in small samples.This paper proposes a bias-corrected jackknife maximum likelihood estimator (JMLE) for the Probit model which corrects bias up to O(1/n-squared) unlike the ordinary MLE which corrects bias up to O(1/n). An application of the JMLE to Spector and Mazzeo (1980) data for analysing the effectiveness of a new method of teaching economics is also presented.

Principal Component Analysis (PCA) is a very versatile technique for dimension reduction in multivariate data. Classical PCA is very sensitive to outliers and can lead to misleading conclusions in the presence of outliers. This article studies the merits of robust PCA relative to classical PCA when outliers are present. An algorithm due to Filzmoser et al. (2006) based on a modification of the projection pursuit algorithm of Croux and Ruiz-Gazen (2005) is used for robust PCA computations for a financial data set as well as simulated data sets. Our simulation results indicate that robust PCA generally leads to greater reduction in model dimension than classical PCA in data sets with outliers.

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