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In the growing literature of factor analysis, little is done to understand the finite sample properties of an approximate factor model solution. In empirical applications with relatively small samples, the asymptotic theory might be a poor approximation and the resulting distortions might affect the estimation (bias in the point estimate and the standard errors) and the statistical inference. The present paper uses the estimation method of Bai and Ng [Bai, J. and Ng, S., 2002, Determining the number of factors in approximate factor models. Econometrica , 70, 191–221.] and assesses the sampling behavior of the estimated common components, common factors and factor loadings. The study compares the empirical distributions to the asymptotic theory of Bai [Bai, J., 2003, Inference on factor models of large dimension. Econometrica , 71, 135–171.]. Simulation results suggest that the point estimates have a Gaussian distribution for panels with relatively small dimensions. However, these estimates have a significant finite sample bias and the dispersion of their sampling distribution is severely underestimated by the asymptotic theory. [ABSTRACT FROM AUTHOR]

In this paper, some versatile test procedures are considered, which are useful for the case where the association of survival functions is unclear. These procedures are based on a maximum of a class of the weighted Kaplan-Meier statistics. The weight functions used in the procedures account for both the censored and non-censored data points. Numerical simulations with these weight functions show that, under various levels of censoring, the proposed procedures perform well across a wide range of alternative configurations. Implementation of the proposed procedures is illustrated in a real data example. [ABSTRACT FROM AUTHOR]

The article derives Bartlett corrections for improving the chi-square approximation to the likelihood ratio statistics in a class of symmetric nonlinear regression models. This is a wide class of models which encompasses the t model and several other symmetric distributions with longer-than normal tails. In this paper we present, in matrix notation, Bartlett corrections to likelihood ratio statistics in nonlinear regression models with errors that follow a symmetric distribution. We generalize the results obtained by Ferrari, S. L. P. and Arellano-Valle, R. B. (1996). Modified likelihood ratio and score tests in linear regression models using the t distribution . Braz. J. Prob. Statist. , 10 , 15-33, who considered a t distribution for the errors, and by Ferrari, S. L. P. and Uribe-Opazo, M. A. (2001). Corrected likelihood ratio tests in a class of symmetric linear regression models. Braz. J. Prob. Statist. , 15 , 49-67, who considered a symmetric linear regression model. The formulae derived are simple enough to be used analytically to obtain several Bartlett corrections in a variety of important models. We also present simulation results comparing the sizes and powers of the usual likelihood ratio tests and their Bartlett corrected versions. [ABSTRACT FROM AUTHOR]

In this paper we examine how well the asymptotic null distribution of a two sample test due to Lehmann approximates the small sample distribution of the test, compare the validity of this Lehman test with the validity of the two sample t test under the null hypothesis of equal means, and compare the power of this Lehmannn test with the power of the t test. Our general conclusion is that experimenters will prefer to use the t test when the underlying distribution is the scale contaminated compound normal distribution and the sample sizes are less than thirty. [ABSTRACT FROM AUTHOR]

The authors generated exact probability distributions for sample sizes up to 35 in each of three groups (n≤ 105) and up to 10 in each of four groups (n≤ 40). They compared the exact distributions to the chi-square, gamma, and beta approximations. The beta approximation was best in terms of the root mean square error. At specific significance levels, either the gamma or beta approximation was best. These results suggest that the most common approximation, the chi-square approximation, is not a good choice. The authors demonstrate this point using an applied example. Critical value tables for the exact distribution are available online athttp://faculty.virginia.edu/kruskal-wallis. The portion of these tables that provides critical values for equal sample sizes appears in this article. The authors recommend that researchers use critical values from the exact distribution whenever possible. If sample sizes exceed those included in the authors’ exact probability tables, they recommend using the beta approximation instead of the chi-square and gamma approximations. [ABSTRACT FROM PUBLISHER]