Assumption for 1 sample T test: Data are normally distributed. We have discussed in the last article on how to check the normality assumption of a quantitative data. One issue being highlighted was that these formal normality tests are very sensitive to the sample size of the variable concerned. As seen here, table II shows that the normality assumptions for both the systolic and diastolic bloo...

In the model of type I censored exponential lifetimes, coverage probabilities are compared for a number of confidence interval constructions proposed in literature. The coverage probabilities are calculated exactly for sample sizes up to 50 and for different degrees of censoring and different degrees of intended confidence. If not only a fair two-sided coverage is desired, but also fair one-sid...

Many statistical tests require data to be approximately normally distributed. Usually, the first step of data analysis is to test the normality. Also, we often test the normality of residuals after fitting a linear model to the data in order to ensure the normality assumption of the model is satisfied. SAS has offered four statistical tests that provide an easy way to test the normality. Howeve...

Many parametric statistical inferential procedures in finite samples depend crucially on the underlying normal distribution assumption. Dozens of normality tests are available in the literature to test the hypothesis of normality. Availability of such a large number of normality tests has generated a large number of simulation studies to find a best test but no one arrived at a definite answer ...

This paper considers the estimation of average autoregressive roots-near-unity in panels where the time-series have heterogenous local-to-unity parameters. The pooled estimator is shown to have a potentially severe bias and a robust median based procedure is proposed instead. This median estimator has a small asymptotic bias that can be eliminated almost completely by a bias correction procedur...

On the simple normality to base 2 of √ s, for s not a perfect square Abstract Since E. Borel proved in 1909 that almost all real numbers with respect to Lebesgue measure are normal to all bases, an open problem has been whether simple irrational numbers like √ 2 are normal to any base. This paper shows that each number of the form √ s for s not a perfect square is simply normal to the base 2. T...

The regression function can be expressed in term of copula density and marginal distributions. In this paper, we propose a new method of estimating a regression function using the Bernstein estimator for the copula density and the empirical distributions for the marginal distributions. The method is fully non-parametric and easy to implement. We provide some asymptotic results related to this c...

On the simple normality to base 2 of √ s, for s not a perfect square Abstract Since E. Borel proved in 1909 that almost all real numbers with respect to Lebesgue measure are normal to all bases, an open problem has been whether simple irrational numbers like √ 2 are normal to any base. This paper shows that each number of the form √ s for s not a perfect square is simply normal to the base 2. T...

This paper establishes the almost sure convergence and asymptotic normality of levels and differenced quasi maximum-likelihood (QML) estimators of dynamic panel data models. The QML estimators are robust with respect to initial conditions, conditional and time-series heteroskedasticity, and misspecification of the log-likelihood. The paper also provides an ECME algorithm for calculating levels ...