Two New Estimators of Entropy for Testing Normality

We present two new estimators for estimating the entropy of absolutely continuous random variables. Some properties of them are considered, specifically consistency of the first is proved. The introduced estimators are compared with the existing entropy estimators. Also, we propose two new tests for normality based on the introduced entropy estimators and compare their powers with the powers of other tests for normality. The results show that the proposed estimators and test statistics perform very well in estimating entropy and testing normality. A real example is presented and analyzed.Comment: 28 page

New Entropy Estimator with an Application to Test of Normality

In the present paper we propose a new estimator of entropy based on smooth estimators of quantile density. The consistency and asymptotic distribution of the proposed estimates are obtained. As a consequence, a new test of normality is proposed. A small power comparison is provided. A simulation study for the comparison, in terms of mean squared error, of all estimators under study is performed

A comprehensive empirical power comparison of univariate goodness-of-fit tests for the Laplace distribution

In this paper, we do a comprehensive survey of all univariate goodness-of-fit tests that we could find in the literature for the Laplace distribution, which amounts to a total of 45 different test statistics. After eliminating duplicates and considering parameters that yield the best power for each test, we obtain a total of 38 different test statistics. An empirical power comparison study of unmatched size is then conducted using Monte Carlo simulations, with 400 alternatives spanning over 20 families of distributions, for various sample sizes and confidence levels. A discussion of the results follows, where the best tests are selected for different classes of alternatives. A similar study was conducted for the normal distribution in Rom\~ao et al. (2010), although on a smaller scale. Our work improves significantly on Puig & Stephens (2000), which was previously the best-known reference of this kind for the Laplace distribution. All test statistics and alternatives considered here are integrated within the PoweR package for the R software.Comment: 37 pages, 1 figure, 20 table

A test for normality based on the empirical distribution function

In this paper, a goodness-of-fit test for normality based on the comparison of the theoretical and empirical distributions is proposed. Critical values are obtained via Monte Carlo for several sample sizes and different significance levels. We study and compare the power of forty selected normality tests for a wide collection of alternative distributions. The new proposal is compared to some traditionaltest statistics, such as Kolmogorov-Smirnov, Kuiper, Cramér-von Mises, Anderson-Darling, Pearson Chi-square, Shapiro-Wilk, Shapiro-Francia, Jarque-Bera, SJ, Robust Jarque-Bera, and also to entropy-based test statistics. From the simulation study results it is concluded that the best performance against asymmetric alternatives with support on the whole real line and alternative distributions with support on the positive real line is achieved by the new test. Other findings derivedfrom the simulation study are that SJ and Robust Jarque-Bera tests are the most powerful ones for symmetric alternatives with support on the whole real line, whereas entropy-based tests are preferable for alternatives with support on the unit interval

New Entropy Estimators with Smaller Root Mean Squared Error

New estimators of entropy of continuous random variable are suggested. The proposed estimators are investigated under simple random sampling (SRS), ranked set sampling (RSS), and double ranked set sampling (DRSS) methods. The estimators are compared with Vasicek (1976) and Al-Omari (2014) entropy estimators theoretically and by simulation in terms of the root mean squared error (RMSE) and bias values. The results indicate that the suggested estimators have less RMSE and bias values than their competing estimators introduced by Vasicek (1976) and Al-Omari (2014)

Some goodness-of-fit tests and efficient estimation in longitudinal surveys under missing data

In statistical analysis, distribution assumptions are often subject to be tested. In this dissertation, the problem of testing two important distribution assumptions, the normal distribution and uniform distribution, is considered. Specifically, a new characterization of multivariate normality based on univariate projections is developed. On the other hand, a powerful affine invariant test of multivariate normality is proposed. Moreover, this dissertation also presents an asymptotic distribution free test of multivariate uniformity based on $m$-nearest neighbors. Both tests have demonstrated good power performance by numerical studies. Incomplete data is another commonly encountered issue in practice. This dissertation also reports an efficient estimation method for population mean in longitudinal surveys under monotone missing pattern. The proposed method is developed using the generalized method of moments technique by incorporating all the available information at each time point. Efficiency of the method over the direct propensity score type estimator is also demonstrated by limited numerical studies

Measuring Inequality Using Censored Data: A Multiple Imputation Approach

To measure income inequality with right censored (topcoded) data, we propose multiple imputation for censored observations using draws from Generalized Beta of the Second Kind distributions to provide partially synthetic datasets analyzed using complete data methods. Estimation and inference uses Reiter's (Survey Methodology 2003) formulae. Using Current Population Survey (CPS) internal data, we find few statistically significant differences in income inequality for pairs of years between 1995 and 2004. We also show that using CPS public use data with cell mean imputations may lead to incorrect inferences about inequality differences. Multiply-imputed public use data provide an intermediate solution.Income inequality, topcoding, partially synthetic data, CPS, current population survey, generalized beta of the second kind distribution

Measuring Inequality Using Censored Data: A Multiple Imputation Approach

To measure income inequality with right censored (topcoded) data, we propose multiple imputation for censored observations using draws from Generalized Beta of the Second Kind distributions to provide partially synthetic datasets analyzed using complete data methods. Estimation and inference uses Reiter’s (Survey Methodology 2003) formulae. Using Current Population Survey (CPS) internal data, we find few statistically significant differences in income inequality for pairs of years between 1995 and 2004. We also show that using CPS public use data with cell mean imputations may lead to incorrect inferences about inequality differences. Multiply-imputed public use data provide an intermediate solution.income inequality, topcoding, partially synthetic data, CPS, Current Population Survey, Generalized Beta of the Second Kind distribution