Testing equality of two normal covariance matrices with monotone missing data

Abstract

The problem of testing equality of two multivariate normal covariance matrices is considered. Assuming that the incomplete data are of monotone pattern, a quantity similar to the Likelihood Ratio Test Statistic is proposed. A satisfactory approximation to the distribution of the quantity is derived. Hypothesis testing based on the approximate distribution is outlined. The merits of the test are investigated using Monte Carlo simulation. Monte Carlo studies indicate that the test is very satisfactory even for moderately small samples. The proposed methods are illustrated using an example.     

Heteroscedastic Global Tests that the Regression Parameters for Two or More Independent Groups are Identical

Simulation results are reported on methods that allow both within group and between group heteroscedasticity when testing the hypothesis that independent groups have identical regression parameters. The methods are based on a combination of extant techniques, but their finite-sample properties have not been studied. Included are results on the impact of removing all leverage points or just bad leverage points. The method used to identify leverage points can be important and can improve control over the Type I error probability. Results are illustrated using data from the Well Elderly II study.     

The quantile-based flattened logistic distribution: Some properties and applications

In this paper, the quantile-based flattened logistic distribution has been studied. Some classical and quantile-based properties of the distribution have been obtained. Closed form expressions of L-moments, L-moment ratios and expectation of order statistics of the distribution have been obtained. A quantile-based analysis concerning the method of matching L-moments estimation is employed to estimate the parameters of the proposed model. We further derive the asymptotic variance–covariance matrix of the matching L-Moments estimators of the proposed model. Finally, we apply the proposed model to simulated as well as two real life datasets and compare the fit with the logistic distribution.     

Computing maximum likelihood estimates from type II doubly censored exponential data

It is well-known that, under Type II double censoring, the maximum likelihood (ML) estimators of the location and scale parameters, θ and δ, of a twoparameter exponential distribution are linear functions of the order statistics. In contrast, when θ is known, theML estimator of δ does not admit a closed form expression. It is shown, however, that theML estimator of the scale parameter exists and is unique. Moreover, it has good large-sample properties. In addition, sharp lower and upper bounds for this estimator are provided, which can serve as starting points for iterative interpolation methods such as regula falsi. Explicit expressions for the expected Fisher information and Cramér-Rao lower bound are also derived. In the Bayesian context, assuming an inverted gamma prior on δ, the uniqueness, boundedness and asymptotics of the highest posterior density estimator of δ can be deduced in a similar way. Finally, an illustrative example is included.     

Merging information for semiparametric density estimation

Summary.  The density ratio model specifies that the likelihood ratio of m −1 probability density functions with respect to the m th is of known parametric form without reference to any parametric model. We study the semiparametric inference problem that is related to the density ratio model by appealing to the methodology of empirical likelihood. The combined data from all the samples leads to more efficient kernel density estimators for the unknown distributions. We adopt variants of well-established techniques to choose the smoothing parameter for the density estimators proposed.     

Living Arrangements, Employment Status, and the Economic Well-Being of Mothers: Evidence from Brazil, Chile, and the U.S

Using data from Brazil, Chile, and the U.S., we estimate country specific models of household income that characterize mothers according to their marital status, living arrangement, and employment status. We assess the predicted economic well-being of each type of mother relative to a benchmark of married mothers in the same country, and at various points in the income distribution. We find dramatic cross-country differences in the distribution of mothers across categories, but few differences in each type's relative economic status. In all three countries and at all points in the income distribution, mothers who are the only adults in their households have the lowest levels of predicted income, while married mothers—followed closely by cohabitors—have the highest levels.     

Estimator Choice and Fisher's Paradox: A Monte Carlo Study

This paper argues that Fisher's paradox can be explained away in terms of estimator choice. We analyse by means of Monte Carlo experiments the small sample properties of a large set of estimators (including virtually all available single-equation estimators), and compute the critical values based on the empirical distributions of the t-statistics, for a variety of Data Generation Processes (DGPs), allowing for structural breaks, ARCH effects etc. We show that precisely the estimators most commonly used in the literature, namely OLS, Dynamic OLS (DOLS) and non-prewhitened FMLS, have the worst performance in small samples, and produce rejections of the Fisher hypothesis. If one employs the estimators with the most desirable properties (i.e., the smallest downward bias and the minimum shift in the distribution of the associated t-statistics), or if one uses the empirical critical values, the evidence based on US data is strongly supportive of the Fisher relation, consistently with many theoretical models.     

Divergence-based estimation and testing with misclassified data

The well-known chi-squared goodness-of-fit test for a multinomial distribution is generally biased when the observations are subject to misclassification. In Pardo and Zografos (2000) the problem was considered using a double sampling scheme and ø-divergence test statistics. A new problem appears if the null hypothesis is not simple because it is necessary to give estimators for the unknown parameters. In this paper the minimum ø-divergence estimators are considered and some of their properties are established. The proposed ø-divergence test statistics are obtained by calculating ø-divergences between probability density functions and by replacing parameters by their minimum ø-divergence estimators in the derived expressions. Asymptotic distributions of the new test statistics are also obtained. The testing procedure is illustrated with an example.     

Assessing accuracy of a continuous screening test in the presence of verification bias

Summary.  In studies to assess the accuracy of a screening test, often definitive disease assessment is too invasive or expensive to be ascertained on all the study subjects. Although it may be more ethical or cost effective to ascertain the true disease status with a higher rate in study subjects where the screening test or additional information is suggestive of disease, estimates of accuracy can be biased in a study with such a design. This bias is known as verification bias. Verification bias correction methods that accommodate screening tests with binary or ordinal responses have been developed; however, no verification bias correction methods exist for tests with continuous results. We propose and compare imputation and reweighting bias-corrected estimators of true and false positive rates, receiver operating characteristic curves and area under the receiver operating characteristic curve for continuous tests. Distribution theory and simulation studies are used to compare the proposed estimators with respect to bias, relative efficiency and robustness to model misspecification. The bias correction estimators proposed are applied to data from a study of screening tests for neonatal hearing loss.     

Local dependence estimation using semiparametric archimedean copulas

The authors define a new semiparametric Archimedean copula family which has a flexible dependence structure. The generator of the family is a local interpolation of existing generators. It has locally‐defined dependence parameters. The authors present a penalized constrained least‐squares method to estimate and smooth these parameters. They illustrate the flexibility of their dependence model in a bi‐variate survival example.