Comparing Equal-Tail Probability and Unbiased Confidence Intervals for the Intraclass Correlation Coefficient

The conventional confidence interval for the intraclass correlation coefficient assumes equal-tail probabilities. In general, the equal-tail probability interval is biased and other interval procedures should be considered. Unbiased confidence intervals for the intraclass correlation coefficient are readily available. The equal-tail probability and unbiased intervals have exact coverage as they are constructed using the pivotal quantity method. In this article, confidence intervals for the intraclass correlation coefficient are built using balanced and unbalanced one-way random effects models. The expected length of confidence intervals serves as a tool to compare the two procedures. The unbiased confidence interval outperforms the equal-tail probability interval if the intraclass correlation coefficient is small and the equal-tail probability interval outperforms the unbiased interval if the intraclass correlation coefficient is large.     

A New Goodness-of-Fit Test Based on the Empirical Characteristic Function

In this article, we present a goodness-of-fit test for a distribution based on some comparisons between the empirical characteristic function c_n(t) and the characteristic function of a random variable under the simple null hypothesis, c₀(t). We do this by introducing a suitable distance measure. Empirical critical values for the new test statistic for testing normality are computed. In addition, the new test is compared via simulation to other omnibus tests for normality and it is shown that this new test is more powerful than others.     

A Decomposition of Pearson–Fisher and Dzhaparidze–Nikulin Statistics and Some Ideas for a More Powerful Test Construction

An explicit decomposition on asymptotically independent distributed as chi-squared with one degree of freedom components of the Pearson–Fisher and Dzhaparidze–Nikulin tests is presented. The decomposition is formally the same for both tests and is valid for any partitioning of a sample space. Vector-valued tests, components of which can be not only different scalar tests based on the same sample, but also scalar tests based on components or groups of components of the same statistic are considered. Numerical examples illustrating the idea are presented.     

Invariance of linearity of regression and related characterizations of some classical discrete distributions

Rao (1963) introduced what we call an additive damage model. In this model, original observation is subjected to damage according to a specified probability law by the survival distribution. In this paper, we consider a bivariate observation with second component subjected to damage. Using the invariance of linearity of regression of the first component on the second under the transition of the second component from the original to the damaged state, we obtain the characterizations of the Poisson, binomial and negative binomial distributions within the framework of the additive damage model.     

Estimation of functions of the parameters of a normal distribution

Several authors have considered the problem of estimating parameters of a distribution after some fixed Gaussian inducing transformation has been applied to the observations. This paper extends this work to the situation where the observations represent a noisy version of a true process, the parameters of the latter requiring estimation     

Time series analysis of stratospheric ozone

Time series analyses of monthly average total ozone measured at 37 stations throughout the world were used to estimate the extent to which the average ozone trend correlates with the depletion curve hypothesized as due to chlorofluorocarbons (CFCs). Statistical characteristics of stations in the ensemble were used to help define appropriate model and station selection criteria. The maximum likelihood procedure developed herein estimates the weighted average trend, its. variance, and the intra- and inter-station variance components of the trend. Correlations among trends at different stations are also taken into account. The models were subjected to much checking and criticism. Variations in statistical methodology are used to show that the results are insensitive to details of the model selection criteria. The method does not discriminate well between the hypothesized CFC trend and a linear trend. The trend estimates represent the sum of all long-term global effects. The variance includes all effects that differ from station-to-station. The estimated trend and 2α limits for 14 stations with 20-year records (1958-79) is an ozone increase through 1979 of (1.5+1.0) percent. At the 23 stations with shorter records, the trend is (1.0=1.7) percent. It is concluded that no significant depletion in stratospheric ozone has occurred from any cause through the end of 1979.     

Locally most powerful rank tests

It is the purpose of this present paper to introduce a new concept of locally most powerful rank tests. In the sequel we obtain finite sample results undervery mild regularity conditions. The approach is more v general than the related treatment of Hájek and ?idák (1967). In contrast to those authors, we need no assumptions concerning the derivatives of the underlying denstities. For instance, in the case of a regression problem in location, the density of the location family must be only square integrable. Thus the results also apply to discontinuous densities. We treat hypotheses H. of the following kind against parametric alternatives; H₀, H₁(secttest of symmetry) and H(test of independence).     

Classification procedures using principal component analysis and stepwise discriminant function

Classification procedures are examined in the case when the dimensionality exceeds the sample size. Two particular suggestions are (i) Principal components analysis and (ii) Two-step discriminant analysis. Comparisons are made in the two sample and the several sample cases. Extensions to growth curve model are investigated using the two stage discriminant analysis.     

Umvu estimators for the population mean and variance based on random effects models for lognormal data

Cross-classified data are often obtained in controlled experimental situations and in epidemiologic studies. As an example of the latter, occupational health studies sometimes require personal exposure measurements on a random sample of workers from one or more job groups, in one or more plant locations, on several different sampling dates. Because the marginal distributions of exposure data from such studies are generally right-skewed and well-approximated as lognormal, researchers in this area often consider the use of ANOVA models after a logarithmic transformation. While it is then of interest to estimate original-scale population parameters (e.g., the overall mean and variance), standard candidates such as maximum likelihood estimators (MLEs) can be unstable and highly biased. Uniformly minimum variance unbiased (UMVU) cstiniators offer a viable alternative, and are adaptable to sampling schemes that are typiral of experimental or epidemiologic studies. In this paper, we provide UMVU estimators for the mean and variance under two random effects ANOVA models for logtransformed data. We illustrate substantial mean squared error gains relative to the MLE when estimating the mean under a one-way classification. We illustrate that the results can readily be extended to encompass a useful class of purely random effects models, provided that the study data are balanced.