Optimal spacing of quantiles for the estimation of the mixing parameters in a mixture of two exponential distributions

Methods for estimating the mixing parameters in a mixture of two exponential distributions are proposed. The estimators proposed are consistent and BAN(best asymptotically normal). The optimal spacings for estimating these mixture parameters are calculated.     

A survey of tests for exponentiality

A wide selection of tests for exponentiality is discussed and compared. Power computations, using simulations, were done for each procedure. Certain tests (e.g. Gnedenko (1969), Lin and Mudholkar (1980), Harris (1376), Cox and Oakes (1384), and Deshpande (1983)) performed well for alternative distributions with non-monotonic hazard rates, while others (e.g. Deshpande (1983), Gail and Gastwirth (1978), Kolmogorov-Smirnov (LillViefors (1969)), Hahn and Shapiro (1967), Hollander and Proschan (1972), and Cox and Oakes (1984)) fared well for monotonic hazard rates. Of all the procedures compared, the score test presented in Cox and Oakes (1984) appears to be the best if one does not have a particular alternative in mind.     

Estimate of variance of u-statistics

Let g(x₁,… , x_k) be a symmetric function with k arguments. Let U be a U-statistic based on a random sample of size n with kernel function g . In this paper, the problem of estimating var(U) is considered. Several estimators are compared by computer simulations and we conclude that two estimators, one is constructed as a U-statistic and the other is the bootstrap estimator, give good estimates for many U-statistics.     

Improved estimation of a finite population mean based on paired observations

This paper considers an improvement of the customary estimator of a finite population mean under a single stage sampling design when paired data, are available on each unit of the sample. Guided by the well known problem of “corninon mean”, a mixture i.e. a weighted combination of the mean of the principal characteristic and that of the auxiliary (possibly transformed) characteristic is proposed. It is shown that, under some conditions, improveinent (with respect to MSE) over the traditional estimator is possible for a broad range of the values of the mixing constant. An estimator of the MSE of the proposed estimator is also provided.     

Alternative covariance estimates in a replicated measurement error model with correlated,heteroscedastic errors

The article concerns covariance estimates in a replicated measurement error model with correlated, heteroscedastic errors. Freedman has conjectured that using more of the data will improve estimates of covariance matrices and result in a more efficient estimate of the coefficient of the regression model. The paper confirms the conjecture asymptotically for the case that all random variables are normally distributed, but the gain is not substantial.     

A new goodness of fit test for the equality of multinomial cell probabilities versus trend alternatives

In this paper, a new test statistic is presented for testing the null hypothesis of equal multinomial cell probabilities versus various trend alternatives. Exact asymptotic critical values are obtained, The power of the test is compared with several other statistics considered by Choulakian et al (1995), The test is shown to have better power for certain trend alternatives.     

Genealogies and Gene-ideologies: The Legitimacy of the Beta Israel (Falasha)

The migration of the vast majority of Beta Israel (Falasha) to Israel has been accompanied by major shifts in the discourse regarding their ‘Jewishness’ and ‘Ethiopian-ness’. This article discusses the adoption of traditions of Danite descent in place of traditions of Solomonic descent and the emergence of genetics as the most important identity marker, replacing reckonings of lineage. The first shift is connected to the migration of the Beta Israel from Ethiopia to Israel; the second to changing concepts of what represents ‘proof’ of identity in the modern and post-modern world.     

Cox regression analysis in presence of collinearity: an application to assessment of health risks associated with occupational radiation exposure

This paper considers the analysis of time to event data in the presence of collinearity between covariates. In linear and logistic regression models, the ridge regression estimator has been applied as an alternative to the maximum likelihood estimator in the presence of collinearity. The advantage of the ridge regression estimator over the usual maximum likelihood estimator is that the former often has a smaller total mean square error and is thus more precise. In this paper, we generalized this approach for addressing collinearity to the Cox proportional hazards model. Simulation studies were conducted to evaluate the performance of the ridge regression estimator. Our approach was motivated by an occupational radiation study conducted at Oak Ridge National Laboratory to evaluate health risks associated with occupational radiation exposure in which the exposure tends to be correlated with possible confounders such as years of exposure and attained age. We applied the proposed methods to this study to evaluate the association of radiation exposure with all-cause mortality.     

Adaptive sampling without replacement of clusters

In a common form of adaptive cluster sampling, an initial sample of units is selected by random sampling without replacement and, whenever the observed value of the unit is sufficiently high, its neighboring units are added to the sample, with the process of adding neighbors repeated if any of the added units are also high valued. In this way, an initial selection of a high-valued unit results in the addition of the entire network of surrounding high-valued units and some low-valued “edge” units where sampling stops. Repeat selections can occur when more than one initially selected unit is in the same network or when an edge unit is shared by more than one added network. Adaptive sampling without replacement of networks avoids some of this repeat selection by sequentially selecting initial sample units only from the part of the population not already in any selected network. The design proposed in this paper carries this step further by selecting initial units only from the population, exclusive of any previously selected networks or edge units.