Estimating ability parameters in latent trait models in general, and in the Rasch model in particular is almost always hampered by noise in the data. This noise can be caused by guessing, inattention to easy questions, and other factors which are unrelated to ability. In this study several alternative formulations which attempt to deal with these problems without a reparameterization are tested through a Monte Carlo simulation. It was found that although no one of the tested schemes is uniformly superior to all others, a modified jackknife stood out as the best one in general, it was also super efficient (more efficient than the asymptotically optimal estimator) for tests with forty or fewer items. It is proposed that this sort of jackknifing scheme for estimating ability be considered for practical work.

The use of U-statistics based on rank correlation coefficients in estimating the strength of concordance among a group of rankers is examined for cases where the null hypothesis of random rankings is not tenable. The studentized U-statistics is asymptotically distribution-free, and the Student-t approximation is used for small and moderate sized samples. An approximate confidence interval is constructed for the strength of concordance. Monte Carlo results indicate that the Student-t approximation can be improved by estimating the degrees of freedom.

Several ways of using the traditional analysis of variance to test heterogeneity of spread in factorial designs with equal or unequal n are compared using both theoretical and Monte Carlo results. Two types of spread variables, (1) the jackknife pseudovalues of s2 and (2) the absolute deviations from the cell median, are shown to be robust and relatively powerful. These variables seem to be generally superior to the Z-variance and Box-Scheffé procedures.

A jackknife-like procedure is developed for producing standard errors of estimate in maximum likelihood factor analysis. Unlike earlier methods based on information theory, the procedure developed is computationally feasible on larger problems. Unlike earlier methods based on the jackknife, the present procedure is not plagued by the factor alignment problem, the Heywood case problem, or the necessity to jackknife by groups. Standard errors may be produced for rotated and unrotated loading estimates using either orthogonal or oblique rotation as well as for estimates of unique factor variances and common factor correlations. The total cost for larger problems is a small multiple of the square of the number of variables times the number of observations used in the analysis. Examples are given to demonstrate the feasibility of the method.

With increasingly thin margins and new technologies, it is important that farm managers know their cost of field operations on a per unit basis (e.g., acre, ton, bale). Accurate per unit costs give confidence when constructing enterprise budgets and evaluating new technologies, such as no-till. Custom rates are often used as a proxy for per unit costs; however, this research, using entropy and jackknife estimation procedures, found that custom rates understate total ownership and operating costs by approximately 25% for an average Kansas farm. Estimates from these models are then used to benchmark actual costs against expected cost.

Many tests have rejected the implications of the consumption CAPM for data on U.S. asset returns. All of the tests, though, assume that the pricing errors satisfy the Central Limit Theorem. I provide empirical evidence that the marginal distributions of the pricing errors are so heavy-tailed that they do not satisfy the Central Limit Theorem. Using recent work on jackknifing, I construct a method of testing asset pricing models with heavy-tailed errors. Using this procedure, I find that the consumption CAPM is not rejected by annual U.S. data.

In most real-world contexts the sampling effort needed to attain an accurate estimate of total species richness is excessive. Therefore, methods to estimate total species richness from incomplete collections need to be developed and tested. Using real and computer-simulated parasite data sets, the performances of 9 species richness estimation methods were compared. For all data sets, each estimation method was used to calculate the projected species richness at increasing levels of sampling effort. The performance of each method was evaluated by calculating the bias and precision of its estimates against the known total species richness. Performance was evaluated with increasing sampling effort and across different model communities. For the real data sets, the Chao2 and first-order jackknife estimators performed best. For the simulated data sets, the first-order jackknife estimator performed best at low sampling effort but, with increasing sampling effort, the bootstrap estimator outperformed all other estimators. Estimator performance increased with increasing species richness, aggregation level of individuals among samples and overall population size. Overall, the Chao2 and the first-order jackknife estimation methods performed best and should be used to control for the confounding effects of sampling effort in studies of parasite species richness. Potential uses of and practical problems with species richness estimation methods are discussed.

Let ?(u) be the probability of eventual ruin in the classical Sparre Andersen model of risk theory if the initial risk reserve is u. For a large class of such models ?(u) behaves asymptotically like a multiple of exp (–Ru) where R is the adjustment coefficient; R depends on the premium income rate, the claim size distribution and the distribution of the time between claim arrivals. Estimation of R has been considered by many authors. In the present paper we deal with confidence bounds for R. A variety of methods is used, including jackknife estimation of asymptotic variances and the bootstrap. We show that, under certain assumptions, these procedures result in interval estimates that have asymptotically the correct coverage probabilities. We also give the results of a simulation study that compares the different techniques in some particular cases.