On locally optimal invariant unbiased tests for the variance components ratio in mixed linear models

In the paper the problem of testing of two-sided hypotheses for variance components in mixed linear models is considered. When the uniformly most powerful invariant test does not exist (see e.g. Das and Sinha, in Proceedings of the second international Tampere conference in statistics, 1987; Gnot and Michalski, in Statistics 25:213–223, 1994; Michalski and Zmyślony, in Statistics 27:297–310, 1996) then to conduct the optimal statistical inference on model parameters a construction of a test with locally best properties is desirable, cf. Michalski (in Tatra Mountains Mathematical Publications 26:1–21, 2003). The main goal of this article is the construction of the locally best invariant unbiased test for a single variance component (or for a ratio of variance components). The result has been obtained utilizing Andersson’s and Wijsman’s approach connected with a representation of density function of maximal invariant (Andersson, in Ann Stat 10:955–961, 1982; Wijsman, in Proceedings of fifth Berk Symp Math Statist Prob 1:389–400, 1967; Wijsman, in Sankhyā A 48:1–42, 1986; Khuri et al., in Statistical tests for mixed linear models, 1998) and from generalized Neyman–Pearson Lemma (Dantzig and Wald, in Ann Math Stat 22:87–93, 1951; Rao, in Linear statistical inference and its applications, 1973). One selected real example of an unbalanced mixed linear model is given, for which the power functions of the LBIU test and Wald’s test (the F-test in ANOVA model) are computed, and compared with the attainable upper bound of power obtained by using Neyman–Pearson Lemma.     

Estimation of a relative potency of two preparations with correlated responses

Estimation of a relative potency of two preparations in so-called parallel-line assays is presented. A special type of incomplete Latin square designs where doses of preparations are administered is considered. Testing hypotheses about similarity of preparations and their relative potency in the case of correlated observations are regarded. Confidence interval for the relative potency of preparations is also given. Theoretical considerations are applied to point and interval estimation of potencies of new tuberculins with respect to some international standards tested in experiments on guinea-pigs.     

Double ASN Minimax sampling plans by variables when the standard deviation is unknown

We deal with the double sampling plans by variables proposed by Bowker and Goode (Sampling Inspection by Variables, McGraw–Hill, New York, 1952) when the standard deviation is unknown. Using the procedure for the calculation of the OC given by Krumbholz and Rohr (Allg. Stat. Arch. 90:233–251, 2006), we present an optimization algorithm allowing to determine the ASN Minimax plan. This plan, among all double plans satisfying the classical two-point-condition on the OC, has the minimal ASN maximum.     

Modified inference about the mean of the exponential distribution using moving extreme ranked set sampling

The maximum likelihood estimator (MLE) and the likelihood ratio test (LRT) will be considered for making inference about the scale parameter of the exponential distribution in case of moving extreme ranked set sampling (MERSS). The MLE and LRT can not be written in closed form. Therefore, a modification of the MLE using the technique suggested by Maharota and Nanda (Biometrika 61:601–606, 1974) will be considered and this modified estimator will be used to modify the LRT to get a test in closed form for testing a simple hypothesis against one sided alternatives. The same idea will be used to modify the most powerful test (MPT) for testing a simple hypothesis versus a simple hypothesis to get a test in closed form for testing a simple hypothesis against one sided alternatives. Then it appears that the modified estimator is a good competitor of the MLE and the modified tests are good competitors of the LRT using MERSS and simple random sampling (SRS).     

Integrated methodology for multiple systems estimation and record linkage using a missing data formulation

There are now three essentially separate literatures on the topics of multiple systems estimation, record linkage, and missing data. But in practice the three are intimately intertwined. For example, record linkage involving multiple data sources for human populations is often carried out with the expressed goal of developing a merged database for multiple system estimation (MSE). Similarly, one way to view both the record linkage and MSE problems is as ones involving the estimation of missing data. This presentation highlights the technical nature of these interrelationships and provides a preliminary effort at their integration.     

Inference in hybrid Bayesian networks using dynamic discretization

We consider approximate inference in hybrid Bayesian Networks (BNs) and present a new iterative algorithm that efficiently combines dynamic discretization with robust propagation algorithms on junction trees. Our approach offers a significant extension to Bayesian Network theory and practice by offering a flexible way of modeling continuous nodes in BNs conditioned on complex configurations of evidence and intermixed with discrete nodes as both parents and children of continuous nodes. Our algorithm is implemented in a commercial Bayesian Network software package, AgenaRisk, which allows model construction and testing to be carried out easily. The results from the empirical trials clearly show how our software can deal effectively with different type of hybrid models containing elements of expert judgment as well as statistical inference. In particular, we show how the rapid convergence of the algorithm towards zones of high probability density, make robust inference analysis possible even in situations where, due to the lack of information in both prior and data, robust sampling becomes unfeasible.     

Multi-phase sampling under cost constraints

Multi-phase sampling (M-PhS) scheme is useful when the interest is in the estimation of the population mean of an expensive variable strictly connected with other cheaper (auxiliary) variables. The MSE is an accuracy measure of an estimator. Usually it decreases as the sample size increases. In practice the sample size cannot become arbitrarily large for possible cost constraints. From a practical point of view it would be useful to know the sample sizes which guarantee the best accuracy of the estimates for fixed costs. These “optimum” sample sizes can be, in some cases, computable but not admissible. In other cases, they can be neither admissible nor computable. The main goal of this paper is to propose a solution for both these situations. It will be clear that in both situations the solution is to consider a M-PhS scheme with one or more phases less.