Tests of statistical hypotheses and their use in studies of natural phenomena

Contrary to ideas suggested by the title of the conference at which the present paper was presented, the author is not aware of a conceptual difference between a “test of a statistical hypothesis” and a “test of significance” and uses these terms interchangeably. A study of any serious substantive problem involves a sequence of incidents at which one is forced to pause and consider what to do next. In an effort to reduce the frequency of misdirected activities one uses statistical tests. The procedure is illustrated on two examples: (i) Le Cam’s (and associates’) study of immunotherapy of cancer and (ii) a socio-economic experiment relating to low-income homeownership problems.     

Comments on the special issue of communications in statistics (vol.a8, no. 10) concerned with weather modification experiments

As stated by the Editors of the Special Issue. It was complied with reference to two of my statements; that much of the current weather modification literature is slanted and unreliable. and(2) that progress in the building of a reliable weather modification technology requires an interdisciplinary study of as many completed cloud seeding experiments as possible. The material published in the Special Issue relates to two completed experiments, the Tasmania and the Israeli experiments. It is shown that a realistic appraisal of a completed experiment requires a prolonged effort, including an examination of quite a few relevant publications and, on occasion, Some numerical work on published raw data. It appears that an interdisciplinary reanalysis of the Tasmania experiment can contribute to the development of a reliable cloud seeding technology.     

On the NEH heuristic for minimizing the makespan in permutation flow shops

Over the last 20 years the NEH heuristic of Nawaz, Enscore, and Ham published in this journal has been commonly regarded as the best heuristic for minimizing the makespan in permutation flow shops. In recent years some authors claimed to develop new heuristics that are competitive or outperform NEH. Our study reveals that these claims are not justified. We also address the issue of a fair comparison of the NEH results with those obtained by metaheuristics. Finally we conduct a thorough analysis of NEH leading to its modification which secures the optimality in the two-machine case and improves the general performance.     

Criteria for the equality between ordinary least squares and best linear unbiased estimators under certain linear models

A new necessary and sufficient condition is derived for the equality between the ordinary least-squares estimator and the best linear unbiased estimator of the expectation vector in linear models with certain specific design matrices. This condition is then applied to special cases involving one-way and two-way classification models.     

VARIABLE PRICE ADJUSTMENT COSTS

The fixed (menu) cost approach has been criticized since administrative costs of price changes are small. This paper studies costs which depend on (i) the size or (ii) the frequency of adjustment. The optimal pricing policy is similar to that in the menu cost model which is, therefore, a simple benchmark case. While recent empirical evidence implies rejection of the fixed cost model, it is consistent with the general specification used here. The analysis strongly suggests that nominal inflexibilities at the individual level are not due to administrative costs but result from unfavourable market response to price changes.     

Optimal sequential estimation procedures of a function of a probability of success under LINEX loss

In this paper, we investigate the problem of estimating a function g(p), where p is the probability of success in a sequential sample of independent identically Bernoulli distributed random variables. As a loss associated with estimation we introduce a generalized LINEX loss function. We construct a sequential procedure possessing some asymptotically optimal properties in the case when p tends to zero. In this approach to the problem, the conditions are given, under which the stopping time is asymptotically efficient and normal, and the corresponding sequential estimator is asymptotically normal. The procedure constructed guarantees that its sequential risk is asymptotically equal to a prescribed constant.