On the poisson index of dispersion

A commonly used statistic for testing hypotheses concerning count data is the index of dispersion or variance test (c.f., Fisher 1950, Rao and Chakravarti 1956). The statistic is essentially the ratio of the sample variance to the sample mean,The hypothesis being tested is commonly referred to as the homogeneity hypothesis, often without further detailed specification. However, a closer study of the literature indicates that there are really two different hypotheses of interest.     

Population structure and correlation between auxiliary and target variables may affect precision of estimates in forest inventory

Simulations of forest inventory in several populations compared simple random with “quick probability proportional to size” (QPPS) sampling. The latter may be applied in the absence of a list sampling frame and/or prior measurement of the auxiliary variable. The correlation between the auxiliary and target variables required to render QPPS sampling more efficient than simple random sampling varied over the range 0.3–0.6 and was lower when sampling from populations that were skewed to the right. Two possible analytical estimators of the standard error of the estimate of the mean for QPPS sampling were found to be less reliable than bootstrapping.     

Second Quarter 1973 Survey of the Economic Outlook

The aim of the author is improvement of statistical practice. The author distinguishes between enumerative studies and analytic studies. An enumerative study has for its aim an estimate of the number of units of a frame that belong to a specified class. An analytic study has for its aim a basis for action on the cause-system or the process, in order to improve product of the future. A fair price to pay for an inventory is an example of an enumerative study. Tests of varieties of wheat, insecticides, drugs, manufacturing processes, are examples of analytic studies: the choice of variety or treatment will affect the future out-turn of wheat, future patients, future product. Techniques and methods of inference that are applicable to enumerative studies lead to faulty design and faulty inference for analytic problems.

It is possible, in an enumerative problem, to reduce errors of sampling to any specified level. In contrast, in an analytic problem, it is impossible to compute the risk of making a wrong decision. The author provides a number of examples, and pleads for greater care in the writing and teaching of statistical theory and inference.     

A Nonparametric Test for Autoregressive Conditional Heteroscedasticity: A Markov-Chain Approach

In this article we propose a nonparametric test for autoregressive conditional heteroscedasticity based on finite-state Markov chains. A simple Monte Carlo experiment suggests that in finite samples it performs comparably to the Lagrange multiplier test under conditional normality and is superior for the t, lognormal, and exponential distributions. As an illustration, we apply both tests to Canadian/U.S. forward foreign exchange data.     

Unconditional analogues of Cochran–Mantel–Haenszel tests

The Cochran–Mantel–Haenszel tests are a suite of tests that are usually defined as conditional tests, tests that assume all marginal totals are known before sighting the data. Here unconditional analogues of these tests are defined for the more usual situation when the marginal totals are not known before sighting the data.     

Estimation for a first-order bifurcating autoregressive process with heavy-tail innovations

Asymptotics of an alternative extreme-value estimator for the autocorrelation parameter in a first-order bifurcating autoregressive (BAR) process with non-gaussian innovations are derived. This contrasts with traditional estimators whose asymptotic behavior depends on the central part of the innovation distribution. Within any BAR model, the main concern is addressing the complex dependency between generations. The inability of traditional methods to handle this dependency motivated an alternative procedure. With the combination of an extreme-value approach and a clever blocking argument, the dependency issue within the BAR process was resolved, which in turn allowed us to derive the limiting distribution for the proposed estimator through the use of regular variation and non-stationary point processes. Finally, the implications of our extreme-value approach are discussed with an extensive simulation study that not only assesses the reliability of our proposed estimate but also presents the findings for a new estimator of an unknown location parameter θ and its implications.