ESTIMATING TEMPORAL FARM INCOME DISTRIBUTIONS USING SPATIAL SMOOTHING TECHNIQUES

The Australian Bureau of Agricultural & Resource Economics (ABARE) has conducted the annual Australian Agricultural and Grazing Industries Survey, covering the broadacre sector, in a consistent format since 1978/79. In this period the incomes of farmers have fluctuated considerably. Interest has focused on temporal income variation because of its relationship to the inherent riskiness of farming. Part of these income fluctuations can be explained by changing commodity prices and by highly variable climatic conditions. This paper outlines a method of measuring the magnitude of this income variation and how it relates to other variables. Due to rotation within the sample of farms surveyed, data are limited for determining the income variability of any particular farm. This paper, using spatial locations of surveyed farms, shows how kernel smoothing techniques can be adapted to estimate the distribution of a farm's income. This analysis uses data collected from 1978/79 to 1991/92. Summary information from these distributions is cross-tabulated against several other variables. This shows that income variability is strongly related to the production mixture of farming businesses.     

Approximate theory of multiway block designs

Optimality properties of multiway block designs are deduced from the general results of J. Kiefer's approximate-design theory. In the model with additive effects these optimality properties solely depend on the two-dimensional marginals of the designs. Uniform designs, and designs whose two-dimensional marginals are products of the one-dimensional marginals, are shown to be optimal. Approximate Youden designs are introduced for the case when the support sets of the two-dimensional marginals are prescribed in advance. They are optimal in a relatively small class of competing designs only.     

A note on adaptation in garch models

In the framework of the Engle-type (G)ARCH models, I demonstrate that there is a family of symmetric and asymmetric density functions for which the asymptotic efficiency of the semiparametric estimator is equal to the asymptotic efficiency of the maximum likelihood estimator. This family of densities is bimodal (except for the normal). I also chracterize the solution to the problem of minimizing the mean squared distance between the parametric score and the semiparametric score in order to search for unimodal densities for which the semiparametric estimator is likely to perform well. The LaPlace density function emerges as one of these cases.     

The exact risk performance of a pre-test estimator in a heteroskedastic linear regression model under the balanced loss function

We examine the risk of a pre-test estimator for regression coefficients after a pre-test for homoskedasticity under the Balanced Loss Function (BLF). We show analytically that the two stage Aitken estimator is dominated by the pre-test estimator with the critical value of unity, even if the BLF is used. We also show numerically that both the two stage Aitken estimator and the pre-test estimator can be dominated by the ordinary least squares estimator when “goodness of fit” is regarded as more important than precision of estimation.     

Properties of the mixed regression estimator when disturbances are not necessarily normal

Small-disturbance approximations for the bias vector and mean squared error matrix of the mixed regression estimator for the coefficients in a linear regression model are derived and efficiency with respect to least squares estimator is examined.     

ASSESSING ERROR RATE ESTIMATORS: THE LEAVE-ONE-OUT METHOD RECONSIDERED

Many comparative studies of the estimators of error rates of supervised classification rules are based on inappropriate criteria. In particular, although they fix the Bayes error rate, their summary statistics aggregate a range of true error rates. This means that their conclusions about the performance of classification rules cannot be trusted. This paper discusses the general issues involved, and then focuses attention specifically on the leave-one-out estimator. The estimator is investigated in a simulation study, both in absolute terms and in comparison with a popular bootstrap estimator. An improvement to the leave-one-out estimator is suggested, but the bootstrap estimator appears to maintain superiority even when the criteria are adjusted.     

An application of the Bernoulli part to local limit theorems for moving averages on stationary sequences

We consider partial sums S_n of a general class of stationary sequences of integer-valued random variables, and we provide sufficient conditions for S_n to satisfy a local limit theorem. To prove this result, we introduce a concept called the Bernoulli part. The amount of Bernoulli part in S_n determines the extent to which the density of S_n is relatively flat. If in addition S_n satisfies a global central limit theorem, the local limit theorem follows.     

认识及其限度--论个体认识的可能性

认识是在人的意识中反映或观念地再现现实的过程.无论对于自身还是其所处世界,人类的认识及认识结果的知识都具有不确定性.认识的限度表现为作为过程的认识和作为状态的认识都无法逃避认识的可能性问题.从本质上讲,认识的限度及个体认识的可能性源于主客二分、心身对立,因此,解决心身问题成为解决上述问题的关键.     

A product-limit estimator for use with length-biased data

The following life-testing situation is considered. At some time in the distant past, n objects, from a population with life distribution F, were put in use; whenever an object failed, it was promptly replaced. At some time τ, long after the start of the process, a statistician starts observing the n objects in use at that time; he knows the age of each of those n objects, and observes each of them for a fixed length of time? ∞, or until failure, whichever occurs first. In the case where T is finite, some of the observations may be censored; in the case where T =∞, there is no censoring. The total life of an object in use at time ∞ is a length-biased observation from F. A nonparametric estimator of the (cumulative) hazard function is proposed, and is used to construct an estimator of F which is of the product-limit type. Strong uniform consistency results (for n → ∞) are obtained. An “Aalen-Johansen” identity, satisfied by any pair of life distributions and their (cumulative) hazard functions, is used in obtaining rate-of-convergence results.     

ON THE HILDRETH-HOUCK ESTIMATOR FOR RANDOM COEFFICIENT REGRESSION MODELS

This paper is concerned with the linear regression model in which the coefficients are random variables. The Hildreth-Houck method is considered for estimating the model. Sufficient conditions for the consistency of the Hildreth-Houck estimator are discussed and its asymptotic normality is established.