Inference for a change-point problem under an OU setting with unequal and unknown volatilities

An Ornstein–Uhlenbeck (OU) process is employed as a versatile model to capture the mean-reverting and stochastic evolution of many variables in various fields of applications including finance and economics. Within the OU setting, we develop a new estimation method to determine the unknown change-point location under the assumption that the volatilities before and after the change point in a time series are unequal. Our method hinges on the concept of a weighted least sum of squared errors approach and enhanced by a fusion of an iterative algorithm. The consistency of the change-point estimator is established. This article highlights a numerical implementation on simulated and observed financial market data demonstrating the significant flexibility and accuracy of our proposed modelling and estimation method. The Canadian Journal of Statistics 48: 62–78; 2020 © 2019 Statistical Society of Canada     

An Estimator of Shannon Entropy of Beta-Generated Distributions and a Goodness-of-Fit Test

The aim of this article is twofold: on the one hand to introduce and study some of the statistical properties of an estimator for the Shannon entropy and on the other hand to develop a goodness-of-fit test for beta-generated distributions and the distribution of order statistics. Beta-generated distributions are a broad class of univariate distributions which has received great attention during the last 15 years, as it obeys nice properties and it extends the distribution of order statistics. The proposed estimator of Shannon entropy of beta-generated distributions is motivated by the respective Vasicek’s estimator, as the latter one is tailored to the class of the beta-generated distributions and the distribution of order statistics. The estimator of Shannon entropy is defined and its consistency is studied. It is, moreover, exploited to build a goodness-of-fit test for the beta-generated distribution and the distribution of order statistics. Simulations are performed to examine the small- and moderate-sample properties of the proposed estimator and to compare the power of the proposed test with the power of competitors under a variety of alternatives.     

刘勰《文心雕龙》"阴阳惨舒"说与中国"绿色"文论的起点

用现代观点诠释刘勰《文心雕龙.物色》篇。不同意认为《物色》篇位置排列“有误”的观点,认为目前的《物色》篇的位置暗含了社会与自然并列的思想。《物色》篇提出的“阴阳惨舒”说揭示了人的心理世界与自然世界的“同构对应”和“物我交感”,也说明了自然景物是文学本原之一。本文认为“阴阳惨舒”说、“联类不穷”说和“情往似赠”说等三说,可以看成中国古代“绿色”文论的起点。     

A Bayesian nonparametric estimator based on left censored data

Summary This paper introduces a Bayesian nonparametric estimator for an unknown distribution function based on left censored observations. Hjort (1990)/Lo (1993) introduced Bayesian nonparametric estimators derived from beta/beta-neutral processes which allow for right censoring. These processes are taken as priors from the class ofneutral to the right processes (Doksum, 1974). The Kaplan-Meier nonparametric product limit estimator can be obtained from these Bayesian nonparametric estimators in the limiting case of a vague prior. The present paper introduces what can be seen as the correspondingleft beta/beta-neutral process prior which allow for left censoring. The Bayesian nonparametyric estimator is obtained as in the corresponding product limit estimator based on left censored data.     

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.     

A hierarchy of lorenz curves based on the generalized tukey's lambda distribution

A hierarchy of Lorenz curves based on the generalized Tukey's Lambda distribution is proposed. Representations of the corresponding distribution and density function are also provided, together with popular inequality measures. Estimation methods are suggested. Finally, a comparison with other parametric families of Lorenz curves is established.     

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.