Testing for intercept‐scale switch in linear autoregression

Autoregressive models with switching regime are a frequently used class of nonlinear time series models, which are popular in finance, engineering, and other fields. We consider linear switching autoregressions in which the intercept and variance possibly switch simultaneously, while the autoregressive parameters are structural and hence the same in all states, and we propose quasi‐likelihood‐based tests for a regime switch in this class of models. Our motivation is from financial time series, where one expects states with high volatility and low mean together with states with low volatility and higher mean. We investigate the performance of our tests in a simulation study, and give an application to a series of IBM monthly stock returns. The Canadian Journal of Statistics 40: 427–446; 2012 © 2012 Statistical Society of Canada     

Notes on interval estimation of the proportion ratio under a three-treatment three-period crossover trial

When comparing two experimental treatments with a placebo, we focus our attention on interval estimation of the proportion ratio (PR) of patient responses under a three-period crossover design. We propose a random effects exponential multiplicative risk model and derive asymptotic interval estimators in closed form for the PR between treatments and placebo. Using Monte Carlo simulations, we compare the performance of these interval estimators in a variety of situations. We use the data comparing two different doses of an analgesic with placebo for the relief of primary dysmenorrhea to illustrate the use of these interval estimators and the difference in estimates of the PR and odds ratio (OR) when the underlying relief rates are not small.     

贪婪与报应——对贝内特《莱西姆台阶》的思考

一般被认为是写实主义者的阿诺德·贝内特其实也进行了现代主义尝试。《菜西姆台阶》就体现了这种尝试。通过主题性和结构性象征体系的运用,贝内特成功地塑造了西方文学史上一个新型的吝啬鬼形象,藉此揭示了西方文明中深刘的内在矛盾。     

A generalized drop-the-loser rule for multi-treatment clinical trials

Urn models are popular for response adaptive designs in clinical studies. Among different urn models, Ivanova's drop-the-loser rule is capable of producing superior adaptive treatment allocation schemes. Ivanova [2003. A play-the-winner-type urn model with reduced variability. Metrika 58, 1–13] obtained the asymptotic normality only for two treatments. Recently, Zhang et al. [2007. Generalized drop-the-loser urn for clinical trials with delayed responses. Statist. Sinica, in press] extended the drop-the-loser rule to tackle more general circumstances. However, their discussion is also limited to only two treatments. In this paper, the drop-the-loser rule is generalized to multi-treatment clinical trials, and delayed responses are allowed. Moreover, the rule can be used to target any desired pre-specified allocation proportion. Asymptotic properties, including strong consistency and asymptotic normality, are also established for general multi-treatment cases.     

Goodness-of-fit tests for exponentiality based on a loss-of-memory type functional equation

Three goodness-of-fit tests for exponentiality based on the functional equation characterization 1?F(2x)=[1?F(x)]² for every x?0 are proposed and shown to compare well to several popular tests against common alternative cdf's. Small-sample critical values for α=0.10,0.05 are developed for the two superior test statistics and the asymptotic null-distributions are characterized.     

On the influence curve for quantal bioassay

Influence curves are defined for estimators of the ED50 in quantal bioassay, assuming a symmetic tolerance distribution. A definition of influence-curve robustness is suggested. Influence curves are obtained for L-,M- and R-estimators, and their robustness is investigated. The influence curve of the logistic maximum likelihood estimator is studied.     

Measuring diversity in biological populations with logarithmic abundance distributions

Fisher's logarithmic distribution for species abundance is derived under a suitable set of conditions. The derivation explains the explicit meaning of the two parameters of the distribution.     

Properties of occurrence-exposure rate processes in multiple decrement theory

In a basic multiple decrement model empirical occurrence-exposure rates are defined for each of k risks to which a cohort from an animal or human population is exposed over a time interval. These rates are viewed as the evolution of a stochastic process. Some asymptotic properties of this process are considered. Weak convergence of the process and its uniform strong convergence are shown under mild conditions.     

D-optimal block designs with at most six varieties

For given positive integers v, b, and k (all of them ≥2) a block design is a k × b array of the variety labels 1,…,v with blocks as columns. For the usual one-way heterogeneity model in standard form the problem is studied of finding a D-optimal block design for estimating the variety contrasts, when no balanced block design (BBD) exists. The paper presents solutions to this problem for v≤6. The results on D-optimality are derived from a graph-theoretic context. Block designs can be considered as multigraphs, and a block design is D-optimal iff its multigraph has greatest complexity (=number of spanning trees).     

Randomization in a complete block design with few blocks

It is known that the distributions of statistics commonly used in experimental design (notably the F statistic) involve certain nuisance parameters which depend on the model and the design. Raudomization was a technique introduced by R.A. Fisher to eliminate some of these parameter and produce a usable distribution function. We will show that there is a close relationship between the analytical properties of the non-randomized distribution and the more combinatorial properties of the nuisance parameters. This relationship allows us to determine theoretically, and practically in some cases, how good an approximation the central F distribution is to the randomized distribution.