Double-blind deconvolution: the analysis of post-synaptic currents in nerve cells

This paper is concerned with the analysis of observations made on a system that is being stimulated at fixed time intervals but where the precise nature and effect of any individual stimulus is unknown. The realized values are modelled as a stochastic process consisting of a random signal embedded in noise. The aim of the analysis is to use the data to unravel the unknown structure of the system and to ascertain the probabilistic behaviour of the stimuli. A method of parameter estimation based on quasi-profile likelihood is presented and the statistical properties of the estimates are established while recognizing that there will be a discrepancy between the model and the true data-generating mechanism. A method of model validation and determination is also advanced and kernel smoothing techniques are proposed as a basis for identifying the amplitude distribution of the stimuli. The data processing techniques described have a direct application to the investigation of excitatory post-synaptic currents recorded from nerve cells in the central nervous system and their use in quantal analysis of such data is illustrated.     

Cancer Risk Estimation for Mixtures of Coal Tars

Two-year chronic bioassays were conducted by using B6C3F1 female mice fed several concentrations of two different mixtures of coal tars from manufactured gas waste sites or benzo(a)pyrene (BaP). The purpose of the study was to obtain estimates of cancer potency of coal tar mixtures, by using conventional regulatory methods, for use in manufactured gas waste site remediation. A secondary purpose was to investigate the validity of using the concentration of a single potent carcinogen, in this case benzo(a)pyrene, to estimate the relative risk for a coal tar mixture. The study has shown that BaP dominates the cancer risk when its concentration is greater than 6,300 ppm in the coal tar mixture. In this case the most sensitive tissue site is the forestomach. Using low-dose linear extrapolation, the lifetime cancer risk for humans is estimated to be: Risk < 1.03 × 10⁻⁴ (ppm coal tar in total diet) + 240 × 10⁻⁴ (ppm BaP in total diet), based on forestomach tumors. If the BaP concentration in the coal tar mixture is less than 6,300 ppm, the more likely case, then lung tumors provide the largest estimated upper limit of risk, Risk < 2.55 × 10⁻⁴ (ppm coal tar in total diet), with no contribution of BaP to lung tumors. The upper limit of the cancer potency (slope factor) for lifetime oral exposure to benzo(a)pyrene is 1.2 × 10⁻³ per μg per kg body weight per day from this Good Laboratory Practice (GLP) study compared with the current value of 7.3 × 10⁻³ per μg per kg body weight per day listed in the U.S. EPA Integrated Risk Information System.     

Length-biased,with-replacement sampling from an exponential finite population

In this article, we study a statistical model which features a finite population of exponentially distributed values and a length-biased, with-replacement sampling mechanism. This mechanism is such that units compete with one another for selection at each draw. It is shown how inference on a number of quantities can be performed using both frequentist and Bayesian strategies. A Monte Carlo study is used to assess the performance of the proposed point and interval estimators.     

Parametric estimation of mixtures of two uniform distributions

In this paper, we consider a mixture of two uniform distributions and derive L-moment estimators of its parameters. Three possible ways of mixing two uniforms, namely with neither overlap nor gap, with overlap, and with gap, are studied. The performance of these L-moment estimators in terms of bias and efficiency is compared to that obtained by means of the conventional method of moments (MM), modified maximum likelihood (MML) method and the usual maximum likelihood (ML) method. These intensive simulations reveal that MML estimators are the best in most of the cases, and the L-moment estimators are less subject to bias in estimation for some mixtures and more efficient in most of the cases than the conventional MM estimators. The L-moment estimators are, in some cases, more efficient than the ML and MML estimators.     

Linear regression with compositional explanatory variables

Compositional explanatory variables should not be directly used in a linear regression model because any inference statistic can become misleading. While various approaches for this problem were proposed, here an approach based on the isometric logratio (ilr) transformation is used. It turns out that the resulting model is easy to handle, and that parameter estimation can be done in like in usual linear regression. Moreover, it is possible to use the ilr variables for inference statistics in order to obtain an appropriate interpretation of the model.     

Monte Carlo Based Ensemble Forecasting

Ensemble forecasting involves the use of several integrations of a numerical model. Even if this model is assumed to be known, ensembles are needed due to uncertainty in initial conditions. The ideas discussed in this paper incorporate aspects of both analytic model approximations and Monte Carlo arguments to gain some efficiency in the generation and use of ensembles. Efficiency is gained through the use of importance sampling Monte Carlo. Once ensemble members are generated, suggestions for their use, involving both approximation and statistical notions such as kernel density estimation and mixture modeling are discussed. Fully deterministic procedures derived from the Monte Carlo analysis are also described. Examples using the three-dimensional Lorenz system are described.     

Cyclic quasi-symmetric designs and self-orthogonal codes of length 63

The enumeration of binary cyclic self-orthogonal codes of length 63 is used to prove that any cyclic quasi-symmetric 2-(63,15,35)$2\text{-}(63,15,35)$ design with block intersection numbers x=3$x=3$ and y=7$y=7$ is isomorphic to the geometric design having as blocks the three-dimensional subspaces in PG(5,2)$\text{<italic>PG</italic>}(5,2)$.     

Estimation and inference for exponential smooth transition nonlinear volatility models

A family of threshold nonlinear generalised autoregressive conditionally heteroscedastic models is considered, that allows smooth transitions between regimes, capturing size asymmetry via an exponential smooth transition function. A Bayesian approach is taken and an efficient adaptive sampling scheme is employed for inference, including a novel extension to a recently proposed prior for the smoothing parameter that solves a likelihood identification problem. A simulation study illustrates that the sampling scheme performs well, with the chosen prior kept close to uninformative, while successfully ensuring identification of model parameters and accurate inference for the smoothing parameter. An empirical study confirms the potential suitability of the model, highlighting the presence of both mean and volatility (size) asymmetry; while the model is favoured over modern, popular model competitors, including those with sign asymmetry, via the deviance information criterion.     

一种对初始值稳健的单位根检验及其应用

常见单位根检验方法对初始值都做了适当的约束,而经验研究中的数据往往由于各种冲击的存在无法满足相应的假定条件。所以,有必要讨论检验功效对初始值稳健的单位根检验方法。本文在研究初始值对单位根检验功效影响的基础上,基于Fisher统计量提出了检验功效关于初始值较稳健的组合p值单位根检验方法并研究了其小样本性质。并且,对我国CPI月环比时间序列的检验发现,随着我国宏观经济调控政策的完善,CPI逐渐趋于平稳。