Model Averaging Using Fractional Polynomials to Estimate a Safe Level of Exposure

Quantitative risk assessment involves the determination of a safe level of exposure. Recent techniques use the estimated dose-response curve to estimate such a safe dose level. Although such methods have attractive features, a low-dose extrapolation is highly dependent on the model choice. Fractional polynomials, basically being a set of (generalized) linear models, are a nice extension of classical polynomials, providing the necessary flexibility to estimate the dose-response curve. Typically, one selects the best-fitting model in this set of polynomials and proceeds as if no model selection were carried out. We show that model averaging using a set of fractional polynomials reduces bias and has better precision in estimating a safe level of exposure (say, the benchmark dose), as compared to an estimator from the selected best model. To estimate a lower limit of this benchmark dose, an approximation of the variance of the model-averaged estimator, as proposed by Burnham and Anderson, can be used. However, this is a conservative method, often resulting in unrealistically low safe doses. Therefore, a bootstrap-based method to more accurately estimate the variance of the model averaged parameter is proposed.     

一般形式线性分式规划的一个解法

本文提出一个直接处理一般形式线性分式规划的算法而不需要把问题的约束条件转化为标准形式。无需非退化假设条件。我们证明了算法在有限步后终止于原问题的最优解。     

Parameter Identification for Drift Fractional Brownian Motions with Application to the Chinese Stock Markets

This article deals with the problem of estimating all the unknown parameters in the drift fractional Brownian motion with discretely sampled data. The estimation procedure is built upon the marriage of the variation method and the ergodic theory. The strong consistencies of these estimators are provided. Moreover, our method and two existing approaches are compared based on the computational running time and the accuracy of estimation via simulation studies. We also apply the proposed method to the real high-frequency financial data within a window of 4 h in the trading day from the Chinese mainland stock market.     

Statistical power of the social network autocorrelation model

The network autocorrelation model has become an increasingly popular tool for conducting social network analysis. More and more researchers, however, have documented evidence of a systematic negative bias in the estimation of the network effect (ρ). In this paper, we take a different approach to the problem by investigating conditions under which, despite the underestimation bias, a network effect can still be detected by the network autocorrelation model. Using simulations, we find that moderately-sized network effects (e.g., ρ = .3) are still often detectable in modest-sized networks (i.e., 40 or more nodes). Analyses reveal that statistical power is primarily a nonlinear function of network effect size (ρ) and network size (N), although both of these factors can interact with network density and network structure to impair power under certain rare conditions. We conclude by discussing implications of these findings and guidelines for users of the autocorrelation model.     

The silence of numbers: A split-sample experiment concerning respondents' linguistic sensitivity in Danish survey studies

This article presents, for the first time in English, findings from a Danish research project on language comprehension and memory as generators of measurement problems in sociological and other social-science survey studies. Utilizing survey questionnaires as instruments of measurements, the article deals with the linguistic sensitivity of Danish adults and the measurement problems it entails. The article uncovers the nature and extent of statistically significant response differences due to moderate linguistic changes. The article problematizes the trustworthiness of Danish social-science survey studies and provides evidence that respondents' answers to survey questions depend to a marked extent on the latter's wording. The empirical basis is a split-sample experiment in which 1900 respondents completed two versions of the 'same' questionnaire.     

Approximation to two independent Gaussian processes from a unique Lévy process and applications

Abstract

In this article, we construct two families of processes, from a unique Lévy process, the finite dimensional distributions of which converge in law towards the finite dimensional distributions of the two independent Gaussian processes. As applications of this result, we obtain families of processes that converge in law towards fractional Brownian motion, sub-fractional Brownian motion and bifractional Brownian motion, respectively.     

Fractional approaches for the distribution of innovation sequence of INAR(1) processes

Abstract

In this paper, we present a fractional decomposition of the probability generating function of the innovation process of the first-order non-negative integer-valued autoregressive [INAR(1)] process to obtain the corresponding probability mass function. We also provide a comprehensive review of integer-valued time series models, based on the concept of thinning operators with geometric-type marginals. In particular, we develop two fractional approaches to obtain the distribution of innovation processes of the INAR(1) model and show that the distribution of the innovations sequence has geometric-type distribution. These approaches are discussed in detail and illustrated through a few examples.     

Book Reviews

Books reviewed:
Robert E., Kass and Paul W., Vos, Geometrical Foundations of Asymptotic Inference: Curved Exponential Families
G.S., Maddala and C.R., Rao, (eds) Handbook of Statistics 15: Robust Inference
Gregory C., Reinsel, Elements of Multivariate Time Series Analysis
Murray, Rosenblatt, Gaussian and Non-Gaussian Linear Time Series and Random Fields
William S., Mallios, The Analysis of Sports Forecasting: Modeling Parallels Between Sports Gambling and Financial Markets
Alain, Desrosières, The Politics of Large Numbers — A History of Statistical Reasoning
Mahmut, Parlar, Interactive Operations Research with MAPLE Methods and Models     

Book Reviews

Books reviewed:
Anthony, Atkinson & Marco, Riani, Robust Diagnostic Regression Analysis
N., Balakrishnan & C.R., Rao, Order Statistics: Theory & Methods. Handbook of Statistics, Volume 16
N., Balakrishnan & C.R., Rao, Order Statistics: Applications. Handbook of Statistics, Volume 17
C.R., Rao & G.J., Székely, Statistics for the 21st Century: Methodologies for Applications of the Future
D.A., Nolan & T.P., Speed, Stat Labs: Mathematical Statistics Through Applications
W.N., Venables & B.D., Ripley, S Programming
Peter W.M., John, Statistical Design and Analysis of Experiments