Approximation methods for lognormal characteristic functions

ABSTRACT

The characteristic function of the lognormal distribution is of interest in a number of scientific fields yet an analytic solution remains elusive, making reliable and efficient approximations necessary. In this article, we build on the results of N. C. Beaulieu and A. Saberali in ‘New approximations to the lognormal characteristic function’, by introducing a Taylor- and Bessel function-based partial expansion of the integrand and a Chebyshev quadrature approach. Through computer simulations we show that the Taylor expansion remains accurate and efficient for all commonly computed values, and specify the range of values for which the other two approaches show a significantly stronger performance.     

查尔斯·泰勒的现代市民社会模式评析

政治哲学家查尔斯·泰勒认为,流行于现代西方社会的市民社会概念具有深远的历史根源,这些根源为近代以来的反专制主义学说以两种不同的路径（源自于洛克的L-流和孟德斯鸠的M-流）所继承和发展,并且为现代市民社会概念提供了两条不同的理论进路。在泰勒看来,鉴于两种进路都有可能演化为市民社会的消失、自由的丧失与专制政治的复现,因而应将二者融为一体,在融汇中克服各自缺陷,以建构能够真正保障自由的现代市民社会,即个人自由与政治自由、消极自由与积极自由相结合的市民社会。     

Second-order variance estimation in poststratified two-stage sampling

The linearization or Taylor series variance estimator and jackknife linearization variance estimator are popular for poststratified point estimators. In this note we propose a simple second-order linearization variance estimator for the poststratified estimator of the population total in two-stage sampling, using the second-order Taylor series expansion. We investigate the properties of the proposed variance estimator and its modified version and their empirical performance through some simulation studies in comparison to the standard and jackknife linearization variance estimators. Simulation studies are carried out on both artificially generated data and real data.     

Corrected asymptotic distribution of statistics based on the multinomial law

Investigators and epidemiologists often use statistics based on the parameters of a multinomial distribution. Two main approaches have been developed to assess the inferences of these statistics. The first one uses asymptotic formulae which are valid for large sample sizes. The second one computes the exact distribution, which performs quite well for small samples. They present some limitations for sample sizes N neither large enough to satisfy the assumption of asymptotic normality nor small enough to allow us to generate the exact distribution. We analytically computed the 1/N corrections of the asymptotic distribution for any statistics based on a multinomial law. We applied these results to the kappa statistic in 2×2 and 3×3 tables. We also compared the coverage probability obtained with the asymptotic and the corrected distributions under various hypothetical configurations of sample size and theoretical proportions. With this method, the estimate of the mean and the variance were highly improved as well as the 2.5 and the 97.5 percentiles of the distribution, allowing us to go down to sample sizes around 20, for data sets not too asymmetrical. The order of the difference between the exact and the corrected values was 1/N² for the mean and 1/N³ for the variance.     

An investigation of a quadratic design criterion for estimation of the hemodynamic response function

Optimal experimental design for estimation of the hemodynamic response function (HRF) is investigated using a nonlinear model with a quadratic mean squared error design criterion. This criterion is used, along with a genetic algorithm, to select locally optimal designs that are shown to be, in most cases, more efficient than designs selected with the more commonly used linear expansion criterion. These designs are also shown to result in lower overall asymptotic estimator variance and bias. The investigation focuses on a single stimulus type, but the criterion can also be used with multiple stimulus types.     

由泰勒规则货币政策对我国股票市场货币政策传导效力的实证研究

 本文基于泰勒型货币政策规则对我国1992-2005年考虑股票市场资产价格泡沫的货币政策反应函数进行了实证检验，发现我国在制定货币政策操作规则时，利率平滑倾向显著，赋予通货膨胀和产出缺口的权重较大，但不重视应对资本市场价格较大波动。说明我国的货币政策资本市场传导机制不畅，导致我国居民和公司资产负债表不健康，应对金融风险能力非常弱。     

社群主义与自由主义之间本体论差异的辨析——基于泰勒与柏林自由观的比较分析

自由主义者以赛亚.柏林与社群主义者查尔斯.泰勒都认可自由是重要的价值规范,但前者把自由看作是免于外在干涉的个人的选择自由,后者则把参与自治看作是自由的实质。二者自由观的差异体现着自由主义与社群主义之间的本体论差异,即个人与社会何为本原的差异。自由主义认为应当依据个人的性质来解释社会的行动、结构和状况,应当依据个人的善来解释社会的善;而社群主义则认为应当依据社会来解释构成性的个人,应当依据社会的共同善来解释个人的善。     

A comparison of alternative variance estimation strategies for estimating the slope of a linear regression in sample surveys

The balanced half-sample, jackknife and linearization methods are used to estimate the variance of the slope of a linear regression under a variety of computer generated situations. The basic sampling design is one in which two PSU's are selected from each of a number of strata . The variance estimation techniques are compared with a Monte Carlo experiment. Results show that variance estimates may be highly biased and variable unless sizeable numbers of observations are available from each stratum. The jackknife and linearization estimates appear superior to the balanced half sample method - particularly when the number of strata or the number of available observations from each stratum is small.     

Computing A-optimal Designs for Weighted Polynomial Regression by Taylor Expansion

This article is concerned with the problem of constructing A-optimal design for polynomial regression with analytic weight function on the interval [m ? a, m + a], m, a > 0. It is shown that the structure of the optimal design depends on a and weight function only, as a close to 0. Moreover, if the weight function is an analytic function a, then a scaled version of optimal support points, and weights are analytic functions of a at a = 0. We make use of a Taylor expansion to provide a recursive procedure for calculating the A-optimal designs. Examples are presented to illustrate the procedures for computing the optimal designs.