Sequential experimental design and response optimisation

We consider the situation where one wants to maximise a functionf(θ,x) with respect tox, with θ unknown and estimated from observationsy _k . This may correspond to the case of a regression model, where one observesy _k =f(θ,x _k )+ε _k , with ε _k some random error, or to the Bernoulli case wherey _k ∈{0, 1}, with Pr[y _k =1|θ,x _k |=f(θ,x _k ). Special attention is given to sequences given by , with an estimated value of θ obtained from (x₁, y₁),...,(x _k ,y _k ) andd _k (x) a penalty for poor estimation. Approximately optimal rules are suggested in the linear regression case with a finite horizon, where one wants to maximize ∑ _i=1 ^N w _i f(θ, x _i ) with {w _i } a weighting sequence. Various examples are presented, with a comparison with a Polya urn design and an up-and-down method for a binary response problem.     

Quantile plots for mean effects in the presence of variance effects for 2k-p designs

In robust parameter design, variance effects and mean effects in a factorial experiment are modelled simultaneously. If variance effects are present in a model, correlations are induced among the naive estimators of the mean effects. A simple normal quantile plot of the mean effects may be misleading because the mean effects are no longer iid under the null hypothesis that they are zero. Adjusted quantiles are computed for the case when one variance effect is significant and examples of 8-run and 16-run fractional factorial designs are examined in detail. We find that the usual normal quantiles are similar to adjusted quantiles for all but the largest and smallest ordered effects for which they are conservative. Graphically, the qualitative difference between the two sets of quantiles is negligible (even in the presence of large variance effects) and we conclude that normal probability plots are robust in the presence of variance effects.     

Finite nonparametric grach model for foreign exchange volatility

GARCH model has been commonly used to describe the volatility of foreign exchange returns, which typically depends on returns many lags before, While the GARCH model provides a simple geometric decaying structure for persistence in time, it restricts tiie impact of variables to Quadratic functions. A finite nonparametric GARCH model is proposed that allows the variables' impact to be a smooth function of any form. A direct local polynomial estimation method for this finite GARCH model is proposed based on results on proportional additive model, and is applied to the German Mark (DEM)/US Dollar (USD) daily returns data. Estimators uf both the decaying rate and the impact function are obtained. Diagnostics show satisfactory out-of-sampie prediction based on the proposed model, which helps to better understand the dynamics of foreign exchange volatility.     

Adapting by calibration the sample size of a phase III trial on the basis of phase II data

The problem of estimating the sample size for a phase III trial on the basis of existing phase II data is considered, where data from phase II cannot be combined with those of the new phase III trial. Focus is on the test for comparing the means of two independent samples. A launching criterion is adopted in order to evaluate the relevance of phase II results: phase III is run if the effect size estimate is higher than a threshold of clinical importance. The variability in sample size estimation is taken into consideration. Then, the frequentist conservative strategies with a fixed amount of conservativeness and Bayesian strategies are compared. A new conservative strategy is introduced and is based on the calibration of the optimal amount of conservativeness – calibrated optimal strategy (COS). To evaluate the results we compute the Overall Power (OP) of the different strategies, as well as the mean and the MSE of sample size estimators. Bayesian strategies have poor characteristics since they show a very high mean and/or MSE of sample size estimators. COS clearly performs better than the other conservative strategies. Indeed, the OP of COS is, on average, the closest to the desired level; it is also the highest. COS sample size is also the closest to the ideal phase III sample size M_I, showing averages and MSEs lower than those of the other strategies. Costs and experimental times are therefore considerably reduced and standardized. However, if the ideal sample size M_I is to be estimated the phase II sample size n should be around the ideal phase III sample size, i.e. n?2M_I/3. Copyright © 2010 John Wiley & Sons, Ltd.     

Comparison of estimators of the location parameter using pitman's closeness criterion

Necessary and sufficient conditions for a linear estimator to dominate another linear estimator of a location parameter under the Pitman's criterion of comparison are discussed. Consequently it is demonstrated that a linear biased estimator can not dominate a linear unbiased estimator under Pitman's criterion and that the sample mean is the Closest Linear Unbiased Estimator (CLUE). It is also shown that the ridge regression estimator with a known biasing constant can not dominate the ordinary least squares estimator. If an estimator δdominates an estimator δin the average loss sense then sufficient conditions are obtained under which δis also preferred over δunder Pitman's criterion. Further we obtain sufficient conditions under which preference under the Pitman's criterion will lead to preference under the mean squared error sense.     

浅析翻译主体的能动性和受动性

在翻译过程中，译者作为翻译的主体，在尊重翻译对象的前提下，必须突破客观受动因素的制约，充分发挥主观能动性。译者一方面要对这些客观制约因素有清楚的理解和认识，同时又要善于在客观中发挥主体性，在制约中发挥能动性，真正做到有思想、有创新，延续原作的生命，搭建文化沟通的桥梁。     

A Continuous Representation of the Family of Stable Law Distributions

Conventional parametric representations of stable law distributions do not allow all members of the family to be obtained as continuous limits of the parameters. Model building (or simulation) using such representations will be numerically unstable near such limits in consequence. Existing tables are not satisfactory near such limits as interpolation cannot be carried out. We show that these difficulties are overcome by using a new shifted Cartesian representation which characterizes the entire stable law family in a completely continuous way. Standardization is still possible with this representation so that tabulation, using just two bounded parameters, can be carried out. Its use is illustrated in a non-regular threshold estimation problem involving stable distributions which are discontinuous limits in conventional representations.     

Profile upper Confidence Limits from Discrete Data

When the data are discrete, standard approximate confidence limits often have coverage well below nominal for some parameter values. While ad hoc adjustments may largely solve this problem for particular cases, Kabaila & Lloyd (1997) gave a more systematic method of adjustment which leads to tight upper limits, which have coverage which is never below nominal and are as small as possible within a particular class. However, their computation for all but the simplest models is infeasible. This paper suggests modifying tight upper limits by an initial replacement of the unknown nuisance parameter vector by its profile maximum likelihood estimator. While the resulting limits no longer possess the optimal properties of tight limits exactly, the paper presents both numerical and theoretical evidence that the resulting coverage function is close to optimal. Moreover these profile upper limits are much (possibly many orders of magnitude) easier to compute than tight upper limits.     

应用AutoLISP对AutoCAD进行二次开发时的研究

AutoLISP语言是AutoCAD用户广泛使用的二次开发工具，本文结合笔者的开发体会，提出了在AutoLISP编程中需要注意的几个问题。     

正交优化法的软件设计及其应用

本文用BASIC语言编制了正交优化法软件，并通过实例对其应用进行探讨，研究结果表明：用正交优化法处理化学、环保等方面的非线性模型的参数估值和非线性回归问题是非常有效的。