Monte carlo approximation to edgeworth expansions

Since the 1930s, empirical Edgeworth expansions have been employed to develop techniques for approximate, nonparametric statistical inference. The introduction of bootstrap methods has increased the potential usefulness of Edgeworth approximations. In particular, a recent paper by Lee & Young introduced a novel approach to approximating bootstrap distribution functions, using first an empirical Edgeworth expansion and then a more traditional bootstrap approximation to the remainder. In principle, either direct calculation or computer algebra could be used to compute the Edgeworth component, but both methods would often be difficult to implement in practice, not least because of the sheer algebraic complexity of a general Edgeworth expansion. In the present paper we show that a simple but nonstandard Monte Carlo technique is a competitive alternative. It exploits properties of Edgeworth expansions, in particular their parity and the degrees of their polynomial terms, to develop particularly accurate approximations.     

回归正交设计在苯二酚体系分光光度测定中的应用研究

本文以苯二酚体系的分光光度测定为基础，研究了回归的正交设计这一数理统计的优化试验设计方法，从实验上探讨了应用该法的最佳条件，为该法在多组分体系分光光度测定时更精确，更有效提供了依据。     

基于正交试验的雾化施液抛光工艺参数研究

为了研究雾化施液化学机械抛光工艺参数对抛光效果的影响,以抛光盘转速、抛光压力、雾化器电压、氧化剂质 量分数为因素,以材料去除率和表面粗糙度为评价指标设计正交试验,再对试验结果进行直观分析和权矩阵分析,得到 了各因素对试验结果的影响趋势和程度,并得到了最佳参数组合。结果表明：在雾化施液抛光过程中抛光效果随抛光盘 转速的增大而增大;随抛光压力的增大呈先增大后减小的趋势;随雾化器电压的增大而增大;随氧化剂质量分数的增大 而增大。且影响程度顺序由大到小为：氧化剂质量分数、抛光压力、雾化器电压、抛光盘转速。当抛光盘转速为60 r／ mm、抛光压力48 kPa、雾化器电压55 V、氧化剂质量分数为2.5%时,得到材料去除率和表面粗糙度均达到最佳,此时的 抛光效果最好。     

沉淀法羟基磷灰石超细粉体的正交实验设计及探讨

以Ca(NO3)2和(NH4)2HPO4为原料,采用沉淀法合成羟基磷灰石(HAP)粉体。采用正交实验设计讨论了反应物浓度、反应温度、分散剂聚乙二醇的添加量对羟基磷灰石粉体粒径的影响,并在此基础上考察了热处理温度对粉体粒径的影响。采用激光粒度仪测定粉体的粒径,并用XRD、IR等手段对粉体进行表征。实验结果表明,合成羟基磷灰石的最佳工艺条件:温度为60℃、浓度为0.8mol/L、分散剂聚乙二醇的添加量为3%。随热处理温度的升高,羟基磷灰石粉体颗粒长大并发生团聚。经XRD和IR测试结果分析表明,采用该方案可制备出纯度较高的羟基磷灰石超细粉体。     

CBN刀精车GCr15轴承钢的试验研究

本文利用正交试验法,通过用ＣＢＮ刀对ＧＣｒ１５轴承钢精车切削试验并对试验数据进行了多元线性处理,得出了在此切削条件下的切削用量三因素与刀具耐用度的Ｔａｙｌｏｒ公式,为解决难加工材料ＧＣｒ１５轴承钢的精车及实际生产提供了经验。     

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     

Generation of random matrices with orthonormal columns and multivariate normal wariates with given sample mean and covariance

In this paper, an algorithm for generating random matrices with orthonormal columns is introduced. As pointed out by a referee, the algorithm is almost identical to Wedderburn's (1975) unpublished method. The method can also be considered as an extension of Stewart's (1980) method, which was designed to generate random orthogonal matrices. It is found outperforming a simple extension of the QR factorization method and that of Heiberger's (1978) method. This paper also demonstrates how the algorithm can be used in generating multivariate normal variates with given sample mean and sample covariance matrix.     

A uniform saddlepoint expansion for the null‐distribution of the wilcoxon‐mann‐whitney statistic

The authors give the exact coefficient of 1/N in a saddlepoint approximation to the Wilcoxon‐Mann‐Whitney null‐distribution. This saddlepoint approximation is obtained from an Edgeworth approximation to the exponentially tilted distribution. Moreover, the rate of convergence of the relative error is uniformly of order O (1/N) in a large deviation interval as defined in Feller (1971). The proposed method for computing the coefficient of 1/N can be used to obtain the exact coefficients of 1/Nⁱ, for any i. The exact formulas for the cumulant generating function and the cumulants, needed for these results, are those of van Dantzig (1947‐1950).     

Central limit theorems for four new types of U-designs

Orthogonal array (OA)-based Latin hypercube designs, also called U-designs, have been popularly adopted in designing a computer experiment. Nested U-designs, sliced U-designs, strong OA-based U-designs and correlation controlled U-designs are four types of extensions of U-designs for different applications in computer experiments. Their elaborate multi-layer structure or multi-dimensional uniformity, which makes them desirable for different applications, brings difficulty in analysing the related statistical properties. In this paper, we derive central limit theorems for these four types of designs by introducing a newly constructed discrete function. It is shown that the means of the four samples generated from these four types of designs asymptotically follow the same normal distribution. These results are useful in assessing the confidence intervals of the gross mean. Two examples are presented to illustrate the closeness of the simulated density plots to the corresponding normal distributions.     

EXACT AND APPROXIMATED RELATIONS BETWEEN NEGATIVE HYPERGEOMETRIC AND NEGATIVE BINOMIAL PROBABILITIES

We derive orthogonal expansions in terms of the Meixner polynomials of the first kind for hypergeometric probabilities. We show how these expansions can be used to obtain negative binomial approximations to negative hypergeometric probabilities. Some limit properties of these approximations are studied and also the extension of these results to cumulative probabilities.