Confidence Bounds and Hypothesis Tests for Normal Distribution Coefficients of Variation

For normally distributed populations, we obtain confidence bounds on a ratio of two coefficients of variation, provide a test for the equality of k coefficients of variation, and provide confidence bounds on a coefficient of variation shared by k populations.     

On the non-existence of generalised Hadamard matrices

The determinant of a generalized Hadamard matrix over its group ring factored out by the relation Σ_gεG G = 0 is shown to have certain number theoretic properties. These are exploited to prove the non-existence of many generalised Hadamard matrices for groups whose orders are divisible by 3, 5 or 7. For example the GH(15, C₁₅), GH(15, C₃) and GH(15, C₅) do not exist. Also for certain n and G we find the set of determinants of the GH(n, G) matrices.     

A change point method for Phase II monitoring of generalized linear profiles

In this article, we adopt the change point approach to monitor the generalized linear profiles in phase II Statistical process control (SPC). Generalized linear profiles include a large class of profiles defined in one framework. In contrast to the conventional change point approach, we adopt the Rao score test rather than the likelihood ratio test. Simulated results show that our approach has a good performance over any possible single step change in process parameters for two special cases of generalized linear profiles, namely Poisson and binomial profiles. Some diagnostic aids are also given and a real example is introduced to shed light on the merits of our approach in real applications.     

《古赋辩体》之后的元朝赋论

《古赋辩体》之后的元朝赋论大都深受祝尧"祖骚宗汉"复古思想的影响,不过他们对祝尧所论也多有补益,有的对其未曾涉及的领域有所论述,有的对其偏颇与矛盾之处有所更正,有的还扩大了学习古赋的范围。虽然这些赋论由于缺乏系统性,历来关注较少,但对于元后期辞赋的复古思潮却起了推波助澜的作用,具有独特的价值,可视为对祝尧赋论的补充。     

An efficient algorithm for estimating the parameters of superimposed exponential signals

An efficient computational algorithm is proposed for estimating the parameters of undamped exponential signals, when the parameters are complex valued. Such data arise in several areas of applications including telecommunications, radio location of objects, seismic signal processing and computer assisted medical diagnostics. It is observed that the proposed estimators are consistent and the dispersion matrix of these estimators is asymptotically the same as that of the least squares estimators. Moreover, the asymptotic variances of the proposed estimators attain the Cramer–Rao lower bounds, when the errors are Gaussian.     

Flat and Multimodal Likelihoods and Model Lack of Fit in Curved Exponential Families

Abstract. It is well known that curved exponential families can have multimodal likelihoods. We investigate the relationship between flat or multimodal likelihoods and model lack of fit, the latter measured by the score (Rao) test statistic W _U of the curved model as embedded in the corresponding full model. When data yield a locally flat or convex likelihood (root of multiplicity >1, terrace point, saddle point, local minimum), we provide a formula for W _U in such points, or a lower bound for it. The formula is related to the statistical curvature of the model, and it depends on the amount of Fisher information. We use three models as examples, including the Behrens–Fisher model, to see how a flat likelihood, etc. by itself can indicate a bad fit of the model. The results are related (dual) to classical results by Efron from 1978.     

Regular group divisible designs and Bhaskar Rao designs with block size three

Some recursive constructions are given for Bhaskar Rao designs. Using examples of these designs found by Shyam J. Singh, Rakesh Vyas and new ones given here we show the necessary conditions λ≡0 (mod 2), λυ(υ?1)≡0 (mod 24) are sufficient for the existence of Bhaskar Rao designs with one association class and block size 3. This result is used with a result of Street and Rodger to obtain regular partially balanced block designs with 2υ treatments, block size 3, λ₁=0, group size 2 and υ groups.     

关于闽南语皮（纸）影戏本的研究——读《欧洲汉学研究会不定期刊》第2辑

<欧洲汉学研究会不定期刊>(Occasional Pagers,European Association of Chinese Studies)第2辑(1979),收入了施博尔(施舟人)、饶宗颐、龙彼得三教授研究闽南语皮(纸)影戏本的学术经典之作.施博尔(施舟人)、饶宗颐、龙彼得三教授的参与,提升了闽南语皮(纸)影戏本之研究的学术水准,海峡两岸学者当继续戮力推展此一高水准的学术研究工作.     

Measuring technological breadth and depth of patent documents using Rao’s Quadratic Entropy

ABSTRACT

In this article we propose indices for technological breadth and depth of patent documents. We conceptually compare and contrast several indices that have been used in the existing literature, explaining main limitations. Motivated by the drawbacks of those we demonstrate how Rao’s Quadratic Entropy, a statistical index used in ecology for measuring biodiversity, can be decomposed to separately measure technological breadth and depth. The properties of breadth and depth are then investigated using patents for business data processing. For the technological domains with the highest patenting activity, we show how the novel measures of technological breadth and depth can be used to rank the patenting entities by average breadth, and identify ones with inventions that on average exceed the domain-specific average depth. Practical implications of the proposed indices are also exemplified and discussed in the context of competitor analysis for entrepreneurial ventures in the area of network security for business data processing.