Note on the Cramér-Rao inequality in the nonregular case: the family of uniform distributions

We consider the family of uniform distributions with range of unit length. The main result of this note asserts that the average variance of any unbiased estimator of the midpoint of the range is not less than (2(n+1))(n+2))^-1 and this lower bound is sharp. The proof is based upon a nonregular version of the Cramér-Rao inequality.     

The interpretation of maximum-likelihood estimation

Maximum-likelihood estimation is interpreted as a procedure for generating approximate pivotal quantities, that is, functions u(X;θ) of the data X and parameter θ that have distributions not involving θ. Further, these pivotals should be efficient in the sense of reproducing approximately the likelihood function of θ based on X, and they should be approximately linear in θ. To this end the effect of replacing θ by a parameter ϕ = ϕ(θ) is examined. The relationship of maximum-likelihood estimation interpreted in this way to conditional inference is discussed. Examples illustrating this use of maximum-likelihood estimation on small samples are given.     

Estimation of the MSE matrix of the stein estimator

Uniformly minimum-variance unbiased (UMVU) estimators of the total risk and the mean-squared-error (MSE) matrix of the Stein estimator for the multivariate normal mean with unknown covariance matrix are proposed. The estimated MSE matrix is helpful in identifying the components which contribute most to the total risk. It also contains information about the performance of the shrinkage estimator with respect to other quadratic loss functions.     

On the distribution of quadratic forms in normal random variables

This paper provides necessary and sufficient conditions for a quadratic form in singular normal random variables to be distributed as a given linear combination of independent noncentral chi-square variables. Using this result, an extension of Cochran's theorem to quadratic forms of noncentral chi-square variables is derived.     

Accurate ARL computation for EWMA-S<Superscript>2</Superscript> control charts

Originally, the exponentially weighted moving average (EWMA) control chart was developed for detecting changes in the process mean. The average run length (ARL) became the most popular performance measure for schemes with this objective. When monitoring the mean of independent and normally distributed observations the ARL can be determined with high precision. Nowadays, EWMA control charts are also used for monitoring the variance. Charts based on the sample variance S² are an appropriate choice. The usage of ARL evaluation techniques known from mean monitoring charts, however, is difficult. The most accurate method—solving a Fredholm integral equation with the Nyström method—fails due to an improper kernel in the case of chi-squared distributions. Here, we exploit the collocation method and the product Nyström method. These methods are compared to Markov chain based approaches. We see that collocation leads to higher accuracy than currently established methods.     

Multiparameter estimation of discrete exponential distributions

Let X₁, …, X_p be independent random variables, all having the same distribution up to a possibly varying unspecified parameter, where each of the p distributions belongs to the family of one parameter discrete exponential distributions. The problem is to estimate the unknown parameters simultaneously. Hudson (1978) shows that the minimum variance unbiased estimator (MVUE) of the parameters is inadmissible under squared error loss, and estimators better than the MVUE are proposed. Essentially, these estimators shrink the MVUE towards the origin. In this paper, we indicate that estimators shifting the MVUE towards a point different from the origin or a point determined by the observations can be obtained.     

中小板ETF的价格发现能力研究

使用日内5分钟交易高频数据,通过误差修正模型和方差分解等技术研究中小板ETF与其标的指数间的价格发现,进而探讨信息传递过程。实证结果显示：中小板ETF价格与中小板P指数间存在协整关系,达到了长期均衡;价格发现能力上,中小板P指数领先中小板ETF;中小板P指数受到新信息影响所产生的冲击大于中小板ETF价格所产生的冲击,中小板P指数对预测误差方差的解释能力强于中小板ETF价格,中小板P指数为信息传递的领先指标。我国ETF市场的有效性有待提升。     

中国林业科技进步贡献率的要素分解及测算研究——基于2002—2011年31个省(市、自治区)的统计数据

中国林业经济增长受到传统资本、劳动和林地面积等投入要素的影响之外,林业科技进步因素的作用越来越重要。将广义林业科技进步细分为狭义林业科技进步,采用中国31个省(市、自治区)林业相关面板统计数据,运用扩展的C-D生产函数结合索洛余值法,测算中国狭义林业科技进步贡献率。研究结果表明:2003—2011年连续9年,狭义林业科技进步、林业固定资产投资、林业从业人员、林地面积、林业人力资本累积效应及林业产业结构变动因素对中国林业经济增长的平均贡献率分别为15.34%、61.47%、2.79%、10.77%、9.14%、0.49%。基于上述分析,提出进一步提升中国林业科技贡献率的具体对策建议。     

LMDI方法分析结构效应对天津市碳排放的影响及对策

文章对1995—2010年天津市能源消费碳排放进行分析,基于对数平均迪氏指数法（ LMDI）,对碳排放进行因素分解实证研究,并进行情景分析,寻求天津市碳减排对策。研究发现,虽然人均GDP效应、人口效应以及能源强度效应贡献量相对较大,但结构效应对于天津碳排放的影响也不容忽视,其对于能源消费碳排放的拉动或减缓作用与低碳能源比重、第三产业比重的大小有很强的关联性。情景分析进一步表明优化产业及能源结构对碳减排的积极作用。     

重庆市规模以上工业企业能耗的结构性分析

针对已有相关研究中地域针对性较弱的现状,以及工业节能在重庆节能减排工作中的重要地位,基于2004—2011年统计年鉴中重庆市规模以上工业企业产值能耗和增加值能耗的相关数据,采用“单位GDP能耗因素的数学分解方法”进行数据分析,将工业节能总量分解为一级结构节能量、二级结构节能量以及技术节能量,并讨论各因素的变动趋势和对节能总量的贡献程度,得到关于影响能耗变动的决定性因素的结论：首先是技术因素,其次是二级结构因素。同时,经过纵向比较,发现重庆工业技术性节能进入瓶颈的问题,并针对这一问题提出建议。