Improving density estimators of discretely observed processes by interpolation

We consider density estimation for a smooth stationary process _Xt$X_t$, t∈R$t\in \mathbf{R}$, based on a discrete sample _Yi=_XΔi$Y_i=X_{\mathrm{\Delta }i}$, i=0,…,n=T/Δ$i=0,\dots ,n=T/\Delta$. By a suitable interpolation scheme of order p  , we augment data to form an approximation _Xp,t$X_{p,t}$, t∈[0,T]$t\in [0,T]$, of the continuous-time process and base our density estimate on the augmented sample path. Our results show that this can improve the rate of convergence (measured in terms of n) of the density estimate. Among other things, this implies that recording n   observations using a small Δ$\Delta$ can be more efficient than recording n independent observations.     

中美抽样调查发展的比较与思考

 中美两国引入概率抽样调查的历史背景有相似之处,但在科学应用、普及推广和应用效果方面却存在巨大差距。造成差距的主要原因是：统计体制的差异、民族文化的不同、理论与实践结合程度的差异等。文章立足中国国情,深入分析了这些原因,对构建适合中国经济社会制度和文化的政府统计调查模式进行了比较深入的思考,提出的建议有助于实现政府统计的科学发展。     

Discrete distributions in the extended FGM family: The p.g.f. approach

In this article the probability generating functions of the extended Farlie–Gumbel–Morgenstern family for discrete distributions are derived. Using the probability generating function approach various properties are examined, the expressions for probabilities, moments, and the form of the conditional distributions are obtained. Bivariate version of the geometric and Poisson distributions are used as illustrative examples. Their covariance structure and estimation of parameters for a data set are briefly discussed. A new copula is also introduced.     

Network cohesion and social support

This article analyses the effects of personal network cohesion on different types of social support using two dimensions of cohesion: network closure (defined as a tightly knit set of actors around the ego) and cliquishness (defined as the extent to which an actor is connected with a number of cohesive sub-sets of alters). Data were obtained from a personal networks’ survey conducted in Catalonia (Spain), which was completed by 441 adults and gathered information about exchange of social support in networks made of 30 alters. A multilevel analysis disentangles the effects on support of these two structural dimensions at the network-level from compositional effects at the network and tie-level. The results show that network closure does not play a relevant role in support once confounders at the network and tie levels are controlled for. However, cliquishness has a significant association with labor-related support and housing support, net of statistical controls. Implications of these results in network research are discussed.     

Classification into two normal populations with a common mean and unequal variances

The problem of classification into two univariate normal populations with a common mean is considered. Several classification rules are proposed based on efficient estimators of the common mean. Detailed numerical comparisons of probabilities of misclassifications using these rules have been carried out. It is shown that the classification rule based on the Graybill-Deal estimator of the common mean performs the best. Classification rules are also proposed for the case when variances are assumed to be ordered. Comparison of these rules with the rule based on the Graybill-Deal estimator has been done with respect to individual probabilities of misclassification.     

Monitoring two-stage processes with a profile at the second stage

In the multistage processes, quality of a process or a product at each stage is related to the previous stage(s). This property is referred to as a cascade property. Sometimes, quality of a process is characterized by a profile. In this paper, we consider a two-stage process with a normal quality characteristic in the first stage and a simple linear regression profile in the second stage. Then we propose two methods to monitor quality characteristics in both stages. The performance of the proposed two methods is evaluated through a numerical example in terms of average run length criterion.     

Minimum local distance density estimation

We present a local density estimator based on first-order statistics. To estimate the density at a point, x, the original sample is divided into subsets and the average minimum sample distance to x over all such subsets is used to define the density estimate at x. The tuning parameter is thus the number of subsets instead of the typical bandwidth of kernel or histogram-based density estimators. The proposed method is similar to nearest-neighbor density estimators but it provides smoother estimates. We derive the asymptotic distribution of this minimum sample distance statistic to study globally optimal values for the number and size of the subsets. Simulations are used to illustrate and compare the convergence properties of the estimator. The results show that the method provides good estimates of a wide variety of densities without changes of the tuning parameter, and that it offers competitive convergence performance.     

不同密度处理对吉林省西部地区糜子光合作用的影响

本实验在高密度26万株/hm~2(D_1)、中密度22万株/hm~2(D_2)和低密度18万株/hm~2(D_3)三个密度处理下进行糜子栽培,并且测定了各个生长期内在不同密度处理下糜子的各项光合作用指标。对测定结果进行研究分析表明:栽培密度能够对糜子生育中、后期的叶面积(LAI)、光合速率(Pn)、气孔导度(Gs),蒸腾速率(Tr)等指标具有很大的影响,从而影响了糜子的光合作用能力。在该实验所设定的三个密度处理中,以中密度22万株/hm~2(D_2)处理下的糜子具有最大的光合作用能力。