Approximation of the Bivariate Renewal Function

Recently, Kambo and his co-researchers (2012) proposed a method of approximation for evaluating the one-dimensional renewal function based on the first three moments. Their method is simple and elegant, which gives exact values for well-known distributions. In this article, we propose an analogous method for the evaluation of bivariate renewal function based on the first two moments of the variables and their joint moment. The proposed method yields exact results for certain widely used bivariate distributions like bivariate exponential distribution, bivariate Weibull distributions, and bivariate Pareto distributions. An illustrative example in the form of a two-dimensional warranty problem is considered and comparisons of our method are made with the results of other models.     

Towards Uniformly Efficient Trend Estimation Under Weak/Strong Correlation and Non‐stationary Volatility

In this paper, we consider the deterministic trend model where the error process is allowed to be weakly or strongly correlated and subject to non‐stationary volatility. Extant estimators of the trend coefficient are analysed. We find that under heteroskedasticity, the Cochrane–Orcutt‐type estimator (with some initial condition) could be less efficient than Ordinary Least Squares (OLS) when the process is highly persistent, whereas it is asymptotically equivalent to OLS when the process is less persistent. An efficient non‐parametrically weighted Cochrane–Orcutt‐type estimator is then proposed. The efficiency is uniform over weak or strong serial correlation and non‐stationary volatility of unknown form. The feasible estimator relies on non‐parametric estimation of the volatility function, and the asymptotic theory is provided. We use the data‐dependent smoothing bandwidth that can automatically adjust for the strength of non‐stationarity in volatilities. The implementation does not require pretesting persistence of the process or specification of non‐stationary volatility. Finite‐sample evaluation via simulations and an empirical application demonstrates the good performance of proposed estimators.     

Efficient Estimation in Heteroscedastic Partially Linear Varying Coefficient Models

This article considers statistical inference for the heteroscedastic partially linear varying coefficient models. We construct an efficient estimator for the parametric component by applying the weighted profile least-squares approach, and show that it is semiparametrically efficient in the sense that the inverse of the asymptotic variance of the estimator reaches the semiparametric efficiency bound. Simulation studies are conducted to illustrate the performance of the proposed method.     

Interval estimation for conformance proportions of multiple quality characteristics

A conformance proportion is an important and useful index to assess industrial quality improvement. Statistical confidence limits for a conformance proportion are usually required not only to perform statistical significance tests, but also to provide useful information for determining practical significance. In this article, we propose approaches for constructing statistical confidence limits for a conformance proportion of multiple quality characteristics. Under the assumption that the variables of interest are distributed with a multivariate normal distribution, we develop an approach based on the concept of a fiducial generalized pivotal quantity (FGPQ). Without any distribution assumption on the variables, we apply some confidence interval construction methods for the conformance proportion by treating it as the probability of a success in a binomial distribution. The performance of the proposed methods is evaluated through detailed simulation studies. The results reveal that the simulated coverage probability (cp) for the FGPQ-based method is generally larger than the claimed value. On the other hand, one of the binomial distribution-based methods, that is, the standard method suggested in classical textbooks, appears to have smaller simulated cps than the nominal level. Two alternatives to the standard method are found to maintain their simulated cps sufficiently close to the claimed level, and hence their performances are judged to be satisfactory. In addition, three examples are given to illustrate the application of the proposed methods.     

雄安新区科技企业创新能力评价研究

科技企业是实现科技创新的驱动者和科技成果转化的重要载体,也是推动研究开发的重要参与者,科学评价科技企业创新能力有助于企业自身不断发展壮大。在分析国内外新区科技企业创新驱动发展相关理论研究的基础上,从研发投入、研发基础、研发效益和现代科技四个角度,运用层次分析法构建科技企业创新能力评价系统,并通过实证分析说明评价系统的可靠性;根据评价系统测算出现阶段雄安新区科技企业创新能力,通过与成熟新区科技企业的比较,发现其短板和不足,力图为决策者科学合理评价、管理科技企业创新发展提供有益参考。     

Modeling spatial overdispersion via the generalized Waring point process

Modeling spatial overdispersion requires point process models with finite‐dimensional distributions that are overdisperse relative to the Poisson distribution. Fitting such models usually heavily relies on the properties of stationarity, ergodicity, and orderliness. In addition, although processes based on negative binomial finite‐dimensional distributions have been widely considered, they typically fail to simultaneously satisfy the three required properties for fitting. Indeed, it has been conjectured by Diggle and Milne that no negative binomial model can satisfy all three properties. In light of this, we change perspective and construct a new process based on a different overdisperse count model, namely, the generalized Waring (GW) distribution. While comparably tractable and flexible to negative binomial processes, the GW process is shown to possess all required properties and additionally span the negative binomial and Poisson processes as limiting cases. In this sense, the GW process provides an approximate resolution to the conundrum highlighted by Diggle and Milne.