Likelihood and higher-order approximations to tail areas: A review and annotated bibliography

Recent developments in higher-order asymptotic theory for statistical inference have emphasized the fundamental role of the likelihood function in providing accurate approximations to cumulative distribution functions. This paper summarizes the main results, with an emphasis on classes of problems for which relatively easily implemented solutions exist. A survey of the literature indicates the large number of problems solved and solvable by this method. Generalizations and extensions, with suggestions for further development, are considered.     

Quantifying Potential Health Impacts of Cadmium in Cigarettes on Smoker Risk of Lung Cancer: A Portfolio-of-Mechanisms Approach

This article introduces an approach to estimating the uncertain potential effects on lung cancer risk of removing a particular constituent, cadmium (Cd), from cigarette smoke, given the useful but incomplete scientific information available about its modes of action. The approach considers normal cell proliferation; DNA repair inhibition in normal cells affected by initiating events; proliferation, promotion, and progression of initiated cells; and death or sparing of initiated and malignant cells as they are further transformed to become fully tumorigenic. Rather than estimating unmeasured model parameters by curve fitting to epidemiological or animal experimental tumor data, we attempt rough estimates of parameters based on their biological interpretations and comparison to corresponding genetic polymorphism data. The resulting parameter estimates are admittedly uncertain and approximate, but they suggest a portfolio approach to estimating impacts of removing Cd that gives usefully robust conclusions. This approach views Cd as creating a portfolio of uncertain health impacts that can be expressed as biologically independent relative risk factors having clear mechanistic interpretations. Because Cd can act through many distinct biological mechanisms, it appears likely (subjective probability greater than 40%) that removing Cd from cigarette smoke would reduce smoker risks of lung cancer by at least 10%, although it is possible (consistent with what is known) that the true effect could be much larger or smaller. Conservative estimates and assumptions made in this calculation suggest that the true impact could be greater for some smokers. This conclusion appears to be robust to many scientific uncertainties about Cd and smoking effects.     

Confidence Intervals Based on Local Linear Smoother

Point-wise confidence intervals for a non-parametric regression function in conjunction with the popular local linear smoother are considered. The confidence intervals are based on the asymptotic normal distribution of the local linear smoother. Their coverage accuracy is evaluated by developing Edgeworth expansion for the coverage probability. It is found that the coverage error near the boundary of the support of the regression function is of a larger order than that in the interior, which implies that the local linear smoother is not adaptive to the boundary in terms of coverage. This is quite unexpected as the local linear smoother is adaptive to the boundary in terms of the mean squared error.     

农业科技成果转化为现实生产力的对策

根据目前影响我国农业技术成果迅速转化为现实生产力的因素,提出了加速农业技术成果转化的对策。     

A note on the joint distribution of correlated quadratic forms

In the present paper, the authors obtained exact and asymptotic expressions for the joint distribution of correlated quadratic forms when the underlying distribution is a multivariate normal.     

Edgeworth expansion and the bootstrap for stratified sampling without replacement from a finite population

An Edgeworth expansion for a linear combination of stratum means in stratified sampling without replacement from a finite population is derived. The expansion is applied to a bootstrap proposed for this context to show that the bootstrap captures the second-order term of the expansion.     

On the Advantage of Quantity Leadership When Outsourcing Production to a Competitive Contract Manufacturer

This study investigates a supply chain comprising an original equipment manufacturer (OEM) and a contract manufacturer (CM), in which the CM acts as both upstream partner and downstream competitor to the OEM. The two parties can engage in one of three Cournot competition games: a simultaneous game, a sequential game with the OEM as the Stackelberg leader, and a sequential game with the CM as the Stackelberg leader. On the basis of these three basic games, this study investigates the two parties' Stackelberg leadership/followership decisions. When the outsourcing quantity and wholesale price are exogenously given, either party may prefer Stackelberg leadership or followership. For example, when the wholesale price or the proportion of production outsourced to the CM is lower than a threshold value, both parties prefer Stackelberg leadership and, consequently, play a simultaneous game in the consumer market. When the outsourcing quantity and wholesale price are decision variables, the competitive CM sets a wholesale price sufficiently low to allow both parties to coexist in the market, and the OEM outsources its entire production to this CM. This study also examines the impact of the supply chain parties' bargaining power on contract outcomes by considering a wholesale price that is determined via the generalized Nash bargaining scheme, finding a Stackelberg equilibrium to be sustained when the CM's degree of bargaining power is great and the non‐competitive CM's wholesale price is high.     

《齐齐哈尔大学学报》（哲社版）2010—2011年载文量分析

以《学报》2010—2011年公开发行的12期为统计对象,运用文献计量学方法,对发文量等情况进行统计分析,揭示内在变化规律,为作者、读者提供有益的参考信息。     

Asymptotic Properties and Variance Estimators of the M-quantile Regression Coefficients Estimators

M-quantile regression is defined as a “quantile-like” generalization of robust regression based on influence functions. This article outlines asymptotic properties for the M-quantile regression coefficients estimators in the case of i.i.d. data with stochastic regressors, paying attention to adjustments due to the first-step scale estimation. A variance estimator of the M-quantile regression coefficients based on the sandwich approach is proposed. Empirical results show that this estimator appears to perform well under different simulated scenarios. The sandwich estimator is applied in the small area estimation context for the estimation of the mean squared error of an estimator for the small area means. The results obtained improve previous findings, especially in the case of heteroskedastic data.     

The Cornish-Fisher expansion for a class of statistics in first order autoregression

ABSTRACT

This article is concerned with the derivation and study of the Cornish-Fisher expansion for a wide class of estimators of the parameter in the first order autoregressive process. Second and third order Cornish-Fisher approximations to the quantile of the distribution of the corresponding asymptotically normal standardized statistic are stated explicitly and their accuracy is examined, both theoretically and numerically, by comparing them with the exact value of the quantile obtained by Monte Carlo simulation.