Premium rates based on genetic studies: How reliable are they?

Underwriting the risk of rare disorders in long-term insurance often relies on rates of onset estimated from quite small epidemiological studies. These estimates can have considerable sampling uncertainty and any function based upon them, such as a premium rate, is also an estimate subject to uncertainty. This is particularly relevant in the case of genetic disorders, because the acceptable use of genetic information may depend on establishing its reliability as a measure of risk. The sampling distribution of a premium rate is hard to estimate without access to the original data, which is rarely possible. From two studies of adult polycystic kidney disease (APKD) we obtain, not the original data, but the cases and exposures used for Kaplan-Meier estimates of the survival probability. We use three resampling methods with these data, namely: (a) the standard bootstrap; (b) the weird bootstrap; and (c) simulation of censored random lifetimes. Rates of onset were obtained from each simulated sample using kernel-smoothed Nelson-Aalen estimates, hence critical illness insurance premium rates for a mutation carrier or a member of an affected family. From 10,000 such samples we estimate the sampling distributions of the premium rates, finding considerable uncertainty. Very careful consideration should be given before using small-sample epidemiological data to deal with insurance problems.     

DIMENSION-REDUCTION TYPE TESTFOR LINEARITY OF ASTOCHASTIC REGRESSION MODEL

1.IntroductionLinearregressionmodelsarewidelyusedinstatisticalanalysisofexperimentalandobservationaldata,thatis,oneoftenemploysastandardlinearmodely=or K: E,a.s.,(1.1)todostatisticalanalysis,whereydenotesascalaroutcomevariableand2denotesaP-dimensionalcolumnvectorofregressorvariables.Thismodelmeansthattheprojectionofthepdimensionalexplanatory2ontotheone-dimensionalsubspaceadZcapturesalltheinformationweneedtoknowabouttheoutcomevariabley.Thisisadimension-reductionmodel.Hencewemayreachthegoalofd…     

删失场合半参数回归模型的二阶段估计

对于半参数回归模型ｙｉ＝ｘ′ｉβ＋ｇ（ｔｉ）＋ｅｉ，１≤ｉ≤ｎ，ｇ为Ｒ１上未知函数，β为ｐ×１维待估参数向量．本文考虑当ｙｉ被随机删失时β和ｇ的估计．基于模型的可加性，利用综合数据法得到β的二阶段估计β～＊ｎ和ｇ的估计ｇ＊ｎ，并证明了它们的强相合性．     

NA样本密度函数估计一致渐近正态性的收敛速度

在平稳NA样本下,讨论了未知密度函数估计的一致渐近正态性.在适当的条件下给出了该密度函数估计一致渐近正态性的收敛速度.这个速度几乎达到n^{-1/6}     

Kohn-Sham Density Matrix and the Kernel Energy MethodSCI北大核心CSCD

The kernel energy method(KEM) has been shown to provide fast and accurate molecular energy calculations for molecules at their equilibrium geometries.KEM breaks a molecule into smaller subsets,called kernels,for the purposes of calculation.The results from the kernels are summed according to an expression characteristic of KEM to obtain the full molecule energy.A generalization of the kernel expansion to density matrices provides the full molecule density matrix and orbitals.In this study,the kernel expansion for the density matrix is examined in the context of density functional theory(DFT) Kohn-Sham(KS) calculations.A kernel expansion for the one-body density matrix analogous to the kernel expansion for energy is defined,and is then converted into a normalizedprojector by using the Clinton algorithm.Such normalized projectors are factorizable into linear combination of atomic orbitals(LCAO) matrices that deliver full-molecule Kohn-Sham molecular orbitals in the atomic orbital basis.Both straightforward KEM energies and energies from a normalized,idempotent density matrix obtained from a density matrix kernel expansion to which the Clinton algorithm has been applied are compared to reference energies obtained from calculations on the full system without any kernel expansion.Calculations were performed both for a simple proof-of-concept system consisting of three atoms in a linear configuration and for a water cluster consisting of twelve water molecules.In the case of the proof-of-concept system,calculations were performed using the STO-3 G and6-31 G(d,p) bases over a range of atomic separations,some very far from equilibrium.The water cluster was calculated in the 6-31 G(d,p) basis at an equilibrium geometry.The normalized projector density energies are more accurate than the straightforward KEM energy results in nearly all cases.In the case of the water cluster,the energy of the normalized projector is approximately four times more accurate than the straightforward KEM energy result.The KS density matrices of this study are applicable to quantum crystallography.     

线性变换可对角化的几个等价条件

本文揭示了线性变换的象与核在研究线性变换对角化问题中的重要意义。给出了线性变换可对角化的几个等价条件     

矩阵化为标准形的一个定理的应用

本文探讨了化矩阵为标准形定理的一些应用。     

蓄水沟保墒蓄水效应和对仁用杏树生长与结果的影响

在丘陵旱坡地仁用杏园应用蓄水沟可明显减少地表径流和土壤侵蚀，增加和保持土壤水分。明显促进仁用杏树树高、地径、冠幅、新稍等生长指标，并明显增加仁用杏的产量和杏仁商品质量。该项技术投资少，易推广，是一项经济实用的保水增墒技术。     

New permutation statistics: Variation and a variant

For each permutation π we introduce the variation statistic of π, as the total number of elements on the right between each two adjacent elements of π. We modify this new statistic to get a slightly different variant, which behaves more closely like Mahonian statistics such as maj. In this paper we find an explicit formula for the generating function for the number of permutations of length n according to the variation statistic, and for that according to the modified version.