A variant of K nearest neighbor quantile regression

Compared with local polynomial quantile regression, K nearest neighbor quantile regression (KNNQR) has many advantages, such as not assuming smoothness of functions. The paper summarizes the research of KNNQR and has carried out further research on the selection of k, algorithm and Monte Carlo simulations. Additionally, simulated functions are Blocks, Bumps, HeaviSine and Doppler, which stand for jumping, volatility, mutagenicity slope and high frequency function. When function to be estimated has some jump points or catastrophe points, KNNQR is superior to local linear quantile regression in the sense of the mean squared error and mean absolute error criteria. To be mentioned, even high frequency, the superiority of KNNQR could be observed. A real data is analyzed as an illustration.     

Saddlepoint approximations to tail expectations under non-Gaussian base distributions: option pricing applications

The saddlepoint approximation formulas provide versatile tools for analytic approximation of the tail expectation of a random variable by approximating the complex Laplace integral of the tail expectation expressed in terms of the cumulant generating function of the random variable. We generalize the saddlepoint approximation formulas for calculating tail expectations from the usual Gaussian base distribution to an arbitrary base distribution. Specific discussion is presented on the criteria of choosing the base distribution that fits better the underlying distribution. Numerical performance and comparison of accuracy are made among different saddlepoint approximation formulas. Improved accuracy of the saddlepoint approximations to tail expectations is revealed when proper base distributions are chosen. We also demonstrate enhanced accuracy of the generalized saddlepoint approximation formulas under non-Gaussian base distributions in pricing European options on continuous integrated variance under the Heston stochastic volatility model.     

关于多元Ismail-May算子的一致逼近

主要讨论了多元Ismail—May算子的一致逼近问题，利用多元分解技巧和已有的一元结论给出了多元Ismail—May算子逼近阶的估计和特征刻划．     

Optimal testing and repairing a failed series system

We consider a series repairable system that includes n components and assume that it has just failed because exactly one of its components has failed. The failed component is unknown. Probability of each component to be responsible for the failure is given. Each component can be tested and repaired at given costs. Both testing and repairing operations are assumed to be perfect, that is, the result of testing a component is a true information that this component is failed or active (not failed), and the result of repairing is that the component becomes active. The problem is to find a sequence of testing and repairing operations over the components such that the system is always repaired and the total expected cost of testing and repairing the components is minimized. We show that this problem is equivalent to minimizing a quadratic pseudo-boolean function. Polynomially solvable special cases of the latter problem are identified and a fully polynomial time approximation scheme (FPTAS) is derived for the general case. Computer experiments are provided to demonstrate high efficiency of the proposed FPTAS. In particular, it is able to find a solution with relative error ɛ = 0.1 for problems with more than 4000 components within 5 minutes on a standard PC with 1.2 Mhz processor.     

一类正交多项式的两种并行算法

通过修正计算Chebyshev多项式的Forsythe算法和Clenshaw算法 ,提出了求解一类正交多项式的两种并行算法 ,并对其稳定性进行了分析 .     

单个守恒律Riemann问题近似解的边界层分析

使用折线逼近法构造了单个守恒律Riemann问题的近似解,给出了近似解的边界层误差估计.     

LOCAL POLYNOMIAL QUASI-LIKELIHOOD REGRESSION ON RANDOM FIELDS

In this paper, local quasi‐likelihood regression is considered for stationary random fields of dependent variables. In the case of independent data, local polynomial quasi‐likelihood regression is known to have several appealing features such as minimax efficiency, design adaptivity and good boundary behaviour. These properties are shown to carry over to the case of random fields. The asymptotic normality of the regression estimator is established and explicit formulae for its asymptotic bias and variance are derived for strongly mixing stationary random fields. The extension to multi‐dimensional covariates is also provided in full generality. Moreover, evaluation of the finite sample performance is made through a simulation study.     

重尾分布信源的排队等待时间的分析方法

介绍了一种变换近似方法,该方法通过变换近似获得重尾分布的拉普拉斯变换,解决了不存在拉普拉斯变换分布的信源排队等待时间分析问题,为实际网络排队缓冲器的设计提供了参考。     

The Jackknife applied to incomplete blood sampling models

A nonparametric alternative to the extended parametric Satterthwaite method taking into account the correlation between samples obtained from the same animal is presented. Confidence intervals are computed using a modified jackknife standard error. The performance of the method is studied by means of simulation. This nonparametric method has a smaller coverage rate than the parametric one, but still close to the nominal confidence level. In addition, its confidence interval is shorter than that of the parametric method using the generalized Satterthwaite approximation. Copyright © 2003 John Wiley & Sons, Ltd.     

Truncated Sequential Change-point Detection based on Renewal Counting Processes

The typical approach in change-point theory is to perform the statistical analysis based on a sample of fixed size. Alternatively, one observes some random phenomenon sequentially and takes action as soon as one observes some statistically significant deviation from the "normal" behaviour. Based on the, perhaps, more realistic situation that the process can only be partially observed, we consider the counting process related to the original process observed at equidistant time points, after which action is taken or not depending on the number of observations between those time points. In order for the procedure to stop also when everything is in order, we introduce a fixed time horizon n at which we stop declaring "no change" if the observed data did not suggest any action until then. We propose some stopping rules and consider their asymptotics under the null hypothesis as well as under alternatives. The main basis for the proofs are strong invariance principles for renewal processes and extreme value asymptotics for Gaussian processes.