体育测量中误差分析及可靠性系数估计初探

一、问题的提出: 在体育实践活动的各种测最中(包括身体的各种素质、运动技能以及知觉性运动和动觉等测量),不管测量仪器多么精密,测量进行得多么精细,测量的结果总是不可避免地带有误差。为了保证测量结果的可靠性,我们有必要对测量中产生的误差进行分析,掌握误差的性质和出现的规律,以便采用不同的方法控制和处理。

正态分布两样本均数比较方法的评价

目的:对正态分布两样本均数比较常用的方法进行评价 ,为实际工作中统计方法的合理选择提供参考和依据。方法:采用 SAS软件编程 ,模拟方差齐或不齐、样本例数相等或不等、方差与例数顺向或反向等情况 ,分别采用 t检验、u检验、Satterthwaite法、Cochran- cox法及 Wilcoxon秩和检验进行检验 ,观察不同方法的 型误差估计值 (E )、 型误差估计值 (E )、检验效能以及检验效率。 结果:t检验较适用于方差齐两样本均数的比较 ;样本含量较大时可选用 u检验 ;Satterthwaite法、Cochran- cox法则无论方差齐否、样本含量大小均可适当选用。当两样本例数均较大时 ,5种方法的效能较接近。 结论 :在实际工作中 ,应选择较合理的统计分析方法。在总体分布不明确时 ,可以适当选择秩和检验。

两个大样本均数比较方法的评价

目的 对适用于两个大样本均数比较的t检验、u检验及u′检验评价。方法 用SAS软件编程模拟计算 ,以三种检验的Ⅰ型、Ⅱ型和 (Ⅰ型 +Ⅱ型 )误差作为评价指标。结果 给出在所有条件下的Ⅰ型、Ⅱ型误差估计值。结论 例数相等时 ,无论方差是否齐性 ,只要例数超过 5 0 ,三种方法较接近 ;例数不等时 ,当方差齐性时 ,选用t检验或u′检验比u检验更合适 ,当方差不齐时 ,选用u检验比t检验及u′检验更合适。

基于偏最小二乘回归的高精度同步时钟

为提高同步时钟的稳定性与精确度,提出了一种基于偏最小二乘回归(PLSR)的高精度同步时钟产生方法。该方法首先将卫星时钟和晶振时钟偏差方程的非线性关系转化为拟线性关系,然后对方程进行PLSR建模,得到晶振时钟误差估计值。当卫星时钟工作正常时,根据误差估计值修正晶振的频率,对晶振时钟的累计误差实时主动补偿,继而产生高精度同步时钟;当卫星时钟失效时,由晶振时钟参考失效前的误差估计值提供高精度同步时钟。仿真结果表明,该方法产生的同步时钟具备高精度、高稳定性的优点,在卫星时钟失效一段时间后仍可输出稳定性好的高精度时间同步信号。

SAS软件中k个相关样本的非参数检验方法的评价

目的 :对 SAS软件中处理 k个相关样本的非参数检验方法进行评价。方法 :利用 SAS软件中的过程经编程模拟计算 ,以 型、 型及 ( 型 + 型 )误差作为评价指标。结果 :给出所有模拟条件下的 型、 型及误差值。结论 :当处理组数 k=3时 ,Friedmanχ2 检验与 RF检验完全等价 ;当 k>3且配伍组数 b不太大时 ,若要控制 型误差应选 Friedm anχ2检验 ,若要控制 型或误差 ,应选 RF检验 ;当 b较大时 。

SAS软件中处理k个独立样本的非参数检验方法的评价

目的 对SAS软件中处理k个独立样本的非参数检验方法进行评价。方法 利用SAS软件中的过程经编程模拟计算 ,以检验方法的Ⅰ型、Ⅱ型及 (Ⅰ +Ⅱ )型误差作为评价指标。结果 给出所有模拟条件下的Ⅰ型、Ⅱ型误差估计值。结论 当样本例数较小时 ,如要控制Ⅰ型误差应选H检验 ,如要控制Ⅱ型误差应选RF检验 ;当样本例数较大时 ,RF与H检验基本相同。若要控制误差 ,无论样本例数多大 。

多个率的多重比较方法的选择

目的:对适用于多个率的多重比较方法进行评价和选择。方法:用SAS软件编程模拟计算,以条件及非条件情形下各种方法的Ⅰ型误差、Ⅱ型误差和误差(Ⅰ型+Ⅱ型)值作为评价和选择的指标。结果:给出在所有条件及非条件情形下的Ⅰ型、Ⅱ型误差估计值。结论:给出了控制Ⅰ型误差、Ⅱ型误差或误差3种不同情况下,多个实验组与对照组比较及多组间的两两比较方法的不同选择。

基于UKF的雷达和机载ESM扩维跟踪

为有效提高异类传感器融合跟踪的效果,提出了一种基于UKF的雷达和机载ESM扩维跟踪算法。首先将目标和机载ESM的状态信息组合起来,形成一个高维的状态向量,从而有效抑制滤波中GPS定位误差所带来的影响;接着在此基础上采用UKF来实现目标的定位跟踪,以求进一步减小扩维后线性化误差加大等问题的影响。仿真结果表明,该算法可更好地实现对目标的定位跟踪。

Anisotropic Interpolation Error Estimates of a Nonconforming Element

The main aim of this paper is to study the local anisotropic interpolation error estimates. We show that the interpolation of a nonconforming element satisfy the anisotropic property for both the second and fourth order problems.

A-Posteriori Error Estimation for the Legendre Spectral Galerkin Method in One-Dimension

In this paper, a-posteriori error estimators are proposed for the Legendre spectral Galerkin method for two-point boundary value problems. The key idea is to postprocess the Galerkin approximation, and the analysis shows that the postproeess improves the order of convergence. Consequently, we obtain asymptotically exact aposteriori error estimators based on the postprocessing results. Numerical examples are included to illustrate the theoretical analysis.

Error estimates of numerical methods for the nonlinear Dirac equation in the nonrelativistic limit regime

We present several numerical methods and establish their error estimates for the discretization of the nonlinear Dirac equation （NLDE） in the nonrelativistic limit regime, involving a small dimensionless parameter 0 〈 ε〈〈1 which is inversely proportional to the speed of light. In this limit regime, the solution is highly oscillatory in time, i.e., there are propagating waves with wavelength O（ ε^2） and O（1） in time and space, respectively. We begin with the conservative Crank-Nicolson finite difference （CNFD） method and establish rigorously its error estimate which depends explicitly on the mesh size h and time step τ- as well as the small parameter 0 〈 ε≤1 Based on the error bound, in order to obtain ＇correct＇ numerical solutions in the nonrelativistic limit regime, i.e., 0 〈 ε≤1 , the CNFD method requests the ε-scalability： τ- = O（ε3） and h = O（√ε）. Then we propose and analyze two numerical methods for the discretization of NLDE by using the Fourier spectral discretization for spatial derivatives combined with the exponential wave integrator and time- splitting technique for temporal derivatives, respectively. Rigorous error bounds for the two numerical methods show that their ε-scalability is improved to τ = O（ε2） and h = O（1） when 0 〈 ε 〈〈 1. Extensive numerical results are reported to confirm our error estimates.

Local a priori/a posteriori error estimates of conforming finite elements approximation for Steklov eigenvalue problems

Based on the work of Xu and Zhou(2000),this paper makes a further discussion on conforming finite elements approximation for Steklov eigenvalue problems,and proves a local a priori error estimate and a new local a posteriori error estimate in ||·||1,Ω0 norm for conforming elements eigenfunction,which has not been studied in existing literatures.

A posteriori error estimator for eigenvalue problems by mixed finite element method

In this paper,a residual type of a posteriori error estimator for the general second order elliptic eigenpair approximation by the mixed finite element method is derived and analyzed,based on a type of superconvergence result of the eigenfunction approximation.Its efficiency and reliability are proved by both theoretical analysis and numerical experiments.

ASYMPTOTIC NORMALITY OF SOME ESTIMATORS IN A FIXED-DESIGN SEMIPARAMETRIC REGRESSION MODEL WITH LINEAR TIME SERIES ERRORS

Consider a semiparametric regression model with linear time series errors Y_k= x′ _kβ + g(t_k) + ε_k, 1 ≤ k ≤ n, where Y_k's are responses, x_k =(x_(k1),x_(k2),···,x_(kp))′ and t_k ∈ T is contained in R are fixed design points, β =(β_1,β_2,···,β_p)′ is an unknown parameter vector, g(·) is an unknown bounded real-valuedfunction defined on a compact subset T of the real line R, and ε_k is a linear process given byε_k = ∑ from j=0 to ∞ of ψ_je_(k-j), ψ_0=1, where ∑ from j=0 to ∞ of |ψ_j| < ∞, and e_j,j=0, +-1, +-2,···, ard i.i.d. random variables. In this paper we establish the asymptoticnormality of the least squares estimator of β, a smooth estimator of g(·), and estimators of theautocovariance and autocorrelation functions of the linear process ε_k.

An adaptive time stepping method with efcient error control for second-order evolution problems

This work is concerned with time stepping finite element methods for abstract second order evolution problems. We derive optimal order a posteriori error estimates and a posteriori nodal superconvergence error estimates using the energy approach and the duality argument. With the help of the a posteriori error estimator developed in this work, we will further propose an adaptive time stepping strategy. A number of numerical experiments are performed to illustrate the reliability and efficiency of the a posteriori error estimates and to assess the effectiveness of the proposed adaptive time stepping method.

FINITE ELEMENT APPROXIMATION FOR A CLASS OF PARAMETER ESTIMATION PROBLEMS

This paper investigates the finite element approximation of a class of parameter estimation problems which is the form of performance as the optimal control problems governed by bilinear parabolic equations,where the state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions.The authors derive some a priori error estimates for both the control and state approximations.Finally,the numerical experiments verify the theoretical results.

A LEGENDRE GALERKIN SPECTRAL METHOD FOR OPTIMAL CONTROL PROBLEMS

This paper considers the Legendre Galerkin spectral approximation for the unconstralnea optimal control problems. The authors derive a posteriori error estimate for the spectral approximation scheme of optimal control problem. By choosing the appropriate basis functions, the stiff matrix of the discretization equations is sparse. And the authors use the Fast Legendre Transform to improve the efficiency of this method. Two numerical experiments demonstrating our theoretical results are presented.

A priori error estimates of finite volume element method for hyperbolic optimal control problems

In this paper,optimize-then-discretize,variational discretization and the finite volume method are applied to solve the distributed optimal control problems governed by a second order hyperbolic equation.A semi-discrete optimal system is obtained.We prove the existence and uniqueness of the solution to the semidiscrete optimal system and obtain the optimal order error estimates in L ∞(J;L 2)-and L ∞(J;H 1)-norm.Numerical experiments are presented to test these theoretical results.

Applications of the Kinetic Formulation for Scalar Conservation Laws with a Zero-Flux Type Boundary Condition

The authors are concerned with a zero-flux type initial boundary value problem for scalar conservation laws.Firstly,a kinetic formulation of entropy solutions is established.Secondly,by using the kinetic formulation and kinetic techniques,the uniqueness of entropy solutions is obtained.Finally,the parabolic approximation is studied and an error estimate of order η 1/3 between the entropy solution and the viscous approximate solutions is established by using kinetic techniques,where η is the size of artificial viscosity.

Randomly Weighted LAD-Estimation for Partially Linear Errors-in-Variables Models

The authors consider the partially linear model relating a response Y to predictors （x, T） with a mean function x^Tβ0 ＋ g（T） when the x＇s are measured with an additive error. The estimators of parameter β0 are derived by using the nearest neighbor-generalized randomly weighted least absolute deviation （LAD for short） method. The resulting estimator of the unknown vector 30 is shown to be consistent and asymptotically normal. In addition, the results facilitate the construction of confidence regions and the hypothesis testing for the unknown parameters. Extensive simulations are reported, showing that the proposed method works well in practical settings. The proposed methods are also applied to a data set from the study of an AIDS clinical trial group.