m阶积分算子及其应用

本文引人m阶积分算子，给出函数乘积u（x）．v（x）的m阶积分公式，此公式将函数乘积u(X)．v（x）的n阶导数的Leibniz公式推广到n为负整数情形，此公式同时也是函数f（x）的Taylor公式及Taylor级数的一种推广．     

一种多波形雷达信号全数字产生及处理系统

提出并实现了兼容多种雷达脉压信号的全数字产生及处理系统。其信号包括线性调频信号、非线性调频信号及其多相码、泰勒（Ｔａｙｌｏｒ）四相码信号等。利用级联型ＦＩＲ滤波器ＩＭＳＡ１００组成数字复相关脉压网络对多种带宽（带发达５ＭＨｚ）脉压信号进行实时数字处理；分析了数字方法运用于波形合成中由于ＤＡＣ零阶保持特性造成的信号频谱高频失真的机理；采用提高ＤＡＣ转换速率以获得近似理想冲激串取样的方法，产生了多种性能稳定、波形质量高的宽带雷达脉压信号。文中给出了部分模拟与实验结果。     

关于广义台劳公式的一个注记

本文讨论了广义台劳公式中所取中值的一个渐进性质。     

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.     

An approximation for analyzing a broad class of implicitly and explicitly defined estimators

An approximation is presented that can be used to gain insight into the characteristics – such as outlier sensitivity, bias, and variability – of a wide class of estimators, including maximum likelihood and least squares. The approximation relies on a convenient form for an arbitrary order Taylor expansion in a multivariate setting. The implicit function theorem can be used to construct the expansion when the estimator is not defined in closed form. We present several finite-sample and asymptotic properties of such Taylor expansions, which are useful in characterizing the difference between the estimator and the expansion.     

D-optimal designs for combined polynomial and trigonometric regression on a partial circle

Consider the D-optimal designs for a combined polynomial and trigonometric regression on a partial circle. It is shown that the optimal design is equally supported and the structure of the optimal design depends only on the length of the design interval and the support points are analytic functions of this parameter. Moreover, the Taylor expansion of the optimal support points can be determined efficiently by a recursive procedure. Examples are presented to illustrate the procedures for computing the optimal designs.     

The self as the locus of morality: A comparison between Charles Taylor and George Herbert Mead's theories of the moral constitution of the self

This paper provides a critical comparison of two leading exponents of the relationship between morality and selfhood: Charles Taylor and George Herbert Mead. Specifically, it seeks to provide an assessment of the contribution each approach is able to make to a social theory of morality that has the self at its heart. Ultimately, it is argued that Taylor's phenomenological account neglects the significance of interaction and social relations in his conceptualisation of the relationship between morality and self, which undermines the capacity of his framework to explain how moral understandings and dialogic moral subjectivity develop in a world of shared meaning. I then argue that Mead's pragmatist interactionist approach overcomes many of the flaws in Taylor's framework, and offers a grounded conceptualisation of the relationship between self and morality that is able to provide a basis for a properly social account of moral subjectivity.     

Design‐Based Inference in a Mixture Model for Ordinal Variables for a Two Stage Stratified Design

In this paper we present methods for inference on data selected by a complex sampling design for a class of statistical models for the analysis of ordinal variables. Specifically, assuming that the sampling scheme is not ignorable, we derive for the class of cub models (Combination of discrete Uniform and shifted Binomial distributions) variance estimates for a complex two stage stratified sample. Both Taylor linearization and repeated replication variance estimators are presented. We also provide design‐based test diagnostics and goodness‐of‐fit measures. We illustrate by means of real data analysis the differences between survey‐weighted and unweighted point estimates and inferences for cub model parameters.     

On the Mean Value Theorem for Estimating Functions

Abstract

Feng et al. revealed that the usual mean value theorem (MVT) should not be applied directly to a vector-valued function (e.g., the score function or a general estimating function under a multiparametric model). This note shows that the application of the Cramer–Wold’s device to a corrected version of the MVT is sufficient to obtain standard asymptotics for the estimators attained from vector-valued estimating functions.     

The S-system computation of non-central gamma distribution

The non-central gamma distribution can be regarded as a general form of non-central χ² distributions whose computations were thoroughly investigated (Ruben, H., 1974, Non-central chi-square and gamma revisited. Communications in Statistics, 3(7), 607–633; Knüsel, L., 1986, Computation of the chi-square and Poisson distribution. SIAM Journal on Scientific and Statistical Computing, 7, 1022–1036; Voit, E.O. and Rust, P.F., 1987, Noncentral chi-square distributions computed by S-system differential equations. Proceedings of the Statistical Computing Section, ASA, pp. 118–121; Rust, P.F. and Voit, E.O., 1990, Statistical densities, cumulatives, quantiles, and power obtained by S-systems differential equations. Journal of the American Statistical Association, 85, 572–578; Chattamvelli, R., 1994, Another derivation of two algorithms for the noncentral χ² and F distributions. Journal of Statistical Computation and Simulation, 49, 207–214; Johnson, N.J., Kotz, S. and Balakrishnan, N., 1995, Continuous Univariate Distributions, Vol. 2 (2nd edn) (New York: Wiley). Both distributional function forms are usually in terms of weighted infinite series of the central one. The ad hoc approximations to cumulative probabilities of non-central gamma were extended or discussed by Chattamvelli, Knüsel and Bablok (Knüsel, L. and Bablok, B., 1996, Computation of the noncentral gamma distribution. SIAM Journal on Scientific Computing, 17, 1224–1231), and Ruben (Ruben, H., 1974, Non-central chi-square and gamma revisited. Communications in Statistics, 3(7), 607–633). However, they did not implement and demonstrate proposed numerical procedures. Approximations to non-central densities and quantiles are not available. In addition, its S-system formulation has not been derived. Here, approximations to cumulative probabilities, density, and quantiles based on the method of Knüsel and Bablok are derived and implemented in R codes. Furthermore, two alternate S-system forms are recast on the basis of techniques of Savageau and Voit (Savageau, M.A. and Voit, E.O., 1987, Recasting nonlinear differential equations as S-systems: A canonical nonlinear form. Mathematical Biosciences, 87, 83–115) as well as Chen (Chen, Z.-Y., 2003, Computing the distribution of the squared sample multiple correlation coefficient with S-Systems. Communications in Statistics—Simulation and Computation, 32(3), 873–898.) and Chen and Chou (Chen, Z.-Y. and Chou, Y.-C., 2000, Computing the noncentral beta distribution with S-system. Computational Statistics and Data Analysis, 33, 343–360.). Statistical densities, cumulative probabilities, quantiles can be evaluated by only one numerical solver power low analysis and simulation (PLAS). With the newly derived S-systems of non-central gamma, the specialized non-central χ² distributions are demonstrated under five cases in the same three situations studied by Rust and Voit. Both numerical values in pairs are almost equal. Based on these, nine cases in three similar situations are designed for demonstration and evaluation. In addition, exact values in finite significant digits are provided for comparison. Demonstrations are conducted by R package and PLAS solver in the same PC system. By doing these, very accurate and consistent numerical results are obtained by three methods in two groups. On the other hand, these three methods are performed competitively with respect to speed of computation. Numerical advantages of S-systems over the ad hoc approximation and related properties are also discussed.