基于FrFT和子空间正交的LFM信号参数估计

基于分数阶Fourier变换和子空间正交性,提出了一种低信噪比下线性调频信号检测与参数估计方法。讨论过程中将线性调频信号通过适当的分数阶Fourier变换得到一个单频复正弦信号,在此基础上,利用信号子空间与噪声子空间的正交性处理其正弦信号,再对线性调频信号的检测和参数估计转化为函数极值求解;最后,利用计算机模拟证实了方法的有效性。     

教育产出结构、资源配置与中国经济增长 ——基于中国区域样本的实证考察

 本文以经典的柯布—道格拉斯生产函数为切入点,同时考虑不同类型的教育体系（普通高等教育和职业技术教育）可能对人力资本有效供给的影响,重点考察教育产出 结构、技术进步水平、产业结构变化、生产性资本和科技经费投入的资源配置情况对经济增长的影响,并进行了实证分析,得出如下结论：普通高等教育和职业技术教育这两类人力资本供给对于经济增长的影响存在显著性差异,由于中国人力资本供给的相对过剩和国家对职业教育的投入力度不够,职业型人力资本供给的增长难以对经济增长起到促进作用。技术进步对中国经济增长的巨大推动作用增强了素质型人才的经济产出的影响力,普通高等教育的拓展对中国技术进步和经济增长能够产生积极影响,但由于影响力较弱,无法抵消劳动人力资本供给变化率的负向作用。因此从经济长期增长的角度出发,职业型人才的培养是必不可少的重要环节,在发展高等教育的同时,国家应该多投入一些资源用于职业教育的建设。     

线性GMDH参数模型的无偏估计研究

 多元线性回归分析中,参数无偏性是参数估计方法的一个重要指标。本文对线性GMDH参数模型建立多元线性模型进行了研究,得到以下结论：一,在满足经典线性回归模型的假设条件下,其参数估计量具有无偏的性质;二,在满足其它假设条件下,可以在样本量少于待估参数的情况下建模,估计的参数也是无偏的;三,用参数GMHD方法建模时,它对完全多重共线性是免疫的。     

Likelihood ratio tests for variance components in linear mixed models

Although the asymptotic distributions of the likelihood ratio for testing hypotheses of null variance components in linear mixed models derived by Stram and Lee [1994. Variance components testing in longitudinal mixed effects model. Biometrics 50, 1171–1177] are valid, their proof is based on the work of Self and Liang [1987. Asymptotic properties of maximum likelihood estimators and likelihood tests under nonstandard conditions. J. Amer. Statist. Assoc. 82, 605–610] which requires identically distributed random variables, an assumption not always valid in longitudinal data problems. We use the less restrictive results of Vu and Zhou [1997. Generalization of likelihood ratio tests under nonstandard conditions. Ann. Statist. 25, 897–916] to prove that the proposed mixture of chi-squared distributions is the actual asymptotic distribution of such likelihood ratios used as test statistics for null variance components in models with one or two random effects. We also consider a limited simulation study to evaluate the appropriateness of the asymptotic distribution of such likelihood ratios in moderately sized samples.     

Empirical Likelihood for Non-Smooth Criterion Functions

Abstract.  Suppose that X ₁ ,…,  X _n is a sequence of independent random vectors, identically distributed as a d -dimensional random vector X . Let     be a parameter of interest and     be some nuisance parameter. The unknown, true parameters ( μ ₀ , ν ₀ ) are uniquely determined by the system of equations E { g ( X , μ ₀ , ν ₀ )} =   0 , where g  =  ( g ₁ ,…, g _{p + q} ) is a vector of p + q functions. In this paper we develop an empirical likelihood (EL) method to do inference for the parameter μ ₀ . The results in this paper are valid under very mild conditions on the vector of criterion functions g . In particular, we do not require that g ₁ ,…, g _{p + q} are smooth in μ or ν . This offers the advantage that the criterion function may involve indicators, which are encountered when considering, e.g. differences of quantiles, copulas, ROC curves, to mention just a few examples. We prove the asymptotic limit of the empirical log-likelihood ratio, and carry out a small simulation study to test the performance of the proposed EL method for small samples.     

Sequential estimation of a location parameter from delayed observations

The problem of sequentially estimating a location parameter is considered in the special case when the data arrive at random times. Certain classes of sequential estimation procedures are derived under a location invariant loss function and with the observation cost determined by a function of the moment of stopping and the number of observations up to this moment.     

A new variable selection method for uniform designs

As an important class of space-filling designs, uniform designs (UDs) choose a set of points over a certain domain such that these points are uniformly scattered, under a specific discrepancy measure. They have been applied successfully in many industrial and scientific experiments since they appeared in 1980. A noteworthy and practical advantage is their ability to investigate a large number of high-level factors simultaneously with a fairly economical set of experimental runs. As a result, UDs can be properly used as experimental plans that are intended to derive the significant factors from a list of many potential ones. To this end, a new screening procedure is introduced via penalized least squares. A simulation study is conducted to support the proposed method, which reveals that it can be considered quite promising and expedient, as judged in terms of Type I and Type II error rates.     

A Statistical Test of Change‐Point in Mean that Almost Surely Has Zero Error Probabilities

In this paper we develop a non‐conventional statistical test for the change‐point in a mean model by making use of an almost‐sure (a.s.) convergence (or strong convergence) result that we obtain, in respect of the difference between the sums of squared residuals under the null and alternative hypotheses. We prove that both types of error probabilities of the new test converge to zero almost surely when the sample size goes to infinity. This result does not hold for any conventional statistical test where the type I error probability, i.e. the significance level or the size, is prescribed at a low but non‐zero level (e.g. 0.05). The test developed is easy to use in practice, and is ready to be generalised to other change‐point models provided that the relevant almost‐sure convergence results are available. We also provide a simulation study in the paper to compare the new and conventional tests under different data scenarios. The results obtained are consistent with our asymptotic study. In addition we provide least squares estimators of those parameters used in the change‐point test together with their almost‐sure convergence properties.     

Classification Rules under Autoregressive and General Circulant Covariance

We develop classification rules for data that have an autoregressive circulant covariance structure under the assumption of multivariate normality. We also develop classification rules assuming a general circulant covariance structure. The new classification rules are efficient in reducing the misclassification error rates when the number of observations is not large enough to estimate the unknown variance–covariance matrix. The proposed classification rules are demonstrated by simulation study for their validity and illustrated by a real data analysis for their use. Analyses of both simulated data and real data show the effectiveness of our new classification rules.