STRONG APPROXIMATION FOR PERTURBED EMPIRICAL PROCESSES

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Profile Statistical Inference for Partially Linear Additive Models with a Diverging Number of Parameters

This paper considers partially linear additive models with the number of parameters diverging when some linear constraints on the parametric part are available. This paper proposes a constrained profile least-squares estimation for the parametric components with the nonparametric functions being estimated by basis function approximations. The consistency and asymptotic normality of the restricted estimator are given under some certain conditions. The authors construct a profile likelihood ratio test statistic to test the validity of the linear constraints on the parametric components,and demonstrate that it follows asymptotically chi-squared distribution under the null and alternative hypotheses. The finite sample performance of the proposed method is illustrated by simulation studies and a data analysis.     

LIMIT THEOREMS AND OPTIMAL DESIGN WITH ADAPTIVE URN MODELS

In this paper we study urn model, using some available estimates of successes probabilities, and adding particle parameter, we establish adaptive models. We obtain some strong convergence theorems, rates of convergence, asymptotic normality of components in the urn, and estimates. With these asymptotical results, we show that the adaptive designs given in this paper are asymptotically optimal designs.     

ON ASYMPTOTIC NORMALITY OF PARAMETERS IN MULTIPLE LINEAR ERRORS－IN－VARIABLES MODEL

This paper studies the parameter estimation of multiple dimensional linear errors-in-variables (EV) models in the case where replicated observations are available in some experimental points. Asymptotic normality is established under mild conditions, and the parameters entering the asymptotic variance are consistently estimated to render the result useable in the construction of large-sample confidence regions.     

Detecting Change-Point via Saddlepoint Approximations

It's well-known that change-point problem is an important part of model statistical analysis. Most of the existing methods are not robust to criteria of the evaluation of change-point problem.In this article, we consider "mean-shift" problem in change-point studies. A quantile test of single quantile is proposed based on saddlepoint approximation method. In order to utilize the information at different quantile of the sequence, we further construct a "composite quantile test" to calculate the probability of every location of the sequence to be a change-point. The location of change-point can be pinpointed rather than estimated within a interval. The proposed tests make no assumptions about the functional forms of the sequence distribution and work sensitively on both large and small size samples,the case of change-point in the tails, and multiple change-points situation. The good performances of the tests are confirmed by simulations and real data analysis. The saddlepoint approximation based distribution of the test statistic that is developed in the paper is of independent interest and appealing.This finding may be of independent interest to the readers in this research area.     

CVaR的鞍点解析式及其在CreditRisk+框架下的应用

CVaR是满足一致性的风险度量指标,它测度了超出VaR部分的条件期望.本文在Daniels(1987)基础上,独立导出CVaR的鞍点解析式.利用真实CVaR值已知的伽玛分布和贝塔分布做检验,结果表明CVaR鞍点解析式是CVaR的稳健近似.此外,本文还探索了该方法在风险管理中的应用,所推出的解析式可应用于CreditRisk 框架下损失分布CVaR的计算.     

粗糙近似算子的拓扑性质

通过闭包与内部算子研究模糊粗糙集的拓扑结构,证明了自反、传递关系下的近似空间中模糊集的上、下近似算子分别为一个模糊拓扑的闭包、内部算子,且相应的模糊拓扑满足(TC)条件;反之,满足(TC)条件的模糊拓扑的闭包与内部算子也恰为一自反、传递关系下的近似空间中的上、下近似算子.     

A NEW TEST FOR NORMALITY IN LINEAR AUTOREGRESSIVE MODELS

A nonparametric test for normality of linear autoregressive time series is proposed in this paper. The test is based on the best one-step forecast in mean square with time reverse. Some asymptotic theory is developed for the test, and it is shown that the test is easy to use and has good powers. The empirical percentage points to conduct the test in practice are provided and three examples using real data are included.     

A NEW TEST PROCEDURE FOR NEW BETTER THAN USED IN INCREASING CONVEX ORDERING

A new nonparametric procedure is developed to test the exponentiality against the strict NBUC property of a life distribution. The exact null distribution is derived by the theory of sample spacings, and the asymptotic normality is also established by the large sample theory of L-statistics. Finally, the lower and upper tailed probability of the exact null distribution and some numerical simulation results are presented as well.     

Rough function model and rough membership function

Two pairs of approximation operators, which are the scale lower and upper approximations as well as the real line lower and upper approximations, are defined. Their properties and antithesis characteristics are analyzed. The rough function model is generalized based on rough set theory, and the scheme of rough function theory is made more distinct and complete. Therefore, the transformation of the real function analysis from real line to scale is achieved. A series of basic concepts in rough function model including rough numbers, rough intervals, and rough membership functions are defined in the new scheme of the rough function model. Operating properties of rough intervals similar to rough sets are obtained. The relationship of rough inclusion and rough equality of rough intervals is defined by two kinds of tools, known as the lower （upper） approximation operator in real numbers domain and rough membership functions. Their relative properties are analyzed and proved strictly, which provides necessary theoretical foundation and technical support for the further discussion of properties and practical application of the rough function model.     

Approximate conditional likelihood for generalized linear models with general missing data mechanism

The generalized linear model is an indispensable tool for analyzing non-Gaussian response data, with both canonical and non-canonical link functions comprehensively used. When missing values are present, many existing methods in the literature heavily depend on an unverifiable assumption of the missing data mechanism, and they fail when the assumption is violated. This paper proposes a missing data mechanism that is as generally applicable as possible, which includes both ignorable and nonignorable missing data cases, as well as both scenarios of missing values in response and covariate. Under this general missing data mechanism, the authors adopt an approximate conditional likelihood method to estimate unknown parameters. The authors rigorously establish the regularity conditions under which the unknown parameters are identifiable under the approximate conditional likelihood approach. For parameters that are identifiable, the authors prove the asymptotic normality of the estimators obtained by maximizing the approximate conditional likelihood. Some simulation studies are conducted to evaluate finite sample performance of the proposed estimators as well as estimators from some existing methods. Finally, the authors present a biomarker analysis in prostate cancer study to illustrate the proposed method.     

Generalized F-test for high dimensional regression coefficients of partially linear models

This paper proposes a test procedure for testing the regression coefficients in high dimensional partially linear models based on the F-statistic. In the partially linear model, the authors first estimate the unknown nonlinear component by some nonparametric methods and then generalize the F-statistic to test the regression coefficients under some regular conditions. During this procedure, the estimation of the nonlinear component brings much challenge to explore the properties of generalized F-test. The authors obtain some asymptotic properties of the generalized F-test in more general cases,including the asymptotic normality and the power of this test with p/n ∈(0, 1) without normality assumption. The asymptotic result is general and by adding some constraint conditions we can obtain the similar conclusions in high dimensional linear models. Through simulation studies, the authors demonstrate good finite-sample performance of the proposed test in comparison with the theoretical results. The practical utility of our method is illustrated by a real data example.     

Degree-based moment estimation for ordered networks

The edges between vertices in networks take not only the common binary values, but also the ordered values in some situations (e.g., the measurement of the relationship between people from worst to best in social networks). In this paper, the authors study the asymptotic property of the moment estimator based on the degrees of vertices in ordered networks whose edges are ordered random variables. In particular, the authors establish the uniform consistency and the asymptotic normality of the moment estimator when the number of parameters goes to infinity. Simulations and a real data example are provided to illustrate asymptotic results.     

Asymptotic Properties of Maximum Quasi-Likelihood Estimators in Generalized Linear Models with Diverging Number of Covariates

In this paper, for the generalized linear models (GLMs) with diverging number of covariates, the asymptotic properties of maximum quasi-likelihood estimators (MQLEs) under some regular conditions are developed. The existence, weak convergence and the rate of convergence and asymptotic normality of linear combination of MQLEs and asymptotic distribution of single linear hypothesis test statistics are presented. The results are illustrated by Monte-Carlo simulations.     

An Efficient Multiple Imputation Approach for Estimating Equations with Response Missing at Random and High-Dimensional Covariates

Empirical-likelihood-based inference for parameters defined by the general estimating equations of Qin and Lawless(1994) remains an active research topic. When the response is missing at random(MAR) and the dimension of covariate is not low, the authors propose a two-stage estimation procedure by using the dimension-reduced kernel estimators in conjunction with an unbiased estimating function based on augmented inverse probability weighting and multiple imputation(AIPW-MI) methods. The authors show that the resulting estimator achieves consistency and asymptotic normality. In addition, the corresponding empirical likelihood ratio statistics asymptotically follow central chi-square distributions when evaluated at the true parameter. The finite-sample performance of the proposed estimator is studied through simulation, and an application to HIV-CD4 data set is also presented.     

Single-Index Quantile Regression with Left Truncated Data

The purpose of this paper is two fold. First, the authors investigate quantile regression (QR) estimation for single-index QR models when the response is subject to random left truncation. The random weights are introduced to deal with left truncated data and the associated iteration estimation method is proposed. The asymptotic properties for the proposed QR estimates of the index parameter and unknown link function are both obtained. Further, by combining the QR loss function and the adaptive LASSO penalization, a variable selection procedure for the index parameter is introduced and its oracle property is established. Second, a weighted empirical log-likelihood ratio of the index parameter based on the QR method is introduced and is proved to be asymptotic standard chi-square distribution. Furthermore, confidence regions of the index parameter can be constructed. The finite sample performance of the proposed methods are demonstrated. A real data analysis is also conducted to show the usefulness of the proposed approaches.

     

ASYMPTOTIC BEHAVIOR OF THE ESTIMATES OF HIGHER ORDER SPECTRA UNDER TRUNCATED WINDOW

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用于认知跳频的归一化谱双向搜索感知算法

认知跳频被认为是消除传统跳频系统用频困扰的有效途径之一。针对认知跳频超宽带和多频隙实时频谱感知的需求,给出基于归一化谱双向搜索(bidirectional search of normalized power spectrum, BSNP)的感知算法,BSNP以跳频频隙内的归一化功率谱作为检验统计量,通过顺序执行正向和反向搜索,感知出跳频带宽中已被占用的所有频隙。利用傅里叶变换的渐进正态性和相互独立性,可推导BSNP单次判决虚警概率的数学表达式和判决门限的闭式表达式。分析和仿真表明,BSNP可以准确地找出频带内被占用的频隙,相比于常规谱估计感知算法,可有效克服噪声不确定度对频谱感知性能的 影响。     

Efficient estimation of seemingly unrelated additive nonparametric regression models

This paper is concerned with the estimating problem of seemingly unrelated (SU) nonparametric additive regression models. A polynomial spline based two-stage efficient approach is proposed to estimate the nonparametric components, which takes both of the additive structure and correlation between equations into account. The asymptotic normality of the derived estimators are establishedi. The authors also show they own some advantages, including they are asymptotically more efficient than those based on only the individual regression equation and have an oracle property, which is the asymptotic distribution of each additive component is the same as it would be if the other components were known with certainty. Some simulation studies are conducted to illustrate the finite sample performance of the proposed procedure. Applying the proposed procedure to a real data set is also made.     

Estimation in a semi-varying coefficient model for panel data with fixed effects

This paper considers a semi-varying coefficient model for panel data with fixed effects, proposes the profile-likelihood-based estimators for the parametric and nonparametric components, and establishes convergence rates and asymptotic normality properties for both estimators. Simulation results show that the proposed estimators behave well in finite sample cases.