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高维协方差矩阵的两样本检验AI 解读

We propose two tests for the equality of covariance matrices between two high-dimensional populations. One test is on the whole variance–covariance matrices, and the other is on off-diagonal sub-matrices, which define the covariance between two nonoverlapping segments of the high-dimensional random vectors. The tests are applicable (i) when the data dimension is much larger than the sample sizes, namely the “large $p$, small $n$” situations and (ii) without assuming…

扩散过程的近似最大似然估计AI 解读

The transition density of a diffusion process does not admit an explicit expression in general, which prevents the full maximum likelihood estimation (MLE) based on discretely observed sample paths. Aït-Sahalia [J. Finance 54 (1999) 1361–1395; Econometrica 70 (2002) 223–262] proposed asymptotic expansions to the transition densities of diffusion processes, which lead to an approximate maximum likelihood estimation (AMLE) for parameters. Built on Aït-Sahalia’s [Econometrica…

非线性时间序列回归中均值与方差结构的联合设定检验AI 解读

This paper proposes a nonparametric simultaneous test for parametric specification of the conditional mean and variance functions in a time series regression model. The test is based on an empirical likelihood (EL) statistic that measures the goodness of fit between the parametric estimates and the nonparametric kernel estimates of the mean and variance functions. A unique feature of the test is its ability to distribute natural weights automatically between the mean and the…

析因设计下高维回归系数的检验AI 解读

We propose simultaneous tests for coefficients in high-dimensional linear regression models with factorial designs. The proposed tests are designed for the “large p, small n” situations where the conventional F-test is no longer applicable. We derive the asymptotic distribution of the proposed test statistic under the high-dimensional null hypothesis and various scenarios of the alternatives, which allow power evaluations. We also evaluate the power of the F-test for models…

高维协方差矩阵的检验AI 解读

We propose tests for sphericity and identity of high-dimensional covariance matrices. The tests are nonparametric without assuming a specific parametric distribution for the data. They can accommodate situations where the data dimension is much larger than the sample size, namely the “large p, small n” situations. We demonstrate by both theoretical and empirical studies that the tests have good properties for a wide range of dimensions and sample sizes. We applied the…

高维数据的两样本检验及其基因集检验应用AI 解读

We propose a two-sample test for the means of high-dimensional data when the data dimension is much larger than the sample size. Hotelling’s classical T2 test does not work for this “large p, small n” situation. The proposed test does not require explicit conditions in the relationship between the data dimension and sample size. This offers much flexibility in analyzing high-dimensional data. An application of the proposed test is in testing significance for sets of genes…

美国人口普查双系统准确性与覆盖评估中的局部后分层AI 解读

We consider a local post-stratification approach to analyze the capture–recapture dual system Accuracy and Coverage Evaluation (A.C.E.) data associated with the 2000 U.S. Census. The local post-stratification is carried out via a nonparametric regression estimation of the census enumeration and the correct enumeration functions. We propose a nonparametric population size estimator that is designed to accommodate some key aspects of the A.C.E.: missing values, erroneous…

基于特征函数的经验似然方法及其 Lévy 过程应用AI 解读

Lévy processes have been receiving increasing attention in financial modeling. One distinctive feature of such models is that their characteristic functions are readily available. Inference based on characteristic functions is very useful for studying Lévy processes. By incorporating the recent advances in nonparametric approaches, empirical likelihood methods based on characteristic functions are developed in this paper for parameter estimation, testing a particular…

扩散过程的参数估计与偏差修正AI 解读

This paper considers parameter estimation for continuous-time diffusion processes which are commonly used to model dynamics of financial securities including interest rates. To understand why the drift parameters are more difficult to estimate than the diffusion parameter, as observed in previous studies, we first develop expansions for the bias and variance of parameter estimators for two of the most employed interest rate processes, Vasicek and CIR processes. Then, we…

含缺失值估计方程的经验似然推断AI 解读

We consider an empirical likelihood inference for parameters defined by general estimating equations when some components of the random observations are subject to missingness. As the nature of the estimating equations is wide-ranging, we propose a nonparametric imputation of the missing values from a kernel estimator of the conditional distribution of the missing variable given the always observable variable. The empirical likelihood is used to construct a profile…

利用替代数据改进半参数估计AI 解读

Summary The paper considers estimating a parameter β that defines an estimating function U(y, x, β) for an outcome variable y and its covariate x when the outcome is missing in some of the observations. We assume that, in addition to the outcome and the covariate, a surrogate outcome is available in every observation. The efficiency of existing estimators for β depends critically on correctly specifying the conditional expectation of U given the surrogate and the covariate.…

扩散过程模型设定检验AI 解读

We propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process. The empirical likelihood is used to formulate a statistic, for each kernel smoothing bandwidth, which is effectively a Studentized L2-distance between the kernel transitional density estimator and the parametric transitional density implied by the parametric process. To reduce the sensitivity of the test on smoothing bandwidth…

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存在干扰参数时经验似然的 Bartlett 校正AI 解读

Lazar & Mykland (1999) showed that an empirical likelihood defined by two estimating equations with a nuisance parameter need not be Bartlett-correctable. This paper shows that Bartlett correction of empirical likelihood in the presence of a nuisance parameter depends critically on the way the nuisance parameter is removed when formulating the likelihood for the parameter of interest. We establish in the broad framework of estimating functions that the empirical likelihood…

替代终点研究中的信息回收AI 解读

Recently, there has been a lot of interest in statistical methods for analyzing data with surrogate endpoints. In this article, we consider parameter estimation from a model that relates a variable Y to a set of covariates, X, in the presence of a surrogate, S. We assume that the data are made up of two random samples from the population, a validation set where (Y, X, S) are observed on every subject and a nonvalidation set where only (X, S) are measured. We show how…

时间序列的经验似然拟合优度检验AI 解读

Summary Standard goodness-of-fit tests for a parametric regression model against a series of nonparametric alternatives are based on residuals arising from a fitted model. When a parametric regression model is compared with a nonparametric model, goodness-of-fit testing can be naturally approached by evaluating the likelihood of the parametric model within a nonparametric framework. We employ the empirical likelihood for an α-mixing process to formulate a test statistic that…

分位数的平滑经验似然置信区间AI 解读

Standard empirical likelihood confidence intervals for quantiles are identical to sign-test intervals. They have relatively large coverage error, of size $n^{-1/2}$, even though they are two-sided intervals. We show that smoothed empirical likelihood confidence intervals for quantiles have coverage error of order $n^{-1}$, and may be Bartlett-corrected to produce intervals with an error of order only $n^{-2}$. Necessary and sufficient conditions on the smoothing parameter,…