اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدHigh dimensional generalized empirical likelihood for moment restrictions with dependent data
487
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
This paper considers the maximum generalized empirical likelihood (GEL) estimation and inference on parameters identified by high dimensional moment restrictions with weakly dependent data when the dimensions of the moment restrictions and the parameters diverge along with the sample size. The consistency with rates and the asymptotic normality of the GEL estimator are obtained by properly restricting the growth rates of the dimensions of the parameters and the moment restrictions, as well as the degree of data dependence. It is shown that even in the high dimensional time series setting, the GEL ratio can still behave like a chi-square random variable asymptotically. A consistent test for the over-identification is proposed. A penalized GEL method is also provided for estimation under sparsity setting.
قيم البحث
اقرأ أيضاً
In this paper we develop an online statistical inference approach for high-dimensional generalized linear models with streaming data for real-time estimation and inference. We propose an online debiased lasso (ODL) method to accommodate the special s
tructure of streaming data. ODL differs from offline debiased lasso in two important aspects. First, in computing the estimate at the current stage, it only uses summary statistics of the historical data. Second, in addition to debiasing an online lasso estimator, ODL corrects an approximation error term arising from nonlinear online updating with streaming data. We show that the proposed online debiased estimators for the GLMs are consistent and asymptotically normal. This result provides a theoretical basis for carrying out real-time interim statistical inference with streaming data. Extensive numerical experiments are conducted to evaluate the performance of the proposed ODL method. These experiments demonstrate the effectiveness of our algorithm and support the theoretical results. A streaming dataset from the National Automotive Sampling System-Crashworthiness Data System is analyzed to illustrate the application of the proposed method.
We propose a generalized version of the Dantzig selector. We show that it satisfies sparsity oracle inequalities in prediction and estimation. We consider then the particular case of high-dimensional linear regression model selection with the Huber l
oss function. In this case we derive the sup-norm convergence rate and the sign concentration property of the Dantzig estimators under a mutual coherence assumption on the dictionary.
Statistical methods with empirical likelihood (EL) are appealing and effective especially in conjunction with estimating equations through which useful data information can be adaptively and flexibly incorporated. It is also known in the literature t
hat EL approaches encounter difficulties when dealing with problems having high-dimensional model parameters and estimating equations. To overcome the challenges, we begin our study with a careful investigation on high-dimensional EL from a new scope targeting at estimating a high-dimensional sparse model parameters. We show that the new scope provides an opportunity for relaxing the stringent requirement on the dimensionality of the model parameter. Motivated by the new scope, we then propose a new penalized EL by applying two penalty functions respectively regularizing the model parameters and the associated Lagrange multipliers in the optimizations of EL. By penalizing the Lagrange multiplier to encourage its sparsity, we show that drastic dimension reduction in the number of estimating equations can be effectively achieved without compromising the validity and consistency of the resulting estimators. Most attractively, such a reduction in dimensionality of estimating equations is actually equivalent to a selection among those high-dimensional estimating equations, resulting in a highly parsimonious and effective device for high-dimensional sparse model parameters. Allowing both the dimensionalities of model parameters and estimating equations growing exponentially with the sample size, our theory demonstrates that the estimator from our new penalized EL is sparse and consistent with asymptotically normally distributed nonzero components. Numerical simulations and a real data analysis show that the proposed penalized EL works promisingly.
This paper presents and analyzes an approach to cluster-based inference for dependent data. The primary setting considered here is with spatially indexed data in which the dependence structure of observed random variables is characterized by a known,
observed dissimilarity measure over spatial indices. Observations are partitioned into clusters with the use of an unsupervised clustering algorithm applied to the dissimilarity measure. Once the partition into clusters is learned, a cluster-based inference procedure is applied to a statistical hypothesis testing procedure. The procedure proposed in the paper allows the number of clusters to depend on the data, which gives researchers a principled method for choosing an appropriate clustering level. The paper gives conditions under which the proposed procedure asymptotically attains correct size. A simulation study shows that the proposed procedure attains near nominal size in finite samples in a variety of statistical testing problems with dependent data.
In the low-dimensional case, the generalized additive coefficient model (GACM) proposed by Xue and Yang [Statist. Sinica 16 (2006) 1423-1446] has been demonstrated to be a powerful tool for studying nonlinear interaction effects of variables. In this
paper, we propose estimation and inference procedures for the GACM when the dimension of the variables is high. Specifically, we propose a groupwise penalization based procedure to distinguish significant covariates for the large $p$ small $n$ setting. The procedure is shown to be consistent for model structure identification. Further, we construct simultaneous confidence bands for the coefficient functions in the selected model based on a refined two-step spline estimator. We also discuss how to choose the tuning parameters. To estimate the standard deviation of the functional estimator, we adopt the smoothed bootstrap method. We conduct simulation experiments to evaluate the numerical performance of the proposed methods and analyze an obesity data set from a genome-wide association study as an illustration.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
