ROCKET: Robust Confidence Intervals via Kendall's Tau for Transelliptical Graphical Models
نویسندگان
چکیده
Understanding complex relationships between random variables is of fundamental importance in high-dimensional statistics, with numerous applications in biological and social sciences. Undirected graphical models are often used to represent dependencies between random variables, where an edge between to random variables is drawn if they are conditionally dependent given all the other measured variables. A large body of literature exists on methods that estimate the structure of an undirected graphical model, however, little is known about the distributional properties of the estimators beyond the Gaussian setting. In this paper, we focus on inference for edge parameters in a high-dimensional transelliptical model, which generalizes Gaussian and nonparanormal graphical models. We propose ROCKET, a novel procedure for estimating parameters in the latent inverse covariance matrix. We establish asymptotic normality of ROCKET in ultra high-dimensional setting under mild assumptions, without relying on oracle model selection results. ROCKET requires the same number of samples that are known to be necessary for obtaining a ? n consistent estimator of an element in the precision matrix under a Gaussian model. Hence, it is an optimal estimator under a much larger family of distributions. The result hinges on a tight control of the spectral norm of the non-parametric estimator of the correlation matrix, which is of independent interest. Empirically, ROCKET outperforms the nonparanormal and Gaussian models in terms of achieving accurate inference on simulated data. We also compare the three methods on real data (daily stock returns), and find that the ROCKET estimator is the only method whose behavior across subsamples agrees with the distribution predicted by the theory.
منابع مشابه
Transelliptical Graphical Models
We advocate the use of a new distribution family—the transelliptical—for robust inference of high dimensional graphical models. The transelliptical family is an extension of the nonparanormal family proposed by Liu et al. (2009). Just as the nonparanormal extends the normal by transforming the variables using univariate functions, the transelliptical extends the elliptical family in the same wa...
متن کاملSEQUENTIAL CONFIDENCE INTERVAL FOR TIlE REGRESSION COEFFICIENT
SUMMARY The object of the present investigation is to consider a robust procedure for the problem of providing a bounded-length confidence interval for the regression coefficient (in a simple regression model) based on Kendall's (1955) tau. The problem of estimating the difference in the location parameters in the two-sample case may be viewed as a special case of our problem. It is shown that ...
متن کاملCommunication-efficient Distributed Estimation and Inference for Transelliptical Graphical Models∗
We propose communication-efficient distributed estimation and inference methods for the transelliptical graphical model, a semiparametric extension of the elliptical distribution in the high dimensional regime. In detail, the proposed method distributes the d-dimensional data of size N generated from a transelliptical graphical model into m worker machines, and estimates the latent precision ma...
متن کاملA SAS Macro for Improved Correlation Coefficient Inference
We present a SAS macro for improved statistical inference for measures of association, including Pearson's correlation, Spearman's coefficient, and Kendall's coefficient. While the CORR procedure is a powerful tool for calculating and testing these coefficients, some analyses are lacking. For example, the CORR procedure does not incorporate recent theoretical improvements in confidence interval...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1502.07641 شماره
صفحات -
تاریخ انتشار 2015