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Register a new userNetwork Tomography: Identifiability and Fourier Domain Estimation
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Added by
Aiyou Chen
Publication date
2007
fields
Mathematical Statistics
and research's language is
English
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The statistical problem for network tomography is to infer the distribution of $mathbf{X}$, with mutually independent components, from a measurement model $mathbf{Y}=Amathbf{X}$, where $A$ is a given binary matrix representing the routing topology of a network under consideration. The challenge is that the dimension of $mathbf{X}$ is much larger than that of $mathbf{Y}$ and thus the problem is often called ill-posed. This paper studies some statistical aspects of network tomography. We first address the identifiability issue and prove that the $mathbf{X}$ distribution is identifiable up to a shift parameter under mild conditions. We then use a mixture model of characteristic functions to derive a fast algorithm for estimating the distribution of $mathbf{X}$ based on the General method of Moments. Through extensive model simulation and real Internet trace driven simulation, the proposed approach is shown to be favorable comparing to previous methods using simple discretization for inferring link delays in a heterogeneous network.
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This is a comment to the paper A study of problems encountered in Granger causality analysis from a neuroscience perspective. We agree that interpretation issues of Granger Causality in Neuroscience exist (partially due to the historical unfortunate use of the name causality, as nicely described in previous literature). On the other hand we think that the paper uses a formulation of Granger causality which is outdated (albeit still used), and in doing so it dismisses the measure based on a suboptimal use of it. Furthermore, since data from simulated systems are used, the pitfalls that are found with the used formulation are intended to be general, and not limited to neuroscience. It would be a pity if this paper, even written in good faith, became a wildcard against all possible applications of Granger Causality, regardless of the hard work of colleagues aiming to seriously address the methodological and interpretation pitfalls. In order to provide a balanced view, we replicated their simulations used the updated State Space implementation, proposed already some years ago, in which the pitfalls are mitigated or directly solved.
The purpose of this paper is to construct confidence intervals for the regression coefficients in the Fine-Gray model for competing risks data with random censoring, where the number of covariates can be larger than the sample size. Despite strong motivation from biomedical applications, a high-dimensional Fine-Gray model has attracted relatively little attention among the methodological or theoretical literature. We fill in this gap by developing confidence intervals based on a one-step bias-correction for a regularized estimation. We develop a theoretical framework for the partial likelihood, which does not have independent and identically distributed entries and therefore presents many technical challenges. We also study the approximation error from the weighting scheme under random censoring for competing risks and establish new concentration results for time-dependent processes. In addition to the theoretical results and algorithms, we present extensive numerical experiments and an application to a study of non-cancer mortality among prostate cancer patients using the linked Medicare-SEER data.
We consider a resampling scheme for parameters estimates in nonlinear regression models. We provide an estimation procedure which recycles, via random weighting, the relevant parameters estimates to construct consistent estimates of the sampling distribution of the various estimates. We establish the asymptotic normality of the resampled estimates and demonstrate the applicability of the recycling approach in a small simulation study and via example.
Motivated by modeling and analysis of mass-spectrometry data, a semi- and nonparametric model is proposed that consists of a linear parametric component for individual location and scale and a nonparametric regression function for the common shape. A multi-step approach is developed that simultaneously estimates the parametric components and the nonparametric function. Under certain regularity conditions, it is shown that the resulting estimators is consistent and asymptotic normal for the parametric part and achieve the optimal rate of convergence for the nonparametric part when the bandwidth is suitably chosen. Simulation results are presented to demonstrate the effectiveness and finite-sample performance of the method. The method is also applied to a SELDI-TOF mass spectrometry data set from a study of liver cancer patients.
Inverse probability of treatment weighting (IPTW) is a popular method for estimating the average treatment effect (ATE). However, empirical studies show that the IPTW estimators can be sensitive to the misspecification of the propensity score model. To address this problem, researchers have proposed to estimate propensity score by directly optimizing the balance of pre-treatment covariates. While these methods appear to empirically perform well, little is known about how the choice of balancing conditions affects their theoretical properties. To fill this gap, we first characterize the asymptotic bias and efficiency of the IPTW estimator based on the Covariate Balancing Propensity Score (CBPS) methodology under local model misspecification. Based on this analysis, we show how to optimally choose the covariate balancing functions and propose an optimal CBPS-based IPTW estimator. This estimator is doubly robust; it is consistent for the ATE if either the propensity score model or the outcome model is correct. In addition, the proposed estimator is locally semiparametric efficient when both models are correctly specified. To further relax the parametric assumptions, we extend our method by using a sieve estimation approach. We show that the resulting estimator is globally efficient under a set of much weaker assumptions and has a smaller asymptotic bias than the existing estimators. Finally, we evaluate the finite sample performance of the proposed estimators via simulation and empirical studies. An open-source software package is available for implementing the proposed methods.
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