arXiv subjects

Zhuqing Yu

Publications and source records attributed to Zhuqing Yu.

3 recordsLinked to original sources

arXiv2018

High Dimensional Robust Inference for Cox Regression Models

We consider high-dimensional inference for potentially misspecified Cox proportional hazard models based on low dimensional results by Lin and Wei [1989]. A de-sparsified Lasso estimator is proposed based on the log partial likelihood function and shown to converge to a pseudo-true parameter vector. Interestingly, the sparsity of the true parameter can be inferred from that of the above limiting parameter. Moreover, each component of the above (non-sparse) estimator is shown to be asymptotically normal with a variance that can be consistently estimated even under model misspecifications. In some cases, this asymptotic distribution leads to valid statistical inference procedures, whose empirical performances are illustrated through numerical examples.

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arXiv2018

Minimax Optimal Estimation in Partially Linear Additive Models under High Dimension

In this paper, we derive minimax rates for estimating both parametric and nonparametric components in partially linear additive models with high dimensional sparse vectors and smooth functional components. The minimax lower bound for Euclidean components is the typical sparse estimation rate that is independent of nonparametric smoothness indices. However, the minimax lower bound for each component function exhibits an interplay between the dimensionality and sparsity of the parametric component and the smoothness of the relevant nonparametric component. Indeed, the minimax risk for smooth nonparametric estimation can be slowed down to the sparse estimation rate whenever the smoothness of the nonparametric component or dimensionality of the parametric component is suffciently large. In the above setting, we demonstrate that penalized least square estimators can nearly achieve minimax lower bounds.

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arXiv2017

High Dimensional Inference in Partially Linear Models

We propose two semiparametric versions of the debiased Lasso procedure for the model $Y_i = X_iβ_0 + g_0(Z_i) + ε_i$, where $β_0$ is high dimensional but sparse (exactly or approximately). Both versions are shown to have the same asymptotic normal distribution and do not require the minimal signal condition for statistical inference of any component in $β_0$. Our method also works when $Z_i$ is high dimensional provided that the function classes $E(X_{ij} |Z_i)$s and $E(Y_i|Z_i)$ belong to exhibit certain sparsity features, e.g., a sparse additive decomposition structure. We further develop a simultaneous hypothesis testing procedure based on multiplier bootstrap. Our testing method automatically takes into account of the dependence structure within the debiased estimates, and allows the number of tested components to be exponentially high.

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