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Researcher profile

Fang Han

Fang Han contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
math.STStatistics Theoryecon.EMMethodologyApplicationsInformation Retrievalmath.PR

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Published work

10 published item(s)

preprint2026arXiv

Bias correction for Chatterjee's graph-based correlation coefficient

Azadkia and Chatterjee (2021) recently introduced a simple nearest neighbor (NN) graph-based correlation coefficient that consistently detects both independence and functional dependence. Specifically, it approximates a measure of dependence that equals 0 if and only if the variables are independent, and 1 if and only if they are functionally dependent. However, this NN estimator includes a bias term that may vanish at a rate slower than root-$n$, preventing root-$n$ consistency in general. In this article, we (i) analyze this bias term closely and show that it could become asymptotically negligible when the dimension is smaller than four; and (ii) propose a bias-correction procedure for more general settings. In both regimes, we obtain estimators (either the original or the bias-corrected version) that are root-$n$ consistent and asymptotically normal.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

LLM Agents Enable User-Governed Personalization Beyond Platform Boundaries

Personalization today is fundamentally platform-centric: services build user representations from the behavioral fragments they observe. Yet no platform can construct a complete picture of the user, as competitive incentives, legal constraints, user privacy concerns, and epistemic limits create persistent data barriers. This paper argues for a shift from platform-centric personalization to user-governed personalization, where only the user can integrate fragmented contexts across platforms and the offline world. The key asymmetry lies in data access: only users can aggregate their own cross-platform and offline information. Large language model (LLM) agents make such integration practically feasible for the first time by enabling reasoning over heterogeneous personal data and transforming users' cross-context information into actionable personalization capabilities. We provide proof-of-concept evidence that users equipped with cross-platform data exports and an off-the-shelf LLM agent can outperform single-platform personalization baselines. We conclude by outlining a research agenda for building scalable user-governed personalization systems.

0 citations0 reviewsNo code linkedOpen access
preprint2024arXiv

On Rosenbaum's Rank-based Matching Estimator

In two influential contributions, Rosenbaum (2005, 2020) advocated for using the distances between component-wise ranks, instead of the original data values, to measure covariate similarity when constructing matching estimators of average treatment effects. While the intuitive benefits of using covariate ranks for matching estimation are apparent, there is no theoretical understanding of such procedures in the literature. We fill this gap by demonstrating that Rosenbaum's rank-based matching estimator, when coupled with a regression adjustment, enjoys the properties of double robustness and semiparametric efficiency without the need to enforce restrictive covariate moment assumptions. Our theoretical findings further emphasize the statistical virtues of employing ranks for estimation and inference, more broadly aligning with the insights put forth by Peter Bickel in his 2004 Rietz lecture (Bickel, 2004).

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

On regression-adjusted imputation estimators of the average treatment effect

Imputing missing potential outcomes using an estimated regression function is a natural idea for estimating causal effects. In the literature, estimators that combine imputation and regression adjustments are believed to be comparable to augmented inverse probability weighting. Accordingly, people for a long time conjectured that such estimators, while avoiding directly constructing the weights, are also doubly robust (Imbens, 2004; Stuart, 2010). Generalizing an earlier result of the authors (Lin et al., 2021), this paper formalizes this conjecture, showing that a large class of regression-adjusted imputation methods are indeed doubly robust for estimating the average treatment effect. In addition, they are provably semiparametrically efficient as long as both the density and regression models are correctly specified. Notable examples of imputation methods covered by our theory include kernel matching, (weighted) nearest neighbor matching, local linear matching, and (honest) random forests.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Robust Functional Principal Component Analysis via Functional Pairwise Spatial Signs

Functional principal component analysis (FPCA) has been widely used to capture major modes of variation and reduce dimensions in functional data analysis. However, standard FPCA based on the sample covariance estimator does not work well in the presence of outliers. To address this challenge, a new robust functional principal component analysis approach based on the functional pairwise spatial sign (PASS) operator, termed PASS FPCA, is introduced where we propose estimation procedures for both eigenfunctions and eigenvalues with and without measurement error. Compared to existing robust FPCA methods, the proposed one requires weaker distributional assumptions to conserve the eigenspace of the covariance function. In particular, a class of distributions called the weakly functional coordinate symmetric (weakly FCS) is introduced that allows for severe asymmetry and is strictly larger than the functional elliptical distribution class, the latter of which has been well used in the robust statistics literature. The robustness of the PASS FPCA is demonstrated via simulation studies and analyses of accelerometry data from a large-scale epidemiological study of physical activity on older women that partly motivates this work.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Distribution-free consistent independence tests via center-outward ranks and signs

This paper investigates the problem of testing independence of two random vectors of general dimensions. For this, we give for the first time a distribution-free consistent test. Our approach combines distance covariance with the center-outward ranks and signs developed in Hallin (2017). In technical terms, the proposed test is consistent and distribution-free in the family of multivariate distributions with nonvanishing (Lebesgue) probability densities. Exploiting the (degenerate) U-statistic structure of the distance covariance and the combinatorial nature of Hallin's center-outward ranks and signs, we are able to derive the limiting null distribution of our test statistic. The resulting asymptotic approximation is accurate already for moderate sample sizes and makes the test implementable without requiring permutation. The limiting distribution is derived via a more general result that gives a new type of combinatorial non-central limit theorem for double- and multiple-indexed permutation statistics.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

High dimensional consistent independence testing with maxima of rank correlations

Testing mutual independence for high-dimensional observations is a fundamental statistical challenge. Popular tests based on linear and simple rank correlations are known to be incapable of detecting non-linear, non-monotone relationships, calling for methods that can account for such dependences. To address this challenge, we propose a family of tests that are constructed using maxima of pairwise rank correlations that permit consistent assessment of pairwise independence. Built upon a newly developed Cramér-type moderate deviation theorem for degenerate U-statistics, our results cover a variety of rank correlations including Hoeffding's $D$, Blum-Kiefer-Rosenblatt's $R$, and Bergsma-Dassios-Yanagimoto's $τ^*$. The proposed tests are distribution-free in the class of multivariate distributions with continuous margins, implementable without the need for permutation, and are shown to be rate-optimal against sparse alternatives under the Gaussian copula model. As a by-product of the study, we reveal an identity between the aforementioned three rank correlation statistics, and hence make a step towards proving a conjecture of Bergsma and Dassios.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

On a phase transition in general order spline regression

In the Gaussian sequence model $Y= θ_0 + \varepsilon$ in $\mathbb{R}^n$, we study the fundamental limit of approximating the signal $θ_0$ by a class $Θ(d,d_0,k)$ of (generalized) splines with free knots. Here $d$ is the degree of the spline, $d_0$ is the order of differentiability at each inner knot, and $k$ is the maximal number of pieces. We show that, given any integer $d\geq 0$ and $d_0\in\{-1,0,\ldots,d-1\}$, the minimax rate of estimation over $Θ(d,d_0,k)$ exhibits the following phase transition: \begin{equation*} \begin{aligned} \inf_{\widetildeθ}\sup_{θ\inΘ(d,d_0, k)}\mathbb{E}_θ\|\widetildeθ - θ\|^2 \asymp_d \begin{cases} k\log\log(16n/k), & 2\leq k\leq k_0,\\ k\log(en/k), & k \geq k_0+1. \end{cases} \end{aligned} \end{equation*} The transition boundary $k_0$, which takes the form $\lfloor{(d+1)/(d-d_0)\rfloor} + 1$, demonstrates the critical role of the regularity parameter $d_0$ in the separation between a faster $\log \log(16n)$ and a slower $\log(en)$ rate. We further show that, once encouraging an additional '$d$-monotonicity' shape constraint (including monotonicity for $d = 0$ and convexity for $d=1$), the above phase transition is eliminated and the faster $k\log\log(16n/k)$ rate can be achieved for all $k$. These results provide theoretical support for developing $\ell_0$-penalized (shape-constrained) spline regression procedures as useful alternatives to $\ell_1$- and $\ell_2$-penalized ones.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Optimal estimation of variance in nonparametric regression with random design

Consider the heteroscedastic nonparametric regression model with random design \begin{align*} Y_i = f(X_i) + V^{1/2}(X_i)\varepsilon_i, \quad i=1,2,\ldots,n, \end{align*} with $f(\cdot)$ and $V(\cdot)$ $α$- and $β$-Hölder smooth, respectively. We show that the minimax rate of estimating $V(\cdot)$ under both local and global squared risks is of the order \begin{align*} n^{-\frac{8αβ}{4αβ+ 2α+ β}} \vee n^{-\frac{2β}{2β+1}}, \end{align*} where $a\vee b := \max\{a,b\}$ for any two real numbers $a,b$. This result extends the fixed design rate $n^{-4α} \vee n^{-2β/(2β+1)}$ derived in Wang et al. [2008] in a non-trivial manner, as indicated by the appearances of both $α$ and $β$ in the first term. In the special case of constant variance, we show that the minimax rate is $n^{-8α/(4α+1)}\vee n^{-1}$ for variance estimation, which further implies the same rate for quadratic functional estimation and thus unifies the minimax rate under the nonparametric regression model with those under the density model and the white noise model. To achieve the minimax rate, we develop a U-statistic-based local polynomial estimator and a lower bound that is constructed over a specified distribution family of randomness designed for both $\varepsilon_i$ and $X_i$.

0 citations0 reviewsNo code linkedOpen access