{"ID":5936958,"CreatedAt":"2026-07-07T03:14:33.014478982Z","UpdatedAt":"2026-07-09T16:45:10.440590912Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.05312","arxiv_id":"2607.05312","title":"Locally Private Online Quantile Regression: Estimation and Inference","abstract":"We study estimation and inference for online quantile regression under a one-report user-level $\\eps$-locally differentially private ($\\eps$-LDP) protocol. The main difficulty is that the standard quantile-regression estimating-equation contribution couples covariates with a residual comparison, so a server that receives only privatized reports cannot form the usual online update. We address this by developing a finite-alphabet channel in which each user computes the contribution locally, applies support-aware stochastic quantization and randomized response to one selected-block category, and sends one report. A public decoder corrects the randomized-response distortion and reconstructs a server-side estimating-equation input with the correct conditional mean. These decoded inputs are then used in projected Polyak-Ruppert averaging. For fixed finite channel designs, we establish local privacy, decoder unbiasedness, consistency, asymptotic normality, and Hessian-free self-normalized inference for prespecified scalar contrasts. Simulations and a New York City taxi-trip illustration show that the private trajectory approaches the nonprivate online reference as the privacy budget grows and outperforms direct Laplace and face-exponential geometric releases in the reported regimes.","short_abstract":"We study estimation and inference for online quantile regression under a one-report user-level $\\eps$-locally differentially private ($\\eps$-LDP) protocol. The main difficulty is that the standard quantile-regression estimating-equation contribution couples covariates with a residual comparison, so a server that receiv...","url_abs":"https://arxiv.org/abs/2607.05312","url_pdf":"https://arxiv.org/pdf/2607.05312v1","authors":"[\"Yi Liu\",\"Qirui Hu\"]","published":"2026-07-06T16:52:54Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"stat.ME\"]","methods":"[]","has_code":false}