12 problems

Let $\ell_{\alpha}$ be the pinball loss, fix an intercept $b$, and fit the unregularized quantile-regression slope $\hat{\beta}_{(n+1)}(b)$ on the training data. Let $Z\sim N(0,1)$…

Let $\ell_{\alpha}(u)=\alpha u$ for $u\geq 0$ and $(\alpha-1)u$ for $u<0$ be the pinball loss, let $\hat{\eta}_{n+1}$ be the dual quantile-regression score, and let…

Let $Q_n^{\dagger}(u\mid x)$ be the increasing rearrangement of the quantile regression posterior draw $Q_n(u\mid x)$. Conjecture on posterior consistency. The rearranged quantile…

Let $Q_N^{\dagger}$ denote the increasing rearrangement of the quantile martingale posterior draw $Q_N$, and let $S_N^{\dagger}$ denote the corresponding centered and scaled proces…

The authors' conjecture. The proposed multi-step reweighted convex penalization approach and convolution smoothing will lead to oracle statistical guarantees and fast computational…

The paper considers quantile regression series terms and test statistics under assumptions ensuring asymptotic results for additive univariate series terms, including univariate B-…

The paper studies higher-order bias corrections for conditional quantile regression estimators and develops Bahadur–Kiefer expansions for comparing resampling procedures. Resamplin…

Given covariates $\mathbf{x}^*$ and $\mathbf{z}^*$, consider estimating the conditional quantile function $Q_{Y_i|\mathbf{x}^*,\mathbf{z}^*}(\tau)$ by … where $\hat{\bolds{\beta}}$…

Let $\nu^\dag$ be a fixed multi-index and consider testing the parametric model using local polynomial residual quantile estimators under alternatives of the form … For…

Uniform Bahadur optimality conjecture. The order

Technical-necessity conjecture. Both the requirement of consistent initial estimators and the restriction on the number of iteration steps are necessary only for technical reasons…

The data consist of observations $W_t=(V_t,X_t)$, where $V_t$ is the transformed outcome used in the extremal quantile regression analysis and $X_t$ is the regressor vector. The pr…