Limit Theory for Online Expectile Estimation under Short and Long Range Dependence
Expectiles are tail-sensitive distributional summaries with important applications in financial risk measurement and forecasting, yet statistical theory for their online estimation from dependent data remains limited. We study a one-pass, stochastic-gradient algorithm with constant learning rate $γ$ for estimating the marginal expectile of a stationary causal process. The recursion admits a unique stationary causal solution and geometrically forgets its initialization. Under short-range dependence, its last iterate is asymptotically Gaussian at the $\sqrtγ$ scale, with variance governed by the population curvature and the long-run variance of the expectile score. For long-memory linear pr...
| Authors | Younghun Lee, Jake Zummo, Wei Biao Wu |
|---|---|
| Primary category | stat.ML |
| Published | 12 October 2026 |
| Last updated at source | 12 October 2026 |
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