Cheng Peng, Stanislav Uryasev
arXiv 31 Jan 2023 · Statistics — Methodology
arXiv:2301.13843 · PDF · DOI · OpenAlex · Extracted main text
This paper proposes a new approach to estimating the distribution of a response variable conditioned on observing some factors. The proposed approach possesses desirable properties of flexibility, interpretability, tractability and extendability. The conditional quantile function is modeled by a mixture (weighted sum) of basis quantile functions, with the weights depending on factors. The calibration problem is formulated as a convex optimization problem. It can be viewed as conducting quantile regressions for all confidence levels simultaneously while avoiding quantile crossing by definition. The calibration problem is equivalent to minimizing the continuous ranked probability score (CRPS). Based on the canonical polyadic (CP) decomposition of tensors, we propose a dimensionality reduction method that reduces the rank of the parameter tensor and propose an alternating algorithm for estimation. Additionally, based on Risk Quadrangle framework, we generalize the approach to conditional distributions defined by Conditional Value-at-Risk (CVaR), expectile and other functions of uncertainty measures. Although this paper focuses on using splines as the weight functions, it can be extended to neural networks. Numerical experiments demonstrate the effectiveness of our approach.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Paolo Frumento and Matteo Bottai (2016) Parametric modeling of quantile regression coefficient functions | 1.000 | 5 | 3 | 100% |
| 2 | Dávid Papp (2011) Optimization models for shape-constrained function estimation problems involving nonnegative polynomials and their restrictions | 1.000 | 5 | 3 | 100% |
| 3 | Dávid Papp and Farid Alizadeh (2012) Shape-constrained estimation using nonnegative splines | 1.000 | 5 | 3 | 100% |
| 4 | Brian J. Reich, Montserrat Fuentes, and David B. Dunson (2011) Bayesian spatial quantile regression | 0.811 | 4 | 2 | 100% |
| 5 | C. de Boor and James W. Daniel (1974) Splines with nonnegative $b$-spline coefficients | 0.737 | 3 | 2 | 100% |
| 6 | Heng Lian, Jie Meng, and Zengyan Fan (2015) Simultaneous estimation of linear conditional quantiles with penalized splines | 0.737 | 3 | 2 | 100% |
| 7 | Yuan Yuan, Nan Chen, and Shiyu Zhou (2016) Modeling regression quantile process using monotone b-splines | 0.737 | 3 | 2 | 100% |
| 8 | Cheng Peng, Yizhou Li, and Stan Uryasev (2022) Mixture quantiles calibrated with constrained linear regression self | 0.644 | 2 | 2 | 100% |
| 9 | Paul H. C. Eilers and Brian D. Marx (1996) Flexible smoothing with B-splines and penalties | 0.644 | 2 | 2 | 100% |
| 10 | Paul H.C. Eilers and Brian D. Marx (2003) Multivariate calibration with temperature interaction using two-dimensional penalized signal regression | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 71 scored citations.