Semi-parametric and Nonparametric Inference

半参数和非参数推理

• 批准号: RGPIN-2022-04799
• 负责人: Huang, MeiLing
• 金额: $ 1.31万
• 依托单位: Brock University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=758623
• 关键词: Semi; parametric; Nonparametric; Inference

Objectives of the Proposed Research Program: The objective of my research is to develop novel inference methodology in two areas: 1) Inference methods for heavy-tailed distributions and networks. 2) Weighted and nonparametric inference for quantile regression; Train high quality personnel (HQP) to carry out research. 1. Inference for Heavy-Tailed Distributions and Networks Extreme events occur in financial markets, natural disasters, disease control and industrial risk. It is important to find suitable mathematical models for analyzing of extreme events where heavy-tailed distributions are usually applied. There are theoretical difficulties in the inference of heavy-tailed distributions. The proposed program explores three innovative inference objectives to overcome difficulties: Objective (1)(Prop) . Inference for Distributions and Quantiles: Explore new methods to reduce bias and errors for estimation of high quantiles and distributions. Compare new methods with existing methods theoretically and computationally. Objective (2)(Prop). Cluster and Approximation for Heavy Tailed Distributions: Heavy tailed data is often complicated, such that a single distribution may not fit data well. Explore new cluster, Hermite series, hyperexponential approximation methods for estimating heavy tailed distributions. Objective (3)(Prop). Inference for stochastic Models and Random Networks: Explore innovative inference methods on extreme renewal process and random network related to heavy tailed distributions theoretically and computationally. 2. Weighted and Nonparametric Inference for Quantile Regression Estimation on the tail of a conditional distribution is a challenging objective. This work focuses on estimating the conditional quantiles (Quantile Regression). I will study two novel objectives as follows: Objective (4)(Prop). Weighted Methods for Quantile Regression: Explore the optimal weights that minimize the estimation errors. Utilize several criteria for measurement of the errors. Objective (5)(prop). Direct Nonparametric Methods for Quantile Regression: Develop nonparametric quantile regression with more effective algorithms. Study theoretical efficiency, consistency, rate of convergence, and robustness. Assessment of the Proposed Objectives (1) to (5) 1) The theoretical approach includes probability theory, statistical theory, stochastic processes, integral equations, combinatorics, groups, and approximation. 2) The computational approach includes Monte Carlo simulations, bootstrapping, to confirm the theoretic results. 3) Applications on real-word examples, find best model fitting data with reasonable conclusions. Expected Significance: The program provides a new alternative approach for Statistical inference. The results are expected to overcome theoretical and computational difficulties in this field. The program trains HQPs to bring new ideas and skills for building suitable Mathematical models to solve real-world problems.

建议研究计划的目标：我的研究目标是在两个领域开发新的推理方法：1）重尾分布和网络的推理方法。2)分位数回归的加权和非参数推断;培养高素质的人员（HQP）进行研究。1.重尾分布和网络的推断极端事件发生在金融市场、自然灾害、疾病控制和工业风险中。对于重尾分布的极端事件，寻找合适的数学模型是非常重要的。重尾分布的推断存在理论上的困难。所提出的方案探讨了三个创新的推理目标，以克服困难：目标（1）（道具）。分布和分位数的推断：探索新的方法来减少估计高分位数和分布的偏差和错误。从理论和计算上比较新方法与现有方法。 目标（2）（提案）。重尾分布的聚类和近似：重尾数据通常很复杂，因此单个分布可能无法很好地拟合数据。探索新的簇，埃尔米特级数，超指数近似方法估计重尾分布。 目标（3）（提案）。随机模型和随机网络的推理：从理论和计算上探索与重尾分布相关的极端更新过程和随机网络的创新推理方法。2.条件分布尾部分位数回归估计的加权和非参数推断是一个具有挑战性的目标。这项工作的重点是估计条件分位数（分位数回归）。我将研究两个新的目标如下：目标（4）（道具）。分位数回归的加权方法：探索最小化估计误差的最佳权重。使用几个标准来测量误差。 目标（5）（道具）。分位数回归的直接非参数方法：使用更有效的算法开发非参数分位数回归。研究理论效率、一致性、收敛速度和鲁棒性。（1）至（5）1）理论方法包括概率论、统计理论、随机过程、积分方程、组合学、群和近似。 2)计算方法包括蒙特卡罗模拟，自举，以确认理论结果。 3)通过实例应用，找到了最佳模型拟合数据，得到了合理的结论。 预期显著性：该程序为统计推断提供了一种新的替代方法。这些结果有望克服这一领域的理论和计算困难。该计划培训HQP带来新的想法和技能，以建立合适的数学模型来解决现实世界的问题。