Non-regular statistical estimation

非常规统计估计

• 批准号: RGPIN-2015-04119
• 负责人: Knight, Keith
• 金额: $ 0.8万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=589600
• 关键词: Non; regular; statistical; estimation

Some common estimation procedures in statistics, such as model selection in linear regression, can be extremely sensitive to small changes in the data or to changes in tuning parameters; such procedures can be thought of "non-smooth" and their statistical properties are usually very complicated. For example, the sensitivity or instability of such procedures is often overlooked by applied statisticians when considering the uncertainty of parameter estimates and standard statistical methodology typically underestimates the uncertainty of such estimates. Some "non-smooth" estimation procedures (e.g. model selection) can be rendered more smooth by an appropriate regularization (e.g using the lasso in regression) although such regularization are not always obvious.

统计学中的一些常见估计程序，如线性回归中的模型选择，可能对数据的微小变化或调整参数的变化极其敏感；这种程序可被认为是“非平稳的”，其统计性质通常非常复杂。例如，在考虑参数估计的不确定性时，应用统计学家往往忽视这种程序的敏感性或不稳定性，而标准统计方法通常低估了这种估计的不确定性。通过适当的正则化(例如，在回归中使用套索)，可以使一些“非平滑”估计过程(例如，模型选择)变得更平滑，尽管这种正则化并不总是明显的。