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在金融和经济学等领域,研究者关心包含变量约束和时间相依数据的回归问题.变量约束的两个重要例子是期权定价和投资组合.当这样的约束添加到经典的回归模型中后,本文要解决如下新的问题:如何建立一个约束相关模型,并实现新模型的可识别性,以及构建型模型估计和检验统计量等.为了解决这些基本问题,本文引入重构方法把变量约束处理成拟工具变量,并且进一步修正偏误以及识别模型,使用轮廓估计的方法估计新模型中的非参数回归函数和参数,得到了估计量的相合性和渐近正态性.最后通过模拟研究了小样本性质,并用真实的股票期权数据验证了该模型.
In the fields of finance and economics, researchers are concerned about regression involving variable constraints and time-dependent data.One of the important examples of variable constraints is option pricing and investment portfolios.When such constraints are added to the classical regression model, To solve the following new problems: how to build a constraint-related model, and to achieve the recognition of the new model, as well as the construction model estimation and test statistics, etc .. In order to solve these basic problems, this paper introduces a reconstruction method to deal with variable constraints into And further correcting the errors and identifying the model, using the method of contour estimation to estimate the non-parametric regression function and parameters in the new model, the consistency and asymptotic normality of the estimator are obtained.Finally, The nature of the sample and its validation with real stock option data.