Abstract We address a Bayesian regression model with a functional covariate and a scalar response. The model is misspecified in two ways: the posterior distribution is calculated by using normal errors and, mostly, by restraining the functional regression coefficient to a possibly small subset of L 2 ( [ 0 , 1 ] ) . A first general concentration result shows that the posterior distribution concentrates within Kullback–Leibler type neighborhoods of a set called the asymptotic carrier. This result is valid whether the asymptotic carrier is empty or not and includes the misspecified and the well specified cases. We focus on the particular misspecified case in which the functional regression parameter is restrained to a union of finite dimensional linear spaces. This restriction is motivated by the practical situation in which the functional regression parameter is expressed by a finite combination of B-splines with free knots. We provide sufficient conditions for the posterior concentration with respect to the norm of the parameter space along with a precise description of the asymptotic carrier.

中文翻译：

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具有功能协变量的错误指定的贝叶斯回归模型的后浓度

摘要 我们解决了具有函数协变量和标量响应的贝叶斯回归模型。该模型以两种方式被错误指定：后验分布是通过使用正态误差计算的，并且主要是通过将函数回归系数限制为 L 2 ( [ 0 , 1 ] ) 的一个可能的小子集。第一个一般集中结果表明后验分布集中在称为渐近载体的集合的 Kullback-Leibler 类型邻域内。无论渐近载体是否为空，该结果都是有效的，并且包括错误指定和明确指定的情况。我们关注特定错误指定的情况，其中函数回归参数被限制为有限维线性空间的并集。这种限制是由实际情况引起的，在这种情况下，函数回归参数由 B 样条与自由结的有限组合表示。我们提供了关于参数空间范数的后验集中的充分条件以及渐近载体的精确描述。