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Pure Mathematics 2024
基于B样条的可加Logistic模型估计
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Abstract:
非参数模型因不需要事先假定函数形式，所以相较于参数模型更有灵活性和适应性，但存在维数灾难问题。可加模型的提出能有效克服这一问题，同时又能保留非参数的优点。本文针对可加Logistic模型，采用B样条近似，结合极大似然思想得到函数的估计，并证明了其最优收敛速度。同时通过数值模拟和实证分析，比较了可加Logistic模型和Logistic模型的表现，结果说明可加Logistic模型的表现更优。
Nonparametric model is more flexible and adaptive than parametric model because it does not need to assume the function form in advance, but it has the problem of dimensional disaster. The additive model can effectively overcome this problem, while retaining the advantages of nonparameters. The paper uses B-spline for approximating additive Logistic model, and adopts the maximum likelihood idea to estimate the function, and proves the optimal convergence rate. Mean-while, through numerical simulation and empirical analysis, the performance of the additive Logistic model and the logistic model was compared, and the results showed that the additive logistic model performed better.
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