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This paper studies the function-based semi- parametric regression model Y = X ~ Tβ m (T) ε, where (X, Y) is R p × R on the real value of a random variable , T is the values ??in infinite-dimensional semi- metric space (E, d) the function of random variable (frv), β is P × 1 -dimensional real unknown parameter variables , m (?) for unknown operator , (X, T) and the error ε are independent , when the error satisfy AR (1) process , the establishment of such a function semi- parametric regression model estimates of unknown parameters in the amount of β (β | ∧) and nonparametric part m (?) estimator m (T | ∧) of strong convergence to promote the existing literature relevant results.
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