Some New Results of M-Type Regression Spline Estimators in a Partially Linear Model
TL;DRAbstract
Consider the partially linear modelY_i=X_i~τβ_0+ g_0(T_i)+e_i,where (T_1, X_1~τ, Y_1),…,(T_n,X_n~τ, Y_n) are i. i. d. observations of a random (d+2)-vector (T,X~τ, Y), X=(x_1,…,x_d)~τ is a d-vector of explanatory variables, β_0 is a vector of unknownparameters, T is another explanatory variable ranging over a nondegenerate compactinterval, say [0, 1],g_0(·)is an unknown smooth function, and e_i's are random errors.
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Consider the partially linear modelY_i=X_i~τβ_0+ g_0(T_i)+e_i,where (T_1, X_1~τ, Y_1),…,(T_n,X_n~τ, Y_n) are i. i. d. observations of a random (d+2)-vector (T,X~τ, Y), X=(x_1,…,x_d)~τ is a d-vector of explanatory variables, β_0 is a vector of unknownparameters, T is another explanatory variable ranging over a nondegenerate compactinterval, say [0, 1],g_0(·)is an unknown smooth function, and e_i's are random errors.
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