截断线性模型的Fourier变换估计

Fourier Transform Estimation of the Truncated Linear Model

摘要: 设有模型Y=Xβ₀+U其中β₀为未知参数,X为自变量,误差项U与X独立,且EU=0,U～F（未知）。当W≤t（已知）时才有观察（X,Y）。本文给出模型参数β₀的Fourier变换估计,并证明了估计量\widehat\boldsymbol\beta的强相合性及渐近正态性。

Abstract: Let Y=Xβ₀+U be a truncated linear regression model, where β₀ is a unknown parameter and U is independent of X with mean 0 and unknown cumulative distribution F. the datum （X,Y） is observed only if W≤t（known）. In this paper, β₀ is estimated by Fourier transformation method, and it is shown that the estimate of β₀ is strongly consistent and asymptotically normal.