Abstract
In this paper, we consider the parameter estimation problem of linear regression model when the auxiliary information can be denoted by moment restrictions. We use the weighted least squares method to estimate the model parameters and to obtain the weights based on the auxiliary information by using the empirical likelihood method. The limiting distribution of the estimator is established, and the simulation studies are carried out to demonstrate the feasibility of our theoretical results.
Highlights
Suppose (X1, Y1), (X2, Y2), . . . , (Xn, Yn) is an independent and identically distributed random sample from the following regression model: Yi ατXi + εi, i 1, 2, . . . , n, (1)Linear regression model is widely used in empirical work in economics, medicine, and many other disciplines due to its simple form
Observe that auxiliary information can be used to increase the precision of estimators in sample surveys. erefore, Chambers and Dunstan [1] propose a simple method for estimating the population distribution functions which allows auxiliary population information to be directly incorporated into the estimation process
We discuss how to use auxiliary information to improve the efficiency of regression model parameter estimation when auxiliary information exists
Summary
Suppose (X1, Y1), (X2, Y2), . . . , (Xn, Yn) is an independent and identically distributed random sample from the following regression model: Yi ατXi + εi, i 1, 2, . . . , n,. (Xn, Yn) is an independent and identically distributed random sample from the following regression model: Yi ατXi + εi, i 1, 2, . Empirical likelihood method is widely used in statistical inference of various models. Empirical likelihood method is first proposed by. Empirical likelihood method is used for statistical inference of various models Some statisticians have begun to pay attention to the statistical inference of semiparametric regression model with constraints (see Amini and Roozbeh [16], Roozbeh and Hamzah [17], and Roozbeh et al [18]). Convergence “almost surely” is written as “a.s.” A ⊗ B denotes the Kronecker product of matrices A and B, ‖ · ‖ denotes Euclidean norm of the matrix or vector, Aτ denotes the transposition of the matrix or the column vector A, op(1) denotes a random variable that converges to zero in probability, and Op(1) denotes a random variable that is bounded in probability
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