题目
题目

BU.232.630.F3.SP25 sample quiz 1

单项选择题

Consider the nonlinear model yt=θ1x θ2 t +εt where the sample data (y1,x1),...,(yT,xT) are i.i.d. and E(εt|xt)=0. We know that the nonlinear least square estimator is asymptotically normal, that is √ T ( ˆ θ NL−θ0) d ⤳ N(0,A −1 0 Ω0A −1 0 ) To compute the standard errors we need to estimate A0, ˆ A 0=[ 1 T ∑ T t=1 ˆ θ 1x 2 ˆ θ 2 t log(xt) 1 T ∑ T t=1 ˆ θ 1x 2 ˆ θ 2 t log(xt) 1 T ∑ T t=1 ˆ θ 2 1 x 2 ˆ θ 2 t log2(xt)] What is the missing entry in the matrix ˆ A 0?

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思路分析
Question restatement: We are given a nonlinear model y_t = θ1 x_t^{?} + θ2 t + ε_t (the exact functional form is obscured in the prompt), with i.i.d. sample data and E(ε_t | x_t) = 0. The nonlinear least squares estimator is asymptotically normal with a specific sandwich form for the variance, involving the matrix A0. The task is to identify the missing entry in the estimated A0 matrix, where A0 is defined in terms of derivatives of the model with respect to the parameters and the data, evaluated at the true parameter values. The provided answer option is a single entry that is claimed to fill the missing spot in A0: 1 T ∑ T t=1 x 2 ˆ θ 2 t Option analysis: - Restating the option: The candidate missing entry i......Login to view full explanation

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类似问题

Consider the nonlinear model yt=θ1x θ2 t +εt where the sample data (y1,x1),...,(yT,xT) are i.i.d. and E(εt|xt)=0. We know that the nonlinear least square estimator is asymptotically normal, that is √ T ( ˆ θ NL−θ0) d ⤳ N(0,A −1 0 Ω0A −1 0 ) To compute the standard errors we need to estimate Ω0, ˆ Ω 0=[ 1 T ∑ T t=1 ˆ ε 2 t x 2 ˆ θ 2 t 1 T ∑ T t=1 ˆ ε 2 t ˆ θ 1x 2 ˆ θ 2 t log(xt) 1 T ∑ T t=1 ˆ ε 2 t ˆ θ 2 1 x 2 ˆ θ 2 t log2(xt)] What is the missing entry in the matrix ˆ Ω 0?

Consider the nonlinear model yt=θ1x θ2 t +εt where the sample data (y1,x1),...,(yT,xT) are i.i.d. and E(εt|xt)=0. We know that the nonlinear least square estimator is asymptotically normal, that is √ T ( ˆ θ NL−θ0) d ⤳ N(0,A −1 0 Ω0A −1 0 ) To compute the standard errors we need to estimate A0, ˆ A 0=[ 1 T ∑ T t=1 x 2 ˆ θ 2 t 1 T ∑ T t=1 ˆ θ 1x 2 ˆ θ 2 t log(xt) 1 T ∑ T t=1 ˆ θ 1x 2 ˆ θ 2 t log(xt) ] What is the missing entry in the matrix ˆ A 0?

Consider the nonlinear model yt=θ1x θ2 t +εt where the sample data (y1,x1),...,(yT,xT) are i.i.d. and E(εt|xt)=0. We know that the nonlinear least square estimator is asymptotically normal, that is √ T ( ˆ θ NL−θ0) d ⤳ N(0,A −1 0 Ω0A −1 0 ) To compute the standard errors we need to estimate A0, ˆ A 0=[ 1 T ∑ T t=1 ˆ θ 1x 2 ˆ θ 2 t log What is the missing entry in the matrix 𝐴 ̂ 0 ?

Consider the nonlinear model 𝑦 𝑡 = 𝜃 1 𝑥 𝑡 𝜃 2 𝑧 𝑡 + 𝜀 𝑡 where the sample data ( 𝑦 1 , 𝑥 1 , 𝑧 1 ) , . . . , ( 𝑦 𝑇 , 𝑥 𝑇 , 𝑧 𝑇 ) are i.i.d. and 𝐸 ( 𝜀 𝑡 | 𝑥 𝑡 , 𝑧 𝑡 ) = 0 . We know that the nonlinear least square estimator is asymptotically normal, that is ⤳ 𝑇 ( 𝜃 ̂ 𝑁 𝐿 − 𝜃 0 ) ⤳ 𝑑 𝑁 ( 0 , 𝐴 0 − 1 𝛺 0 𝐴 0 − 1 ) To compute the standard errors we need to estimate 𝐴 0 , 𝐴 ̂ 0 = [ 1 𝑇 ∑ 𝑡 = 1 𝑇 𝑥 𝑡 2 𝜃 ̂ 1 2 ( 𝑥 𝑡 − 1 ) 𝜃 ̂ 2 2 𝑧 𝑡 1 𝑇 ∑ 𝑡 = 1 𝑇 𝑥 𝑡 𝜃 ̂ 1 2 𝑥 𝑡 − 1 𝑧 𝑡 𝜃 ̂ 2 2 𝑧 𝑡 − 1 1 𝑇 ∑ 𝑡 = 1 𝑇 𝑥 𝑡 𝜃 ̂ 1 2 𝑥 𝑡 − 1 𝑧 𝑡 𝜃 ̂ 2 2 𝑧 𝑡 − 1 ] What is the missing entry in the matrix 𝐴 ̂ 0 ?

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