The second-order bias and mean squared error of nonlinear estimators

Rilstone, Paul; Srivastava, V. K.; Ullah, Aman

doi:10.1016/0304-4076(96)89457-7

Cited by 113 publications

(111 citation statements)

References 12 publications

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“…In this paper, we extend the second-order bias and MSE results of Rilstone et al (1996) for the time series dependent observations. These results provide a unified way of developing the properties of a given class of estimators in the linear and nonlinear time series models.…”

Section: Introductionmentioning

confidence: 85%

“…To obtain the second-order bias and MSE ofβ, the assumption of A to C in Rilstone et al (1996) are assumed to hold along with the consistency ofβ and we follow their notations.…”

Section: Second-order Bias and Msementioning

confidence: 99%

“…Then the stochastic expansion ofβ, up to O P ¡ T −3/2 ¢ , in Rilstone et al (1996) in which X = E (X) denotes the expectation of a random vector X, H i = ∇ i ψ T , i = 1, 2, 3, …”

Section: Second-order Bias and Msementioning

confidence: 99%

“…However, most of these works are for some specific estimators and there is little with the dependent observations for nonlinear cases, although see Cordeiro and Klein (1994) and Linton (1997). Recently, Rilstone et al (1996) developed the large-n second-order bias and mean squared error (MSE) of a class of nonlinear estimators. Nevertheless, their results are for the i.i.d.…”

Section: Introductionmentioning

confidence: 99%

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The second-order bias and mean squared error of estimators in time-series models

Bao

Ullah

2007

Journal of Econometrics

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We develop the analytical results on the second-order bias and mean squared error (MSE) of estimators in time series. These results provide a unified approach to developing the properties of a large class of estimators in the linear and nonlinear time series models and they are valid for both the normal and non-normal sample of observations, and where the regressors are stochastic. The estimators included are the generalized method of moments, maximum likelihood, least squares, and other extremum estimators. Our general results are applied to a wide variety of econometric models. Numerical results for some of these models are presented.

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Section: Introductionmentioning

confidence: 85%

“…To obtain the second-order bias and MSE ofβ, the assumption of A to C in Rilstone et al (1996) are assumed to hold along with the consistency ofβ and we follow their notations.…”

Section: Second-order Bias and Msementioning

confidence: 99%

“…Then the stochastic expansion ofβ, up to O P ¡ T −3/2 ¢ , in Rilstone et al (1996) in which X = E (X) denotes the expectation of a random vector X, H i = ∇ i ψ T , i = 1, 2, 3, …”

Section: Second-order Bias and Msementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The second-order bias and mean squared error of estimators in time-series models

Bao

Ullah

2007

Journal of Econometrics

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“…Koenker et al (1994) and Rilstone, Srivastava, and Ullah (1996) give some higher order variance and bias calculations for special cases of GMM. Corcoran (1998) showed that in a class of minimum discrepancy estimators, EL has the only objective function that is Bartlett correctable.…”

Section: Introductionmentioning

confidence: 99%

Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators

Newey¹,

Smith²

2004

Econometrica

658

840

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In an effort to improve the small sample properties of generalized method of moments (GMM) estimators, a number of alternative estimators have been suggested. These include empirical likelihood (EL), continuous updating, and exponential tilting estimators. We show that these estimators share a common structure, being members of a class of generalized empirical likelihood (GEL) estimators. We use this structure to compare their higher order asymptotic properties. We find that GEL has no asymptotic bias due to correlation of the moment functions with their Jacobian, eliminating an important source of bias for GMM in models with endogeneity. We also find that EL has no asymptotic bias from estimating the optimal weight matrix, eliminating a further important source of bias for GMM in panel data models. We give bias corrected GMM and GEL estimators. We also show that bias corrected EL inherits the higher order property of maximum likelihood, that it is higher order asymptotically efficient relative to the other bias corrected estimators.JEL Classification: C13, C30

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State Dependence and Heterogeneity in Health Using a Bias‐corrected Fixed‐effects Estimator

Carro

Traferri

2012

J of Applied Econometrics

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SUMMARYThis paper estimates a dynamic ordered probit model of self-assessed health with two fixed effects: one in the linear index equation and one in the cut-points. This robustly controls for heterogeneity in unobserved health status and in reporting behavior, although we cannot separate both sources of heterogeneity. We find important state dependence effects, and small but significant effects of income and other socioeconomic variables. Having dynamics and flexibly accounting for unobserved heterogeneity matters for those estimates. We also contribute to the bias correction literature in nonlinear panel models by comparing and applying two of the existing proposals to our model.

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The second-order bias and mean squared error of nonlinear estimators

Cited by 113 publications

References 12 publications

The second-order bias and mean squared error of estimators in time-series models

The second-order bias and mean squared error of estimators in time-series models

Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators

State Dependence and Heterogeneity in Health Using a Bias‐corrected Fixed‐effects Estimator

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