Optimal designs for regression models using the second-order least squares estimator

Yin, Yue; Zhou, Julie

doi:10.5705/ss.202015.0285

Cited by 3 publications

(6 citation statements)

References 17 publications

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“…The proof of Theorem 2 is in the Appendix. The results in Theorem 2 are consistent with the numerical results in Gao and Zhou (2017) and Yin and Zhou (2017). Notice that Gao and Zhou (2017) gave the results about the number of support points for D-optimal designs based on the moment theory, but Theorem 2 generalizes the results for both A-and D-optimal designs based on the equivalence results.…”

Section: Polynomial Modelssupporting

confidence: 80%

“…Proof of Lemma 1: From the fact that C = CC and φ A (ξ, θ 0 ) = tr (C B −1 (ξ, θ 0 )) (Yin and Zhou, 2017), we have…”

Section: Appendix: Proofsmentioning

confidence: 99%

“…with Yin and Zhou (2017) while Gao and Zhou (2017) gives a characterization of φ D (ξ, θ 0 ). Those results are stated in Lemmas 1 and 2 below.…”

Section: Optimality Criteriamentioning

confidence: 99%

“…For instance, knowing the number of support points in optimal designs can simplify the numerical determination of optimal designs. Gao and Zhou (2017) and Yin and Zhou (2017) have commented the number of support points in optimal designs under SLSE for various models based on their numerical results. Let n A , n c and n D denote the minimal number of support points in ξ * A , ξ * c and ξ * D , respectively.…”

Section: Number Of Support Points In Optimal Designsmentioning

confidence: 99%

“…Gao and Zhou (2017) applied the CVX program in MATLAB (Grant and Boyd, 2013) for finding the D-optimal designs through the moments of the distribution of x, and their methods can be applied for univariate polynomial and trigonometric regression models. Yin and Zhou (2017) studied and characterized A-optimal designs under the SLSE and developed a numerical algorithm via semidefinite programming (Sturm, 1999).…”

Section: Introductionmentioning

confidence: 99%

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Properties of optimal regression designs under the second-order least squares estimator

Yeh

Zhou

2019

Stat Papers

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We investigate properties of optimal designs under the second-order least squares estimator (SLSE) for linear and nonlinear regression models. First we derive equivalence theorems for optimal designs under the SLSE. We then obtain the number of support points in A-, c-and D-optimal designs analytically for several models. Using a generalized scale invariance concept we also study the scale invariance property of D-optimal designs. In addition, numerical algorithms are discussed for finding optimal designs. The results are quite general and can be applied for various linear and nonlinear models. Several applications are presented, including results for fractional polynomial, spline regression and trigonometric regression models.

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Section: Polynomial Modelssupporting

confidence: 80%

“…Proof of Lemma 1: From the fact that C = CC and φ A (ξ, θ 0 ) = tr (C B −1 (ξ, θ 0 )) (Yin and Zhou, 2017), we have…”

Section: Appendix: Proofsmentioning

confidence: 99%

“…with Yin and Zhou (2017) while Gao and Zhou (2017) gives a characterization of φ D (ξ, θ 0 ). Those results are stated in Lemmas 1 and 2 below.…”

Section: Optimality Criteriamentioning

confidence: 99%

Section: Number Of Support Points In Optimal Designsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Properties of optimal regression designs under the second-order least squares estimator

Yeh

Zhou

2019

Stat Papers

Self Cite

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Second-Order Least Squares Estimation in Nonlinear Time Series Models with ARCH Errors

Salamh

Wang

2021

Econometrics

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Many financial and economic time series exhibit nonlinear patterns or relationships. However, most statistical methods for time series analysis are developed for mean-stationary processes that require transformation, such as differencing of the data. In this paper, we study a dynamic regression model with nonlinear, time-varying mean function, and autoregressive conditionally heteroscedastic errors. We propose an estimation approach based on the first two conditional moments of the response variable, which does not require specification of error distribution. Strong consistency and asymptotic normality of the proposed estimator is established under strong-mixing condition, so that the results apply to both stationary and mean-nonstationary processes. Moreover, the proposed approach is shown to be superior to the commonly used quasi-likelihood approach and the efficiency gain is significant when the (conditional) error distribution is asymmetric. We demonstrate through a real data example that the proposed method can identify a more accurate model than the quasi-likelihood method.

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Second-Order Least Squares Method for Dynamic Panel Data Models with Application

Salamh

Wang

2021

JRFM

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Management of financial risks and sound decision making rely on the accurate information and predictive models. Drawing useful information efficiently from big data with complex structures and building accurate models are therefore crucial tasks. Most commonly used methods for statistical inference in dynamic panel data models are based on the differencing transformation of data. However, differencing data may cause substantial loss of information, and therefore the subsequent analysis may fail to capture important features in the original level data. This point is demonstrated by a real data example where we use a semiparametrically efficient estimation method on the level data to reach a more favorable model. In particular, we study a second-order least squares approach which is based on the first two conditional moments of the response variable given the explanatory variables. This estimator is root-N consistent and its asymptotic variance reaches a lower bound semiparametric efficiency. Monte Carlo simulations show that this estimator performs favorably in finite sample situations compared to the first-differenced GMM and the random effects pseudo ML estimators. We also propose a new diagnostic test to check the working moments assumption based on the proposed estimator. A real data application is presented to further demonstrate the usage of this method.

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Optimal designs for regression models using the second-order least squares estimator

Cited by 3 publications

References 17 publications

Properties of optimal regression designs under the second-order least squares estimator

Properties of optimal regression designs under the second-order least squares estimator

Second-Order Least Squares Estimation in Nonlinear Time Series Models with ARCH Errors

Second-Order Least Squares Method for Dynamic Panel Data Models with Application

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