Asymptotic normality and strong consistency of maximum quasi-likelihood estimates in generalized linear models

Yin, Chuancun; Lincheng, Zhao; Cheng-dong, Wei

doi:10.1007/s11425-004-5169-x

Cited by 28 publications

(14 citation statements)

References 16 publications

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“…Remark Condition (C1) is common in MQLE,

{sup}_{i ⩾ 1} false‖ X_{i} false‖ < \infty

is necessary due to the nonlinearity of

boldh

(see Yin et al ., ), and

{\underset{true̲}{λ}}_{n}

is a sufficient condition for the consistency of MQLE

{\overset{true˜}{β}}_{n}

(see Chen et al ., ). Conditions (C4) and (C5) are for the asymptotic normality of estimates with adaptive designs (see also Lai and Wei, ).…”

Section: Methodsmentioning

confidence: 99%

“…Under Conditions (C1)-(C3), Yin, Zhao and Wei (2006); Yin, Zhang and Zhao (2008) showed that the convergence rate of the MQLE βn is:…”

Section: Adaptive Shrinkage Estimatementioning

confidence: 99%

“…is a sequence of martingale differences with respect to {F i , i ≥ 1}, and S n (β 0 ) is a sum of martingale differences. By Taylor series expansion, there exists βn , which lies between β and β 0 , such that Yin, Zhao and Wei (2006) showed that…”

Section: Supplementary Materialsmentioning

confidence: 99%

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Sequential adaptive variables and subject selection for GEE methods

2019

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Modeling correlated or highly stratified multiple-response data becomes a common data analysis task due to modern data monitoring facilities and methods. Generalized estimating equations (GEE) is one of the popular statistical methods for analyzing this kind of data. In this paper, we present a sequential estimation procedure for obtaining GEE-based estimates. In addition to the conventional random sampling, the proposed method features adaptive subject recruiting and variable selection. Moreover, we equip our method with an adaptive shrinkage property so that it can decide the effective variables during the estimation procedure and build a confidence set with a pre-specified precision for the corresponding parameters. In addition to the statistical properties of the proposed procedure, we assess our method using both simulated data and real data sets.

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“…Remark Condition (C1) is common in MQLE,

{sup}_{i ⩾ 1} false‖ X_{i} false‖ < \infty

is necessary due to the nonlinearity of

boldh

(see Yin et al ., ), and

{\underset{true̲}{λ}}_{n}

is a sufficient condition for the consistency of MQLE

{\overset{true˜}{β}}_{n}

(see Chen et al ., ). Conditions (C4) and (C5) are for the asymptotic normality of estimates with adaptive designs (see also Lai and Wei, ).…”

Section: Methodsmentioning

confidence: 99%

“…Under Conditions (C1)-(C3), Yin, Zhao and Wei (2006); Yin, Zhang and Zhao (2008) showed that the convergence rate of the MQLE βn is:…”

Section: Adaptive Shrinkage Estimatementioning

confidence: 99%

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Sequential adaptive variables and subject selection for GEE methods

2019

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“…The ANN models employed in this study have a hidden layer with a sigmoid activation function, which is often used in biology for the characteristics of smoothness and ease of derivation. The application of the ANN models in the environment research field generally includes: estimating the reference evapotranspiration (ET0) in a river ecosystem [46], predicting the total phosphorus (TP) concentration in the overlying water of the Huai River based on hydrological and hydrodynamic parameters [47], predicting the total dissolved gas (TDG) downstream of spillways of dams [48], and predicting the algae distribution in the large shallow lake based on wind speed index [49]. However, there are few studies on the application of ANN to SD prediction.…”

Section: Artificial Neural Networkmentioning

confidence: 99%

Water Transparency Prediction of Plain Urban River Network: A Case Study of Yangtze River Delta in China

Liao

Shu

et al. 2021

Sustainability

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Water transparency is commonly used to indicate the combined effect of hydrodynamics and the aquatic environment on water quality throughout a river network. However, how water transparency responds to these indicators still needs to be explored, especially their complicated nonlinear relationship; thus, this study represents an analysis of the Suzhou civil river network. Using an artificial neural network (ANN) hydrological model and a multiple linear model (MLR) with in-situ data between 2013–2019, we investigated the Suzhou River’s sensitivity to the six factors and water transparency, which including flow velocity and data from five categories of water-quality monitoring data: total suspended matter (TSS), water temperature (TE), dissolved oxygen (DO), chlorophyll (Chl) and chemical oxygen demand (COD). The results suggest that the ANN model can achieve better performance than the MLR model. Furthermore, results also show a well-established correlation between enhanced hydrodynamics and improved water transparency when the flow velocity ranged from 0.22 to 0.45 m/s. Overall, COD is a vital factor for the SD prediction because including the COD can see a notable improvement in the ANN model (with a correlation coefficient of 0.918). This study demonstrates that the ANN model with hydrodynamic and water quality parameters can achieve a better prediction of water transparency than other discussed models for a coastal plain urban river network.

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“…The moments condition ( 9) is crucial to explain the finite moments behavior of the exponential families. This condition means, in most cases, that there is a compact subset K, not depending on n, of the interior of Θ such that u( Yin et al (2006) for establishing the strongly consistent maximum quasi-likelihood estimates.…”

Section: Regularity Conditionsmentioning

confidence: 99%

Law of the Iterated Logarithm and Model Selection Consistency for GLMs with Independent and Dependent Responses

Yang,

Song,

Zhang

2019

Preprint

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We study the law of the iterated logarithm (LIL) for the maximum likelihood estimation of the parameters in the generalized linear models with independent or weakly dependent (ρ-mixing, m-dependent) responses under mild conditions. The LIL is useful to derive the asymptotic bounds for the discrepancy between the empirical log-likelihood function and the true log-likelihood. As the application of the LIL, the strong consistency of some penalized likelihood based model selection criteria can be shown. Under some regularity conditions, the model selection criterion will be helpful to select the simplest correct model almost surely when the penalty term increases with model dimension and the penalty term has an order higher than O(loglogn) but lower than O(n). Simulation studies are implemented to verify the selection consistency of BIC.

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Asymptotic normality and strong consistency of maximum quasi-likelihood estimates in generalized linear models

Cited by 28 publications

References 16 publications

Sequential adaptive variables and subject selection for GEE methods

Sequential adaptive variables and subject selection for GEE methods

Water Transparency Prediction of Plain Urban River Network: A Case Study of Yangtze River Delta in China

Law of the Iterated Logarithm and Model Selection Consistency for GLMs with Independent and Dependent Responses

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