A moving average Cholesky factor model in covariance modeling for composite quantile regression with longitudinal data

Lv, Jing; Guo, Chaohui; Yang, Hu; Li, Yalian

doi:10.1016/j.csda.2017.02.015

Cited by 12 publications

(4 citation statements)

References 30 publications

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“…Hence

is crucial in putting the forecast into practice. Since

is assumed to follow the Gaussian distribution:

, SCACD generates

via Cholesky decomposition [ 14 , 15 ], resulting in efficient sampling. Positive semidefiniteness is necessary for Cholesky decomposition,

is multiplied by

.…”

Section: Methodsmentioning

confidence: 99%

“…The main works are as follows: For Challenges 1 and 2, this paper first extracts sub-sequences by sliding window, secondly extends time points to larger scale sequences, then finally, designs an adaptive estimation method to encode the latent variables corresponding sub-sequences, and finally uses causal convolutional networks to predict future latent variables. For Challenge 3, SCACD employs the Cholesky [ 14 , 15 ] decomposition of the covariance matrix to maintain the temporal dependence, thus generating the latent variables. Based on the latent variables, SCACD infers the prior distribution of the observed variables and generates an observation sequence with the same approach.…”

Section: Introductionmentioning

confidence: 99%

“…For Challenge 3, SCACD employs the Cholesky [ 14 , 15 ] decomposition of the covariance matrix to maintain the temporal dependence, thus generating the latent variables. Based on the latent variables, SCACD infers the prior distribution of the observed variables and generates an observation sequence with the same approach.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

State Causality and Adaptive Covariance Decomposition Based Time Series Forecasting

Wang

Geng

et al. 2023

Sensors

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Time series forecasting is a very vital research topic. The scale of time series in numerous industries has risen considerably in recent years as a result of the advancement of information technology. However, the existing algorithms pay little attention to generating large-scale time series. This article designs a state causality and adaptive covariance decomposition-based time series forecasting method (SCACD). As an observation sequence, the majority of time series is generated under the influence of hidden states. First, SCACD builds neural networks to adaptively estimate the mean and covariance matrix of latent variables; Then, SCACD employs causal convolution to forecast the distribution of future latent variables; Lastly, to avoid loss of information, SCACD applies a sampling approach based on Cholesky decomposition to generate latent variables and observation sequences. Compared to existing outstanding time series prediction models on six real datasets, the model can achieve long-term forecasting while also being lighter, and the forecasting accuracy is improved in the great majority of the prediction tasks.

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“…Hence

is crucial in putting the forecast into practice. Since

is assumed to follow the Gaussian distribution:

, SCACD generates

via Cholesky decomposition [ 14 , 15 ], resulting in efficient sampling. Positive semidefiniteness is necessary for Cholesky decomposition,

is multiplied by

.…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

State Causality and Adaptive Covariance Decomposition Based Time Series Forecasting

Wang

Geng

et al. 2023

Sensors

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show abstract

“…[16] developed an efficient parameter estimation via MCD for quantile regression with longitudinal data. [17] further proposed a moving average Cholesky factor model, which is transformed from MCD, in covariance modeling for composite quantile regression with longitudinal data. Then, [18] carried out smoothed empirical likelihood inference via MCD for quantile varying coefficient models with longitudinal data.…”

Section: Introductionmentioning

confidence: 99%

ESL-Based Robust Estimation for Mean-Covariance Regression with Longitudinal Data

Lu¹,

Xue²,

Cai³

2020

OJS

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When longitudinal data contains outliers, the classical least-squares approach is known to be not robust. To solve this issue, the exponential squared loss (ESL) function with a tuning parameter has been investigated for longitudinal data. However, to our knowledge, there is no paper to investigate the robust estimation procedure against outliers within the framework of mean-covariance regression analysis for longitudinal data using the ESL function. In this paper, we propose a robust estimation approach for the model parameters of the mean and generalized autoregressive parameters with longitudinal data based on the ESL function. The proposed estimators can be shown to be asymptotically normal under certain conditions. Moreover, we develop an iteratively reweighted least squares (IRLS) algorithm to calculate the parameter estimates, and the balance between the robustness and efficiency can be achieved by choosing appropriate data adaptive tuning parameters. Simulation studies and real data analysis are carried out to illustrate the finite sample performance of the proposed approach.

show abstract

Generalized partial linear models with nonignorable dropouts

Shao

Wang

2021

Metrika

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A moving average Cholesky factor model in covariance modeling for composite quantile regression with longitudinal data

Cited by 12 publications

References 30 publications

State Causality and Adaptive Covariance Decomposition Based Time Series Forecasting

State Causality and Adaptive Covariance Decomposition Based Time Series Forecasting

ESL-Based Robust Estimation for Mean-Covariance Regression with Longitudinal Data

Generalized partial linear models with nonignorable dropouts

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