Linear Bayesian Estimation of Misrecorded Poisson Distribution.

Parameter estimation is an important component of statistical inference, and how to improve the accuracy of parameter estimation is a key issue in research. This paper proposes a linear Bayesian estimation for estimating parameters in a misrecorded Poisson distribution. The linear Bayesian estimation method not only adopts prior information but also avoids the cumbersome calculation of posterior expectations. On the premise of ensuring the accuracy and stability of computational results, we derived the explicit solution of the linear Bayesian estimation. Its superiority was verified through numerical simulations and illustrative examples.

A general averaging method for count data with overdispersion and/or excess zeros in biomedicine.

With the aim of providing better estimation for count data with overdispersion and/or excess zeros, we develop a novel estimation method-optimal weighting based on cross-validation-for the zero-inflated negative binomial model, where the Poisson, negative binomial, and zero-inflated Poisson models are all included as its special cases. To facilitate the selection of the optimal weight vector, a K-fold cross-validation technique is adopted. Unlike the jackknife model averaging discussed in Hansen and Racine (2012), the proposed method deletes one group of observations rather than only one observation to enhance the computational efficiency. Furthermore, we also theoretically prove the asymptotic optimality of the newly developed optimal weighting based on cross-validation method. Simulation studies and three empirical applications indicate the superiority of the presented optimal weighting based on cross-validation method when compared with the three commonly used information-based model selection methods and their model averaging counterparts.

Detecting Structural Change Point in ARMA Models via Neural Network Regression and LSCUSUM Methods.

This study considers the change point testing problem in autoregressive moving average (ARMA) (p,q) models through the location and scale-based cumulative sum (LSCUSUM) method combined with neural network regression (NNR). We estimated the model parameters via the NNR method based on the training sample, where a long AR model was fitted to obtain the residuals. Then, we selected the optimal model orders p and q of the ARMA models using the Akaike information criterion based on a validation set. Finally, we used the forecasting errors obtained from the selected model to construct the LSCUSUM test. Extensive simulations and their application to three real datasets show that the proposed NNR-based LSCUSUM test performs well.