A Comparison of Four Methods of Estimating the Scale Parameter for the Exponential Distribution

In this paper, the estimators of the scale parameter of the exponential distribution obtained by applying four methods, using complete data, are critically examined and compared. These methods are the Maximum Likelihood Estimator (MLE), the Square-Error Loss Function (BSE), the Entropy Loss Function (BEN) and the Composite LINEX Loss Function (BCL). The performance of these four methods was compared based on three criteria: the Mean Square Error (MSE), the Akaike Information Criterion (AIC), and the Bayesian Information Criterion (BIC). Using Monte Carlo simulation based on relevant samples, the comparisons in this study suggest that the Bayesian method is better than the maximum likelihood estimator with respect to the estimation of the parameter that offers the smallest values of MSE, AIC, and BIC. Confidence intervals were then assessed to test the performance of the methods by comparing the 95% CI and average lengths (AL) for all estimation methods, showing that the Bayesian methods still offer the best performance in terms of generating the smallest ALs.

Comparison of six statistical approaches in the selection of appropriate fish growth models

The performance of six statistical approaches,which can be used for selection of the best model to describe the growth of individual fish,was analyzed using simulated and real length-at-age data.The six approaches include coefficient of determination(R2),adjusted coefficient of determination(adj.-R2),root mean squared error(RMSE),Akaike's information criterion(AIC),bias correction of AIC(AICc) and Bayesian information criterion(BIC).The simulation data were generated by five growth models with different numbers of parameters.Four sets of real data were taken from the literature.The parameters in each of the five growth models were estimated using the maximum likelihood method under the assumption of the additive error structure for the data.The best supported model by the data was identified using each of the six approaches.The results show that R2 and RMSE have the same properties and perform worst.The sample size has an effect on the performance of adj.-R2,AIC,AICc and BIC.Adj.-R2 does better in small samples than in large samples.AIC is not suitable to use in small samples and tends to select more complex model when the sample size becomes large.AICc and BIC have best performance in small and large sample cases,respectively.Use of AICc or BIC is recommended for selection of fish growth model according to the size of the length-at-age data.

The improved local linear prediction of chaotic time series

Based on the Bayesian information criterion, this paper proposes the improved local linear prediction method to predict chaotic time series. This method uses spatial correlation and temporal correlation simultaneously. Simulation results show that the improved local linear prediction method can effectively make multi-step and one-step prediction of chaotic time series and the multi-step prediction performance and one-step prediction accuracy of the improved local linear prediction method are superior to those of the traditional local linear prediction method.

Polynomial network autoregressive models with divergent orders

We propose a novel polynomial network autoregressive model by incorporating higher-order connected relationships to simultaneously model the effects of both direct and indirect connections. A quasimaximum likelihood estimation method is proposed to estimate the unknown influence parameters, and we demonstrate its consistency and asymptotic normality without imposing any distribution assumption. Moreover,an extended Bayesian information criterion is set for order selection with a divergent upper order. The application of the proposed polynomial network autoregressive model is demonstrated through both the simulation and the real data analysis.

Retrieved lymph nodes from different anatomic groups in gastric cancer:a proposed optimal number,comparison with other nodal classification strategies and its impact on prognosis

Background:The optimal number of retrieved lymph nodes(LNs)in gastric cancer(GC)is still debatable and previ-ous studies proposing new classification alternatives mostly focused on the number of retrieved LNs without proper consideration on the anatomic nodal groups’location.Here,we assessed the impact of retrieved LNs from different nodal location groups on the survival of GC patients.Methods:Stage I-III gastric cancer patients who had radical gastrectomy were investigated.LN grouping was deter-mined according to the 13th edition of the JCGC.The optimal cut-off values of retrieved LNs in different LN groups(Group 1 and 2)were calculated,based on which a proposed nodal classification(rN)simultaneously accounting the optimal number and location of retrieved LNs was proposed.The performance of rN was then compared to that of LN ratio,log-odds of metastatic LNs(LODDs)and the 8th edition of the Union for International Cancer Control/American Joint Committee on Cancer(UICC/AJCC)N classification.Results:The optimal cut-off values for Group 1 and 2 were 13 and 9,respectively.The 5-year overall survival(OS)was higher for patients in retrieved Group 1 LNs>13(vs.Group 1 LNs≤13,63.2%vs.57.9%,P=0.005)and retrieved Group 2 LNs>9(vs.Group 2 LNs≤9,72.5%vs.60.7%,P=0.009).Patients staged as pN0-3b were sub classified using this Group 1 and 2 nodal analogy.The OS of pN0-N2 patients in retrieved Group 1 LNs>13 or Group 2 LNs>9 were superior to those in retrieved Group 1 LNs≤13 and Group 2 LNs≤9(All P<0.05);except for pN3 patients.The rN clas-sification was formulated and demonstrated better 5-year OS prognostication performance as compared to the LNR,LODDs,and the 8th UICC/AJCC N staging system.Conclusions:The retrieval of>13 and>9 LNs for Group 1 and Group 2,respectively,could represent an alternative lymph node retrieval approach in radical gastrectomy for more precise survival prognostication and minimizing staging migration,especially if>16 LNs is found to be difficult.

Sequential profile Lasso for ultra-high-dimensional partially linear models

In this paper, we study ultra-high-dimensional partially linear models when the dimension of thelinear predictors grows exponentially with the sample size. For the variable screening, we proposea sequential profile Lasso method (SPLasso) and show that it possesses the screening property.SPLasso can also detect all relevant predictors with probability tending to one, no matter whetherthe ultra-high models involve both parametric and nonparametric parts. To select the best subset among the models generated by SPLasso, we propose an extended Bayesian information criterion (EBIC) for choosing the final model. We also conduct simulation studies and apply a realdata example to assess the performance of the proposed method and compare with the existingmethod.