Bias‐reduced marginal Akaike information criteria based on a Monte Carlo method for linear mixed‐effects models

In linear mixed‐effects (LME) models, if a fitted model has more random‐effect terms than the true model, a regularity condition required in the asymptotic theory may not hold. In such cases, the marginal Akaike information criterion (AIC) is positively biased for (?2) times the expected log‐likelihood. The asymptotic bias of the maximum log‐likelihood as an estimator of the expected log‐likelihood is evaluated for LME models with balanced design in the context of parameter‐constrained models. Moreover, bias‐reduced marginal AICs for LME models based on a Monte Carlo method are proposed. The performance of the proposed criteria is compared with existing criteria by using example data and by a simulation study. It was found that the bias of the proposed criteria was smaller than that of the existing marginal AIC when a larger model was fitted and that the probability of choosing a smaller model incorrectly was decreased.     

The cluster correlation-network support vector machine for high-dimensional binary classification

ABSTRACT

Identifying homogeneous subsets of predictors in classification can be challenging in the presence of high-dimensional data with highly correlated variables. We propose a new method called cluster correlation-network support vector machine (CCNSVM) that simultaneously estimates clusters of predictors that are relevant for classification and coefficients of penalized SVM. The new CCN penalty is a function of the well-known Topological Overlap Matrix whose entries measure the strength of connectivity between predictors. CCNSVM implements an efficient algorithm that alternates between searching for predictors’ clusters and optimizing a penalized SVM loss function using Majorization–Minimization tricks and a coordinate descent algorithm. This combining of clustering and sparsity into a single procedure provides additional insights into the power of exploring dimension reduction structure in high-dimensional binary classification. Simulation studies are considered to compare the performance of our procedure to its competitors. A practical application of CCNSVM on DNA methylation data illustrates its good behaviour.     

A computational bootstrap procedure to compare two dependent time series

It is an important problem to compare two time series in many applications. In this paper, a computational bootstrap procedure is proposed to test if two dependent stationary time series have the same autocovariance structures. The blocks of blocks bootstrap on bivariate time series is employed to estimate the covariance matrix which is necessary in order to construct the proposed test statistic. Without much additional effort, the bootstrap critical values can also be computed as a byproduct from the same bootstrap procedure. The asymptotic distribution of the test statistic under the null hypothesis is obtained. A simulation study is conducted to examine the finite sample performance of the test. The simulation results show that the proposed procedure with the bootstrap critical values performs well empirically and is especially useful when time series are short and non-normal. The proposed test is applied to an analysis of a real data set to understand the relationship between the input and output signals of a chemical process.     

A bivariate geometric distribution allowing for positive or negative correlation

In this paper, we propose a new bivariate geometric model, derived by linking two univariate geometric distributions through a specific copula function, allowing for positive and negative correlations. Some properties of this joint distribution are presented and discussed, with particular reference to attainable correlations, conditional distributions, reliability concepts, and parameter estimation. A Monte Carlo simulation study empirically evaluates and compares the performance of the proposed estimators in terms of bias and standard error. Finally, in order to demonstrate its usefulness, the model is applied to a real data set.     

Selecting better process based on difference statistic using double sampling plan

Supplier management plays an important role in the quality improvement process. Recently, supplier selection has received much attention in many production industries. In this paper, we propose a double sampling plan for selecting a better supplier comparing two suppliers with linear profiles. The difference test statistic based on the process yield index S_pkA is used to determine the optimal parameters of the proposed double sampling plan. The efficiency of the proposed sampling plan is compared with the existing single sampling plan.     

Modeling binary responses with stochastic covariates

In a traditional binary regression model, covariates are assumed to be fixed by design. In practice, however, they are most likely to be stochastic and non-normally distributed. We develop modified maximum likelihood estimators for such situations. We show that these estimators are more efficient than the traditional binary regression estimators and robust to data anomalies. We illustrate our results using a real life example.     

Calculation of Phase 2 dose-finding study sample size for reliable Phase 3 dose selection

Sample sizes of Phase 2 dose-finding studies, usually determined based on a power requirement to detect a significant dose–response relationship, will generally not provide adequate precision for Phase 3 target dose selection. We propose to calculate the sample size of a dose-finding study based on the probability of successfully identifying the target dose within an acceptable range (e.g., 80%–120% of the target) using the multiple comparison and modeling procedure (MCP-Mod). With the proposed approach, different design options for the Phase 2 dose-finding study can also be compared. Due to inherent uncertainty around an assumed true dose–response relationship, sensitivity analyses to assess the robustness of the sample size calculations to deviations from modeling assumptions are recommended. Planning for a hypothetical Phase 2 dose-finding study is used to illustrate the main points. Codes for the proposed approach is available at https://github.com/happysundae/posMCPMod .     

亲缘选择能否印证《孟子》之四端说

亲缘选择是一条影响深远的自然法则,也是当代伦理学不得不面对的重要课题。中外学界对亲缘选择与孟子学说的关联均有所关注,也有学者认为亲缘选择能为孟子学说提供强有力的支持。四端说是孟子伦理学体系的核心,故此可设如下的议题：亲缘选择能否印证《孟子》之四端说？根据《孟子》四端说的文本以及历代解读的分析,所得结论是：亲缘选择不止对四端说起不到印证作用,而更迫使当代诠释者对于许多四端说的解读,降低其置信度。与亲缘选择相符的四端说解读,应该重视文化的熏陶作用,应该承认四端为人禽共有,也不该将四端设为纯粹形上对象。亲缘选择对孟子学说的印证效能,需在四端说之外去寻找。