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When people in a society want to make inference about some parameter, each person would potentially want to use data collected by other people. Information (data) exchange in social contexts is usually costly, so to make sound statistical decisions, people need to compromise between benefits and costs of information acquisition. Conflicts of interests and coordination will arise. Classical statistics does not consider peoples interaction in the data collection process. To address this ignorance, this work explores multi-agent Bayesian inference problems with a game theoretic social network model. Bearing our interest in aggregate inference at the societal level, we propose a new concept finite population learning to address whether with high probability, a large fraction of people can make good inferences. Serving as a foundation, this concept enables us to study the long run trend of aggregate inference quality as population grows.

In this paper, we propose a penalised pseudo-partial likelihood method for variable selection with multivariate failure time data with a growing number of regression coefficients. Under certain regularity conditions, we show the consistency and asymptotic normality of the penalised likelihood estimators. We further demonstrate that, for certain penalty functions with proper choices of regularisation parameters, the resulting estimator can correctly identify the true model, as if it were known in advance. Based on a simple approximation of the penalty function, the proposed method can be easily carried out with the NewtonRaphson algorithm. We conduct extensive Monte Carlo simulation studies to assess the finite sample performance of the proposed procedures. We illustrate the proposed method by analysing a dataset from the Framingham Heart Study.

This paper studies a weighted local linear regression smoother for longitudinal/clustered data, which takes a form similar to the classical weighted least squares estimate. As a hybrid of the methods of Chen and Jin (2005) and Wang (2003), the proposed local linear smoother maintains the advantages of both methods in computational and theoretical simplicity, variance minimization and bias reduction. Moreover, the proposed smoother is optimal in the sense that it attains linear minimax efficiency when the within-cluster correlation is correctly specified. In the special case that the joint density of covariates in a cluster exists and is continuous, any working within-cluster correlation would lead to linear minimax efficiency for the proposed method.

Statistical estimation and inference for marginal hazard models with varying coefficients for multivariate failure time data are important subjects in survival analysis. A local pseudo-partial likelihood procedure is proposed for estimating the unknown coefficient functions. A weighted average estimator is also proposed in an attempt to improve the efficiency of the estimator. The consistency and asymptotic normality of the proposed estimators are established and standard error formulas for the estimated coefficients are derived and empirically tested. To reduce the computational burden of the maximum local pseudo-partial likelihood estimator, a simple and useful one-step estimator is proposed. Statistical properties of the one-step estimator are established and simulation studies are conducted to compare the performance of the one-step estimator to that of the maximum local pseudo-partial likelihood estimator. The