基于用户规模的双边平台适应性动态定价策略研究

鉴于交叉网络效应导致用户加入双边平台的效用随用户规模动态变化,提出根据用户规模进行适应性动态定价的策略思想,并运用数值计算方法对该定价策略的效果进行深入研究。首先,引入平台动态竞争建模方法,构建了包含用户规模的双边平台适应性动态定价模型;接着,根据数值计算结果对动态定价与静态定价的效果进行比较;最后,考察了平台竞争主要参数的变化对动态定价策略效果的影响。研究表明：（1）动态定价显著优于静态定价,模型主要参数的取值变动不会改变动态定价具有相对优势这个定性结论;（2）提升服务质量或改变基准用户数不会明显增加动态定价的相对优势,但强交叉网络效应或前瞻性用户都会增强动态定价的相对优势。研究结果有助于平台企业管理者更好地制定平台定价策略。     

Likelihood Ratio Type Two‐Sample Tests for Current Status Data

Abstract. We introduce fully non‐parametric two‐sample tests for testing the null hypothesis that the samples come from the same distribution if the values are only indirectly given via current status censoring. The tests are based on the likelihood ratio principle and allow the observation distributions to be different for the two samples, in contrast with earlier proposals for this situation. A bootstrap method is given for determining critical values and asymptotic theory is developed. A simulation study, using Weibull distributions, is presented to compare the power behaviour of the tests with the power of other non‐parametric tests in this situation.     

Outliers and Patterns of Outliers in Contingency Tables with Algebraic Statistics

Abstract. In this paper, we provide a definition of pattern of outliers in contingency tables within a model‐based framework. In particular, we make use of log‐linear models and exact goodness‐of‐fit tests to specify the notions of outlier and pattern of outliers. The language and some techniques from Algebraic Statistics are essential tools to make the definition clear and easily applicable. We also analyse several numerical examples to show how to use our definitions.     

Estimation of Stratified Mark‐Specific Proportional Hazards Models with Missing Marks

Abstract. An objective of randomized placebo‐controlled preventive HIV vaccine efficacy trials is to assess the relationship between the vaccine effect to prevent infection and the genetic distance of the exposing HIV to the HIV strain represented in the vaccine construct. Motivated by this objective, recently a mark‐specific proportional hazards (PH) model with a continuum of competing risks has been studied, where the genetic distance of the transmitting strain is the continuous ‘mark’ defined and observable only in failures. A high percentage of genetic marks of interest may be missing for a variety of reasons, predominantly because rapid evolution of HIV sequences after transmission before a blood sample is drawn from which HIV sequences are measured. This research investigates the stratified mark‐specific PH model with missing marks where the baseline functions may vary with strata. We develop two consistent estimation approaches, the first based on the inverse probability weighted complete‐case (IPW) technique, and the second based on augmenting the IPW estimator by incorporating auxiliary information predictive of the mark. We investigate the asymptotic properties and finite‐sample performance of the two estimators, and show that the augmented IPW estimator, which satisfies a double robustness property, is more efficient.     

Parametric Inference in Stationary Time Series Models with Dependent Errors

This article is concerned with inference for the parameter vector in stationary time series models based on the frequency domain maximum likelihood estimator. The traditional method consistently estimates the asymptotic covariance matrix of the parameter estimator and usually assumes the independence of the innovation process. For dependent innovations, the asymptotic covariance matrix of the estimator depends on the fourth‐order cumulants of the unobserved innovation process, a consistent estimation of which is a difficult task. In this article, we propose a novel self‐normalization‐based approach to constructing a confidence region for the parameter vector in such models. The proposed procedure involves no smoothing parameter, and is widely applicable to a large class of long/short memory time series models with weakly dependent innovations. In simulation studies, we demonstrate favourable finite sample performance of our method in comparison with the traditional method and a residual block bootstrap approach.     

A generalized Fleming and Harrington's class of tests for interval‐censored data

The class $G^{\rho,\lambda }$ of weighted log‐rank tests proposed by Fleming & Harrington [Fleming & Harrington (1991) Counting Processes and Survival Analysis, Wiley, New York] has been widely used in survival analysis and is nowadays, unquestionably, the established method to compare, nonparametrically, k different survival functions based on right‐censored survival data. This paper extends the $G^{\rho,\lambda }$ class to interval‐censored data. First we introduce a new general class of rank based tests, then we show the analogy to the above proposal of Fleming & Harrington. The asymptotic behaviour of the proposed tests is derived using an observed Fisher information approach and a permutation approach. Aiming to make this family of tests interpretable and useful for practitioners, we explain how to interpret different choices of weights and we apply it to data from a cohort of intravenous drug users at risk for HIV infection. The Canadian Journal of Statistics 40: 501–516; 2012 © 2012 Statistical Society of Canada     

Sample size calculation for recurrent events data in one‐arm studies

In some exceptional circumstances, as in very rare diseases, nonrandomized one‐arm trials are the sole source of evidence to demonstrate efficacy and safety of a new treatment. The design of such studies needs a sound methodological approach in order to provide reliable information, and the determination of the appropriate sample size still represents a critical step of this planning process. As, to our knowledge, no method exists for sample size calculation in one‐arm trials with a recurrent event endpoint, we propose here a closed sample size formula. It is derived assuming a mixed Poisson process, and it is based on the asymptotic distribution of the one‐sample robust nonparametric test recently developed for the analysis of recurrent events data. The validity of this formula in managing a situation with heterogeneity of event rates, both in time and between patients, and time‐varying treatment effect was demonstrated with exhaustive simulation studies. Moreover, although the method requires the specification of a process for events generation, it seems to be robust under erroneous definition of this process, provided that the number of events at the end of the study is similar to the one assumed in the planning phase. The motivating clinical context is represented by a nonrandomized one‐arm study on gene therapy in a very rare immunodeficiency in children (ADA‐SCID), where a major endpoint is the recurrence of severe infections. Copyright © 2012 John Wiley & Sons, Ltd.     

Handling of missing data in long‐term clinical trials: a case study

Missing data in clinical trials is a well‐known problem, and the classical statistical methods used can be overly simple. This case study shows how well‐established missing data theory can be applied to efficacy data collected in a long‐term open‐label trial with a discontinuation rate of almost 50%. Satisfaction with treatment in chronically constipated patients was the efficacy measure assessed at baseline and every 3 months postbaseline. The improvement in treatment satisfaction from baseline was originally analyzed with a paired t‐test ignoring missing data and discarding the correlation structure of the longitudinal data. As the original analysis started from missing completely at random assumptions regarding the missing data process, the satisfaction data were re‐examined, and several missing at random (MAR) and missing not at random (MNAR) techniques resulted in adjusted estimate for the improvement in satisfaction over 12 months. Throughout the different sensitivity analyses, the effect sizes remained significant and clinically relevant. Thus, even for an open‐label trial design, sensitivity analysis, with different assumptions for the nature of dropouts (MAR or MNAR) and with different classes of models (selection, pattern‐mixture, or multiple imputation models), has been found useful and provides evidence towards the robustness of the original analyses; additional sensitivity analyses could be undertaken to further qualify robustness. Copyright © 2012 John Wiley & Sons, Ltd.     

A generalisation of T‐optimality for discriminating between competing models with an application to pharmacokinetic studies

The T‐optimality criterion is used in optimal design to derive designs for model selection. To set up the method, it is required that one of the models is considered to be true. We term this local T‐optimality. In this work, we propose a generalisation of T‐optimality (termed robust T‐optimality) that relaxes the requirement that one of the candidate models is set as true. We then show an application to a nonlinear mixed effects model with two candidate non‐nested models and combine robust T‐optimality with robust D‐optimality. Optimal design under local T‐optimality was found to provide adequate power when the a priori assumed true model was the true model but poor power if the a priori assumed true model was not the true model. The robust T‐optimality method provided adequate power irrespective of which model was true. The robust T‐optimality method appears to have useful properties for nonlinear models, where both the parameter values and model structure are required to be known a priori, and the most likely model that would be applied to any new experiment is not known with certainty. Copyright © 2012 John Wiley & Sons, Ltd.