Misspecified models have attracted much attention in some fields such as statistics and econometrics. When a global misspecification exists, even the model contains a large number of parameters and predictors,the miss...Misspecified models have attracted much attention in some fields such as statistics and econometrics. When a global misspecification exists, even the model contains a large number of parameters and predictors,the misspecification cannot disappear and sometimes it instead goes further away from the true one. Then the inference and correction for such a model are of very importance. In this paper we use the generalized method of moments(GMM) to infer the misspecified model with diverging numbers of parameters and predictors, and to investigate its asymptotic behaviors, such as local and global consistency, and asymptotic normality. Furthermore, we suggest a semiparametric correction to reduce the global misspefication and, consequently, to improve the estimation and enhance the modeling. The theoretical results and the numerical comparisons show that the corrected estimation and fitting are better than the existing ones.展开更多
Prevalent cohort studies involve screening a sample of individuals from a population for disease, recruiting affected individuals, and prospectively following the cohort of individuals to record the occurrence of dise...Prevalent cohort studies involve screening a sample of individuals from a population for disease, recruiting affected individuals, and prospectively following the cohort of individuals to record the occurrence of disease-related complications or death. This design features a response-biased sampling scheme since individuals living a long time with the disease are preferentially sampled, so naive analysis of the time from disease onset to death will over-estimate survival probabilities. Unconditional and conditional analyses of the resulting data can yield consistent estimates of the survival distribution subject to the validity of their respective model assumptions. The time of disease onset is retrospectively reported by sampled individuals, however, this is often associated with measurement error. In this article we present a framework for studying the effect of measurement error in disease onset times in prevalent cohort studies, report on empirical studies of the effect in each framework of analysis, and describe likelihood-based methods to address such a measurement error.展开更多
We examine the conditions under which descriptive inference can be based directly on theobserved distribution in a non-probability sample, under both the super-population and quasirandomisation modelling approaches. R...We examine the conditions under which descriptive inference can be based directly on theobserved distribution in a non-probability sample, under both the super-population and quasirandomisation modelling approaches. Review of existing estimation methods reveals that thetraditional formulation of these conditions may be inadequate due to potential issues of undercoverage or heterogeneous mean beyond the assumed model. We formulate unifying conditions that are applicable to both types of modelling approaches. The difficulties of empiricallyvalidating the required conditions are discussed, as well as valid inference approaches usingsupplementary probability sampling. The key message is that probability sampling may still benecessary in some situations, in order to ensure the validity of descriptive inference, but it can bemuch less resource-demanding given the presence of a big non-probability sample.展开更多
基金Supported by National Natural Science Foundation of China(Nos.11971265,11701318,11871294 and 71572097)Shandong Provincial Natural Science Foundation of China(Nos.ZR2019PF012 and ZR2019BA028)+1 种基金National Key R&D Program of China(2018YFA0703900)a Project of Shandong Province Higher Educational Science and Technology Program(No.J18KA356)
文摘Misspecified models have attracted much attention in some fields such as statistics and econometrics. When a global misspecification exists, even the model contains a large number of parameters and predictors,the misspecification cannot disappear and sometimes it instead goes further away from the true one. Then the inference and correction for such a model are of very importance. In this paper we use the generalized method of moments(GMM) to infer the misspecified model with diverging numbers of parameters and predictors, and to investigate its asymptotic behaviors, such as local and global consistency, and asymptotic normality. Furthermore, we suggest a semiparametric correction to reduce the global misspefication and, consequently, to improve the estimation and enhance the modeling. The theoretical results and the numerical comparisons show that the corrected estimation and fitting are better than the existing ones.
文摘Prevalent cohort studies involve screening a sample of individuals from a population for disease, recruiting affected individuals, and prospectively following the cohort of individuals to record the occurrence of disease-related complications or death. This design features a response-biased sampling scheme since individuals living a long time with the disease are preferentially sampled, so naive analysis of the time from disease onset to death will over-estimate survival probabilities. Unconditional and conditional analyses of the resulting data can yield consistent estimates of the survival distribution subject to the validity of their respective model assumptions. The time of disease onset is retrospectively reported by sampled individuals, however, this is often associated with measurement error. In this article we present a framework for studying the effect of measurement error in disease onset times in prevalent cohort studies, report on empirical studies of the effect in each framework of analysis, and describe likelihood-based methods to address such a measurement error.
文摘We examine the conditions under which descriptive inference can be based directly on theobserved distribution in a non-probability sample, under both the super-population and quasirandomisation modelling approaches. Review of existing estimation methods reveals that thetraditional formulation of these conditions may be inadequate due to potential issues of undercoverage or heterogeneous mean beyond the assumed model. We formulate unifying conditions that are applicable to both types of modelling approaches. The difficulties of empiricallyvalidating the required conditions are discussed, as well as valid inference approaches usingsupplementary probability sampling. The key message is that probability sampling may still benecessary in some situations, in order to ensure the validity of descriptive inference, but it can bemuch less resource-demanding given the presence of a big non-probability sample.
