GMM and Misspecification Correction for Misspecified Models with Diverging Number of Parameters

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.

COMPETITION AMONG DESTINATIONS IN SPATIAL INTERACTION MODELS: A NEW POINT OF VIEW

This paper presents a new perspective on the nature of destination competition in spatial interaction models. The concept of destinations competing with one another on the basis of their spatial proximity to each other is compared with an alternative point of view which argues that competition takes place on the basis of similarities in the spatial influences of competing destinations on decision makers at origins. Potential movers at an origin are facing a set of destinations which compete for their attention. This paper argues that the movers' choices are conditioned by the relative size and number of influences they see (where influence is directly proportional to destination size and inversely proportional to distance). A small amount of supporting empirical evidence concerning recreational day trips, and population migration, is presented.

Measurement Error for Age of Onset in Prevalent Cohort Studies

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.

A NOTE ON THE PROPERTIES OF STEIN-RULE AND INEQUALITY RESTRICTED ESTIMATORS WHEN THE REGRESSION MODEL IS OVER-FITTED

This paper considers the effect of an erroneous inclusion of regressors on the risk propertiesof the Stein-rule,positive-part Stein-rule and inequality restricted and pre-test estimators in a linearregression model.The two Stein-rule estimators are considered when extraneous information is availablein the form of a set of multiple equality constraints on the coefficients,while the inequality estimatorsare considered under the case of a single inequality constraint.It is shown that the inclusion ofwrong regressors has only minimal effect on the properties of the Stein-rule and positive-part Stein-ruleestimators,and no effect at all on the inequality restricted and pre-test estimators when there is asingle inequality constraint.

On valid descriptive inference from non-probability sample

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.