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Estimating invariant laws of linear processes by Ustatistics
"... Suppose we observe an invertible linear process with independent mean zero innovations, and with coefficients depending on a finitedimensional... ..."
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Cited by 11 (10 self)
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Suppose we observe an invertible linear process with independent mean zero innovations, and with coefficients depending on a finitedimensional...
INFERENCE ON COUNTERFACTUAL DISTRIBUTIONS
, 2008
"... In this paper we develop procedures to make inference in regression models about how potential policy interventions affect the entire distribution of an outcome variable of interest. These policy interventions consist of counterfactual changes in the distribution of covariates related to the outco ..."
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Cited by 11 (2 self)
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In this paper we develop procedures to make inference in regression models about how potential policy interventions affect the entire distribution of an outcome variable of interest. These policy interventions consist of counterfactual changes in the distribution of covariates related to the outcome. Under the assumption that the conditional distribution of the outcome is unaltered by the intervention, we obtain uniformly consistent estimates for functionals of the marginal distribution of the outcome before and after the policy intervention. Simultaneous confidence sets for these functionals are also constructed, which take into account the sampling variation in the estimation of the relationship between the outcome and covariates. This estimation can be based on several principal approaches for conditional quantile and distributions functions, including quantile regression and proportional hazard models. Our procedures are general and accommodate both simple unitary changes in the values of a given covariate as well as changes in the distribution of the covariates of general form. An empirical application and a Monte Carlo example illustrate the results.
Estimators for Models with Constraints Involving Unknown Parameters
"... Suppose we have independent observations from a distribution which we know to fulll a finitedimensional linear constraint involving an unknown finitedimensional parameter. We construct efficient estimators for finitedimensional functionals of the distribution. The estimators are obtained by first ..."
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Cited by 3 (3 self)
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Suppose we have independent observations from a distribution which we know to fulll a finitedimensional linear constraint involving an unknown finitedimensional parameter. We construct efficient estimators for finitedimensional functionals of the distribution. The estimators are obtained by first constructing an efficient estimator for the functional when the parameter is known, and then replacing the parameter by an efficient estimator. We consider in particular estimation of expectations.
ASYMPTOTIC BEHAVIOR OF THE UNCONDITIONAL NPMLE OF THE LENGTHBIASED SURVIVOR FUNCTION FROM RIGHT CENSORED PREVALENT COHORT DATA1
, 2001
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Efficiency Calculations for the Maximum Partial Likelihood Estimator in NestedCase Control Sampling
, 2008
"... In making inference on the relation between failure and exposure histories in the Cox semiparametric model, the maximum partial likelihood estimator (MPLE) of the finite dimensional parameter, and the Breslow estimator of the baseline survival function, are known to achieve full efficiency when data ..."
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In making inference on the relation between failure and exposure histories in the Cox semiparametric model, the maximum partial likelihood estimator (MPLE) of the finite dimensional parameter, and the Breslow estimator of the baseline survival function, are known to achieve full efficiency when data is available for all time on all cohort members, even when the covariates are time dependent. When cohort sizes become too large for the collection of complete data, sampling schemes such as nested casecontrol sampling must be used and, under various models, there exist estimators based on the same information as the MPLE having smaller asymptotic variance. Though the MPLE is therefore not efficient under sampling in general, it approaches efficiency in highly stratified situations, or instances where the covariate values are increasingly less dependent upon the past, when the covariate distribution, not depending on the real parameter of interest, is unknown and there is no censoring. In particular, in such situations, when using the nested casecontrol sampling design, both the MPLE and the Breslow estimator of the baseline survival function achieve the information lower bound both in the distributional and the minimax senses in the limit as the number of cohort members tends to infinity. 1
Semiparametric Models: Progress and Problems
, 1985
"... Semiparametric models, models which incorporate both parametric (finite dimensional) and nonparametric (infinitedimensional) components, have received increasing use and attention in statistics in recent years. This paper reviews developments in this very large and rich class of models which spans ..."
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Cited by 1 (0 self)
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Semiparametric models, models which incorporate both parametric (finite dimensional) and nonparametric (infinitedimensional) components, have received increasing use and attention in statistics in recent years. This paper reviews developments in this very large and rich class of models which spans the middle ground between parametric and nonparametric models. Attention is devoted to a preliminary classification of such models with comments on recent work, to lower bounds for estimation, to two potentially useful methods for construction of efficient estimates, and to open problems.
Some Developments in Semiparametric Statistics
"... In this paper we describe the historical development of some parts of semiparametric statistics. The emphasis is on efficient estimation. We understand semiparametric model in the general sense of a model that is neither parametric nor nonparametric. We restrict attention to models with independent ..."
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In this paper we describe the historical development of some parts of semiparametric statistics. The emphasis is on efficient estimation. We understand semiparametric model in the general sense of a model that is neither parametric nor nonparametric. We restrict attention to models with independent and identically distributed observations and to time series.
unknown title
, 2008
"... Nonparametric estimation of distribution and density functions in presence of missing data: an IFS approach ..."
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Nonparametric estimation of distribution and density functions in presence of missing data: an IFS approach
Efficiency of the maximum partial likelihood estimator for nested case control sampling
, 2009
"... In making inference on the relation between failure and exposure histories in the Cox semiparametric model, the maximum partial likelihood estimator (MPLE) of the finite dimensional odds parameter, and the Breslow estimator of the baseline survival function, are known to achieve full efficiency when ..."
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In making inference on the relation between failure and exposure histories in the Cox semiparametric model, the maximum partial likelihood estimator (MPLE) of the finite dimensional odds parameter, and the Breslow estimator of the baseline survival function, are known to achieve full efficiency when data is available for all time on all cohort members, even when the covariates are time dependent. When cohort sizes become too large for the collection of complete data, sampling schemes such as nested case control sampling must be used and, under various models, there exist estimators based on the same information as the MPLE having smaller asymptotic variance. Though the MPLE is therefore not efficient under sampling in general, it approaches efficiency in highly stratified situations, or instances where the covariate values are increasingly less dependent upon the past, when the covariate distribution, not depending on the real parameter of interest, is unknown and there is no censoring. In particular, in such situations, when using the nested case control sampling design, both the MPLE and the Breslow estimator of the baseline survival function achieve the information lower bound both in the distributional and the minimax senses in the limit as the number of cohort members tends to infinity.