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Register a new userEfficient Estimation of Nonlinear Finite Population Parameters Using Nonparametrics
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Added by
Camelia Goga
Publication date
2012
fields
Mathematical Statistics
and research's language is
English
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Currently, the high-precision estimation of nonlinear parameters such as Gini indices, low-income proportions or other measures of inequality is particularly crucial. In the present paper, we propose a general class of estimators for such parameters that take into account univariate auxiliary information assumed to be known for every unit in the population. Through a nonparametric model-assisted approach, we construct a unique system of survey weights that can be used to estimate any nonlinear parameter associated with any study variable of the survey, using a plug-in principle. Based on a rigorous functional approach and a linearization principle, the asymptotic variance of the proposed estimators is derived, and variance estimators are shown to be consistent under mild assumptions. The theory is fully detailed for penalized B-spline estimators together with suggestions for practical implementation and guidelines for choosing the smoothing parameters. The validity of the method is demonstrated on data extracted from the French Labor Force Survey. Point and confidence intervals estimation for the Gini index and the low-income proportion are derived. Theoretical and empirical results highlight our interest in using a nonparametric approach versus a parametric one when estimating nonlinear parameters in the presence of auxiliary information.
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The vast majority of models for the spread of communicable diseases are parametric in nature and involve underlying assumptions about how the disease spreads through a population. In this article we consider the use of Bayesian nonparametric approaches to analysing data from disease outbreaks. Specifically we focus on methods for estimating the infection process in simple models under the assumption that this process has an explicit time-dependence.
We derive new estimators of an optimal joint testing and treatment regime under the no direct effect (NDE) assumption that a given laboratory, diagnostic, or screening test has no effect on a patients clinical outcomes except through the effect of the test results on the choice of treatment. We model the optimal joint strategy using an optimal regime structural nested mean model (opt-SNMM). The proposed estimators are more efficient than previous estimators of the parameters of an opt-SNMM because they efficiently leverage the `no direct effect (NDE) of testing assumption. Our methods will be of importance to decision scientists who either perform cost-benefit analyses or are tasked with the estimation of the `value of information supplied by an expensive diagnostic test (such as an MRI to screen for lung cancer).
This paper proposes a two-fold factor model for high-dimensional functional time series (HDFTS), which enables the modeling and forecasting of multi-population mortality under the functional data framework. The proposed model first decomposes the HDFTS into functional time series with lower dimensions (common feature) and a system of basis functions specific to different cross-sections (heterogeneity). Then the lower-dimensional common functional time series are further reduced into low-dimensional scalar factor matrices. The dimensionally reduced factor matrices can reasonably convey useful information in the original HDFTS. All the temporal dynamics contained in the original HDFTS are extracted to facilitate forecasting. The proposed model can be regarded as a general case of several existing functional factor models. Through a Monte Carlo simulation, we demonstrate the performance of the proposed method in model fitting. In an empirical study of the Japanese subnational age-specific mortality rates, we show that the proposed model produces more accurate point and interval forecasts in modeling multi-population mortality than those existing functional factor models. The financial impact of the improvements in forecasts is demonstrated through comparisons in life annuity pricing practices.
Population size estimation based on the capture-recapture experiment is an interesting problem in various fields including epidemiology, criminology, demography, etc. In many real-life scenarios, there exists inherent heterogeneity among the individuals and dependency between capture and recapture attempts. A novel trivariate Bernoulli model is considered to incorporate these features, and the Bayesian estimation of the model parameters is suggested using data augmentation. Simulation results show robustness under model misspecification and the superiority of the performance of the proposed method over existing competitors. The method is applied to analyse real case studies on epidemiological surveillance. The results provide interesting insight on the heterogeneity and dependence involved in the capture-recapture mechanism. The methodology proposed can assist in effective decision-making and policy formulation.
The true population-level importance of a variable in a prediction task provides useful knowledge about the underlying data-generating mechanism and can help in deciding which measurements to collect in subsequent experiments. Valid statistical inference on this importance is a key component in understanding the population of interest. We present a computationally efficient procedure for estimating and obtaining valid statistical inference on the Shapley Population Variable Importance Measure (SPVIM). Although the computational complexity of the true SPVIM scales exponentially with the number of variables, we propose an estimator based on randomly sampling only $Theta(n)$ feature subsets given $n$ observations. We prove that our estimator converges at an asymptotically optimal rate. Moreover, by deriving the asymptotic distribution of our estimator, we construct valid confidence intervals and hypothesis tests. Our procedure has good finite-sample performance in simulations, and for an in-hospital mortality prediction task produces similar variable importance estimates when different machine learning algorithms are applied.
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