56,071 research outputs found
Nonparametric Additive Model-assisted Estimation for Survey Data
An additive model-assisted nonparametric method is investigated to estimate
the finite population totals of massive survey data with the aid of auxiliary
information. A class of estimators is proposed to improve the precision of the
well known Horvitz-Thompson estimators by combining the spline and local
polynomial smoothing methods. These estimators are calibrated, asymptotically
design-unbiased, consistent, normal and robust in the sense of asymptotically
attaining the Godambe-Joshi lower bound to the anticipated variance. A
consistent model selection procedure is further developed to select the
significant auxiliary variables. The proposed method is sufficiently fast to
analyze large survey data of high dimension within seconds. The performance of
the proposed method is assessed empirically via simulation studies
Bias Transmission and Variance Reduction in Two-Stage Quantile Regression
In this paper, we propose a variance reduction method for quantile regressions with endogeneity problems. First, we derive the asymptotic distribution of two-stage quantile estimators based on the fitted-value approach under very general conditions on both error terms and exogenous variables. Second, we exhibit a bias transmission property derived from the asymptotic representation of our estimator. Third, using a reformulation of the dependent variable, we improve the efficiency of the two-stage quantile estimators by exploiting a trade-off between an asymptotic bias confined to the intercept estimator and a reduction of the variance of the slope estimator. Monte Carlo simulation results show the excellent performance of our approach. In particular, by combining quantile regressions with first-stage trimmed least-squares estimators, we obtain more accurate slope estimates than 2SLS, 2SLAD and other estimators for a broad range of distributions
Inconsistency transmission and variance reduction in two-stage quantile regression
International audienceIn this paper, we propose a new variance reduction method for quantile regressions with endogeneity problems, for alpha-mixing or m-dependent covariates and error terms. First, we derive the asymptotic distribution of two-stage quantile estimators based on the fitted-value approach under very general conditions. Second, we exhibit an inconsistency transmission property derived from the asymptotic representation of our estimator. Third, using a reformulation of the dependent variable, we improve the efficiency of the two-stage quantile estimators by exploiting a tradeoff between an inconsistency confined to the intercept estimator and a reduction of the variance of the slope estimator. Monte Carlo simulation results show the fine performance of our approach. In particular, by combining quantile regressions with first-stage trimmed least-squares estimators, we obtain more accurate slope estimates than 2SLS, 2SLAD and other estimators for a broad set of distributions. Finally, we apply our method to food demand equations in Egypt
Results of evaluating the performance of empirical estimators of natural mortality rate
Natural mortality rate, M, of fish is a highly influential stock assessment parameter. The M parameter is also difficult to estimate directly and reliably. Various empirical estimators have been developed to estimate M indirectly, based on relationships established between M and predictor variables such as growth parameters, lifespan and water temperature (e.g., Beverton and Holt, 1959; Alverson and Carney, 1975; Pauly, 1980; Hoenig, 1983). Despite the importance of these estimators, there is no consensus in the literature on how well they work in terms of prediction error or how their performance may be ranked. Then et al. (2015) evaluated estimators based on various combinations of maximum age (tmax), von Bertalanffy growth parameters (K) and asymptotic length (L∞), and water temperature (T), by seeing how well they reproduce independent, direct estimates of M for more than 200 unique fish species. They also considered the possibility of combining different estimators using a weighting scheme to improve estimation of M. This report documents additional analyses and results to supplement the results in the journal article. The estimators, evaluation criteria, and other important details are given in the journal article
On the Sum of Order Statistics and Applications to Wireless Communication Systems Performances
We consider the problem of evaluating the cumulative distribution function
(CDF) of the sum of order statistics, which serves to compute outage
probability (OP) values at the output of generalized selection combining
receivers. Generally, closed-form expressions of the CDF of the sum of order
statistics are unavailable for many practical distributions. Moreover, the
naive Monte Carlo (MC) method requires a substantial computational effort when
the probability of interest is sufficiently small. In the region of small OP
values, we propose instead two effective variance reduction techniques that
yield a reliable estimate of the CDF with small computing cost. The first
estimator, which can be viewed as an importance sampling estimator, has bounded
relative error under a certain assumption that is shown to hold for most of the
challenging distributions. An improvement of this estimator is then proposed
for the Pareto and the Weibull cases. The second is a conditional MC estimator
that achieves the bounded relative error property for the Generalized Gamma
case and the logarithmic efficiency in the Log-normal case. Finally, the
efficiency of these estimators is compared via various numerical experiments
Combining multiple observational data sources to estimate causal effects
The era of big data has witnessed an increasing availability of multiple data
sources for statistical analyses. We consider estimation of causal effects
combining big main data with unmeasured confounders and smaller validation data
with supplementary information on these confounders. Under the unconfoundedness
assumption with completely observed confounders, the smaller validation data
allow for constructing consistent estimators for causal effects, but the big
main data can only give error-prone estimators in general. However, by
leveraging the information in the big main data in a principled way, we can
improve the estimation efficiencies yet preserve the consistencies of the
initial estimators based solely on the validation data. Our framework applies
to asymptotically normal estimators, including the commonly-used regression
imputation, weighting, and matching estimators, and does not require a correct
specification of the model relating the unmeasured confounders to the observed
variables. We also propose appropriate bootstrap procedures, which makes our
method straightforward to implement using software routines for existing
estimators
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