610 research outputs found

    Generalized bootstrap for estimating equations

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    We introduce a generalized bootstrap technique for estimators obtained by solving estimating equations. Some special cases of this generalized bootstrap are the classical bootstrap of Efron, the delete-d jackknife and variations of the Bayesian bootstrap. The use of the proposed technique is discussed in some examples. Distributional consistency of the method is established and an asymptotic representation of the resampling variance estimator is obtained.Comment: Published at http://dx.doi.org/10.1214/009053604000000904 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Reducing bias and quantifying uncertainty in watershed flux estimates: the R package loadflex

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    Many ecological insights into the function of rivers and watersheds emerge from quantifying the flux of solutes or suspended materials in rivers. Numerous methods for flux estimation have been described, and each has its strengths and weaknesses. Currently, the largest practical challenges in flux estimation are to select among these methods and to implement or apply whichever method is chosen. To ease this process of method selection and application, we have written an R software package called loadflex that implements several of the most popular methods for flux estimation, including regressions, interpolations, and the special case of interpolation known as the period-weighted approach. Our package also implements a lesser-known and empirically promising approach called the “composite method,” to which we have added an algorithm for estimating prediction uncertainty. Here we describe the structure and key features of loadflex, with a special emphasis on the rationale and details of our composite method implementation. We then demonstrate the use of loadflex by fitting four different models to nitrate data from the Lamprey River in southeastern New Hampshire, where two large floods in 2006–2007 are hypothesized to have driven a long-term shift in nitrate concentrations and fluxes from the watershed. The models each give believable estimates, and yet they yield different answers for whether and how the floods altered nitrate loads. In general, the best modeling approach for each new dataset will depend on the specific site and solute of interest, and researchers need to make an informed choice among the many possible models. Our package addresses this need by making it simple to apply and compare multiple load estimation models, ultimately allowing researchers to estimate riverine concentrations and fluxes with greater ease and accuracy

    Estimation with Inequality Constraints on Parameters and Truncation of the Sampling Distribution.

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    Theoretical constraints on economic model parameters often are in the form of inequality restrictions. For example, many theoretical results are in the form of monotonicity or nonnegativity restrictions. Inequality constraints can truncate sampling distributions of parameter estimators, so that asymptotic normality no longer is possible. Sampling theoretic asymptotic inference is thereby greatly complicated or compromised. We use numerical methods to investigate the resulting sampling properties of inequality-constrained estimators produced by popular methods of imposing inequality constraints, with particular emphasis on the method of squaring, which is the most widely used method in the applied literature on estimating integrable neoclassical systems of demand equations. See Barnett and Binner (2004).Asymptotics, truncated sampling distribution, nonidentified sign, inequality constraints, bootstrap, jackknife.

    Consistency of the jackknife-after-bootstrap variance estimator for the bootstrap quantiles of a studentized statistic

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    Efron [J. Roy. Statist. Soc. Ser. B 54 (1992) 83--111] proposed a computationally efficient method, called the jackknife-after-bootstrap, for estimating the variance of a bootstrap estimator for independent data. For dependent data, a version of the jackknife-after-bootstrap method has been recently proposed by Lahiri [Econometric Theory 18 (2002) 79--98]. In this paper it is shown that the jackknife-after-bootstrap estimators of the variance of a bootstrap quantile are consistent for both dependent and independent data. Results from a simulation study are also presented.Comment: Published at http://dx.doi.org/10.1214/009053605000000507 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

    SAS/IML Macros for a Multivariate Analysis of Variance Based on Spatial Signs

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    Recently, new nonparametric multivariate extensions of the univariate sign methods have been proposed. Randles (2000) introduced an affine invariant multivariate sign test for the multivariate location problem. Later on, Hettmansperger and Randles (2002) considered an affine equivariant multivariate median corresponding to this test. The new methods have promising efficiency and robustness properties. In this paper, we review these developments and compare them with the classical multivariate analysis of variance model. A new SAS/IML tool for performing a spatial sign based multivariate analysis of variance is introduced.

    COMPARISON OF RESAMPLING EFFICIENCY LEVELS OF JACKKNIFE AND DOUBLE JACKKNIFE IN PATH ANALYSIS

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    The assumption of normality is often not fulfilled, this causes the estimation of the resulting parameters to be less efficient. The problem with assuming that normality is not satisfied can be overcome by resampling. The use of resampling allows data to be applied free of distributional assumptions. In this study, a research simulation was carried out by applying Jackknife resampling and Double Jackknife resampling in path analysis with the assumption that the normality of the residuals was not fulfilled and the number of resampling was set at 100 with the degree of closeness level of relationship between variables consisting of low closeness, medium closeness, and high closeness. Based on the simulation results, resampling with a power of 100 can overcome the problem of unfulfilled normality assumptions. In addition, the comparison of the relative efficiency level of the resampling jackknife and double jackknife in the path analysis obtained by the resampling double jackknife has more efficiency than the resampling jackknif
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