1,337 research outputs found
Likelihood inference for small variance components
No full textIn this paper, we develop likelihood-based methods for making inferences about the components of variance in a general normal mixed linear model. In particular, we use local asymptotic approximations to construct confidence intervals for the components of variance when the components are close to the boundary of the parameter space. In the process, we explore the question of how to profile the restricted likelihood (REML), show that general REML estimates have a lower probability of being on the boundary than maximum likelihood estimates, and show that the likelihood-ratio test based on the local asymptotic approximation has higher power against local alternatives than the likelihood-ratio test based on the usual chi-squared approximation. We explore the finite sample properties of the proposed intervals by means of a small simulation study
Modelling correlated zero-inflated count data
No full textThis paper extends the two-component approach to modelling count data with extra zeros, considered by Mullahy (1986), Heilbron (1994) and Welsh et al. (1996), to take account of possible serial dependence between repeated observations. Generalized estimating equations (Liang & Zeger, 1986) are constructed for each component of the model by incorporating correlation matrices into each of the maximum likelihood estimating equations. The proposed method is demonstrated on weekly counts of Noisy Friarbirds (Philemon cornic-ulatus), which were recorded by observers for the Canberra Garden Bird Survey (Hermes, 1981
Incomplete detection in enumeration surveys: Whither distance sampling?
No full textWe consider the problem of undercount or incomplete detection in enumeration surveys which are intended to estimate population counts or population abundance. The problem is widespread in ecology but also occurs in other surveys: The census undercount is a well-known example of the problem. After framing the problem in a general context, we focus on line transect sampling and the distance sampling methodology which has been widely applied in surveys of ecological populations. We describe distance sampling data and present a graphical derivation of the distance sampling estimator. Our graphical analysis leads to a new expression for the distance sampling estimator which gives useful insights into the nature of the estimator. We discuss the uniformity assumption on which distance sampling depends and describe the properties of the distance sampling estimator when uniformity does not hold. We then explore the relationship between this and other evaluations of distance sampling. We mention briefly some statistical ideas for treating the general incomplete detection problem and conclude with some reflections on general insights arising from the research
Estimators for the linear regression model based on Winsorized observations
No full textWe develop an asymptotic, robust version of the Gauss-Markov theorem for estimating the regression parameter vector ?? and a parametric function ?? in the linear regression model. In a class of estimators for estimating ?? that are linear in a Winsorized observation vector introduced by Welsh (1987), we show that Welsh's trimmed mean has smallest asymptotic covariance matrix. Also, for estimating a parametric function ??, the inner product of ? and the trimmed mean has the smallest asymptotic variance among a class of estimators linear in the Winsorized observation vector. A generalization of the linear Winsorized mean to the multivariate context is also given. Examples analyzing American lobster data and the mineral content of bones are used to compare the robustness of some trimmed mean methods
A journey in single steps: robust one-step M-estimation
No full textWe present a unified treatment of different types of one-step M-estimation in regression models which incorporates the Newton–Raphson, method of scoring and iteratively reweighted least squares forms of one-step estimator. We use higher order expansions to distinguish between the different forms of estimator and the effects of different initial estimators. We show that the Newton–Raphson form has better properties than the method of scoring form which, in turn, has better properties than the iteratively reweighted least squares form. We also show that the best choice of initial estimator is a smooth, robust estimator which converges at the rate n?1/2. These results have important consequences for the common data-analytic strategy of using a least squares analysis on "clean" data obtained by deleting observations with extreme residuals from an initial least squares fit. It is shown that the resulting estimator is an iteratively reweighted least squares one-step estimator with least squares as the initial estimator, giving it the worst performance of the one-step estimators we consider: inferences resulting from this strategy are neither valid nor robust
Robust fitting of the binomial model
No full textWe consider the problem of robust inference for the binomial model. The discreteness of the data and the fact that the parameter and sample spaces are bounded mean that standard robustness theory gives surprising results. For example, the maximum likelihood estimator (MLE) is quite robust, it cannot be improved on for but can be for m>1. We discuss four other classes of estimators: M-estimators, minimum disparity estimators, optimal MGP estimators, and a new class of estimators which we call E-estimators. We show that E-estimators have a non-standard asymptotic theory which challenges the accepted relationship between robustness concepts and thereby provided new perspectives on these concepts
Line transect sampling in small regions
No full textThis paper develops an approach to estimating population abundance from line transect surveys which uses a calibration survey to estimate the detection function which is then employed as a weight function in constructing the abundance estimate. Nonparametric methods of estimating the detection function via local regression and via a kernel density estimator are considered. The proposed methods are evaluated using a set of Western Australian plant data and weed enumeration data
Robust estimation of the generalized Pareto distribution
No full textOne approach used for analysing extremes is to fit the excesses over a high threshold by a generalized Pareto distribution. For the estimation of the shape and scale parameters in the generalized Pareto distribution, under some restrictions on the value of the scale parameter, maximum likelihood, method of moments and probability-weighted moments' estimators are available. However, these are not robust estimators. In this paper we implement a robust estimation procedure known as the method of medians (He and Fung (1999)) to estimate the parameters in the generalized Pareto distribution. The asymptotic distribution of our estimator is normal for any value of the shape parameter except -1
Distribution-function-based bivariate quantiles
No full textWe introduce bivariate quantiles which are defined through the bivariate distribution function. This approach ensures that, unlike most multivariate medians or the multivariate M-quartiles, the bivariate quantiles satisfy an analogous property to that of the univariate quantiles in that they partition R2 into sets with a specified probability content. The definition of bivariate quantiles leads naturally to the definition of quantities such as the bivariate median, bivariate extremes, the bivariate quantile curve, and the bivariate trimmed mean. We also develop asymptotic representations for the bivariate quantiles
Distance sampling methodology
No full textWe consider the method of distance sampling described in Buckland, Anderson, Burnham and Laake in 1993. We explore the properties of the methodology in simple cases chosen to allow direct and accessible comparisons of distance sampling in the design- and model-based frameworks. In particular, we obtain expressions for the bias and variance of the distance sampling estimator of object density and for the expected value of the recommended analytic variance estimator within each framework. These results enable us to clarify aspects of the performance of the methodology which may be of interest to users and potential users of distance sampling
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