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Nonparametric Density Estimation from Biased Data with Unknown Biasing Function

偏倚函数未知时基于有偏样本的非参数密度估计

We present a kernel estimator for the density of a variable when sampling probabilities depend on that variable. Both the density and sampling bias weight functions are unknown and are estimated nonparametrically. To achieve this, the method requires that two independent samples be taken from a fixed finite population. An estimator of population size follows simply from our density estimator. Asymptotic bias and standard errors for these estimators are provided, and the…

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Using Smoothed Receiver Operating Characteristic Curves to Summarize and Compare Diagnostic Systems

利用平滑 ROC 曲线概括和比较诊断系统

Receiver operating characteristic (ROC) curves are used for summarizing the performance of imperfect diagnostic systems, especially in biomedical research. These curves are also appropriate for summarizing the performance of a discriminant analysis but are under-utilized by statisticians. This article is illustrates the use of these curves for comparing competing diagnostic systems, develops new estimation methods based on kernel density estimation, and studies the…

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Testing Capture Homogeneity in a Recapture Model

再捕获模型中的捕获同质性检验

This paper presents a new method of testing capture homogeneity in recapture experiments where there is time homogeneity. The basic set of statistics used is a lower triangular matrix whose (i, k)th element is the proportion of those animals caught on the next (i + 1)st occasion who have been caught k times until now. Both theoretical and simulation evidence is presented that the new procedure is superior to methods previously suggested.

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Testing capture homogeneity in a recapture model

再捕获模型中的捕获同质性检验

This paper presents a new method of testing capture homogeneity in recapture experiments where there is time homogeneity. The basic set of statistics used is a lower triangular matrix whose (i, k)th element is the proportion of those animals caught on the next (i + 1)st occasion who have been caught k times until now. Both theoretical and simulation evidence is presented that the new procedure is superior to methods previously suggested.

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