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Edgeworth 展开的反演AI 解读

We provide a method for inverting a general Edgeworth expansion, so as to correct a statistic for the effects of non-normality. This technique is applied to the special case of the "Studentized" mean. Explicit formulae are given for the correction terms.

减少采样操作次数的序贯估计AI 解读

SUMMARY A method is proposed for accelerating the sequential estimation procedure due to Anscombe, Chow and Robbins. It enables the number of sampling operations to be reduced by any predetermined factor, at the expense of only a slight increase in the expected sample size. The large sample theory is outlined, and some numerical computations provided to demonstrate the practicality of the procedure for smaller samples.

基于经验特征函数的正态性检验AI 解读

We present a simple test for normality against the alternative that the underlying distribution is long tailed. The test is based on the behaviour of the empirical characteristic function in the neighbourhood of the origin, and is very competitive with several well-known tests for normality.

改进二项与泊松参数单侧置信区间的正态近似AI 解读

We show that the usual normal approximation used during the construction of onesided confidence intervals for binomial or Poisson parameters can be significantly in error due to skewness in the underlying distribution. We provide a simple method of correcting for skewness, and demonstrate that it is effective both in theory and in practice.

Summary We present a class of simple estimates of an exponent of regular variation. Unlike those proposed recently by de Haan and Resnick (1980), ours converge at an algebraic rather than a logarithmic rate, and unlike those considered by Teugels (1980), their form does not depend on the unknown exponent.

密度估计中的交叉验证AI 解读

We examine the cross-validatory method of choosing the window size when estimating a density on a bounded interval. Tt is shown that even if the resulting estimator is consistent it will perform suboptimally for large samples, and should be used cautiously. Alternative techniques, such as that proposed by Silverman (1978a), would be a wiser choice.

分布端点的估计AI 解读

We propose a method of estimating the endpoint, $\theta$, of a distribution when only limited information is available about the behaviour of the distribution in the neighbourhood of $\theta$. By using increasing numbers of extreme order statistics we obtain an estimator which improves on earlier estimators based on only a bounded number of extremes. In a certain particular model our estimator is equal to a maximum likelihood estimator, but it is robust against departures…

构造二项或泊松参数单侧置信区间时的正态近似改进AI 解读

We show that the usual normal approximation used during the construction of onesided confidence intervals for binomial or Poisson parameters can be significantly in error due to skewness in the underlying distribution. We provide a simple method of correcting for skewness, and demonstrate that it is effective both in theory and in practice.

密度估计中的交叉验证AI 解读

We examine the cross-validatory method of choosing the window size when estimating a density on a bounded interval. Tt is shown that even if the resulting estimator is consistent it will perform suboptimally for large samples, and should be used cautiously. Alternative techniques, such as that proposed by Silverman (1978a), would be a wiser choice.

均值序贯估计中三阶段抽样的渐近理论AI 解读

We describe the asymptotic theory of triple sampling as it pertains to the estimation of a mean. We obtain limit theorems for the case of the normal distribution. Our results show that triple sampling combines the simplicity of Stein's double sampling technique with the efficiency of the fully sequential Anscombe-Chow-Robbins procedure.

摘要暂缺

非参数多元二元判别AI 解读

Aitchison & Aitken (1976) introduced a novel and ingenious nonparametric method for estimating probabilities in a multidimensional binary space. The technique is designed for use in multivariate binary discrimination. Their estimator depends crucially on an unknown smoothing parameter λ, and Aitchison & Aitken proposed a maximum likelihood method for determining λ from the sample. Unfortunately this leads to an adaptive estimator which can behave very erratically when there…

混合比例的非参数估计AI 解读

SUMMARY Non-parametric estimates of mixing proportions based on kernel-type density estimators are badly suited to several types of data. They suffer from aberrations due to rounding or truncation of the measurements, and their construction involves the crucial choice of the “window size”, or smoothing parameter. In many circumstances estimators based on the empiric distribution function would be more suitable, and in this paper we investigate their properties. The…

用于判别分析的最优近邻估计量AI 解读

The nonparametric estimators introduced by Hills (1967) and Aitchison & Aitken (1976) can be viewed as weighted near neighbour estimators. In this paper we show how to construct an adaptive weighted near neighbour estimator which minimizes mean squared error. We examine its properties. The estimator is very easy to compute.

关于非参数多元二元判别AI 解读

Aitchison & Aitken (1976) introduced a novel and ingenious nonparametric method for estimating probabilities in a multidimensional binary space. The technique is designed for use in multivariate binary discrimination. Their estimator depends crucially on an unknown smoothing parameter λ, and Aitchison & Aitken proposed a maximum likelihood method for determining λ from the sample. Unfortunately this leads to an adaptive estimator which can behave very erratically when there…