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论非参数核密度估计AI 解读

The paper introduces the idea of inadmissible kernels and shows that an Epanechnikov type kernel is the only admissible kernel. An analysis of kernel density estimates leads to two new methods of bias reduction. We also discuss a general method of improving kernel density estimates in the sense of having smaller mean squared error. Finally we provide a theoretical framework for the operational method of using Abramson's square root law providing tangible and compact forms…

非参数核密度估计的可容许性与偏差改进AI 解读

The paper introduces the idea of inadmissible kernels and shows that an Epanechnikov type kernel is the only admissible kernel. An analysis of kernel density estimates leads to two new methods of bias reduction. We also discuss a general method of improving kernel density estimates in the sense of having smaller mean squared error. Finally we provide a theoretical framework for the operational method of using Abramson's square root law providing tangible and compact forms…

论参数密度估计AI 解读

The paper makes a critical assessment of Aitchison's criterion of density estimation. It seems not to satisfy certain intuitive requirements. A new criterion based on decisions theoretic considerations is introduced. It is shown through examples that the judgement about the choice of density estimates is seriously dependent on the criterion chosen. Some other density estimates are introduced which look similar to Bayesian predictive density estimates without using a prior…

论参数密度估计AI 解读

The paper makes a critical assessment of Aitchison's criterion of density estimation. It seems not to satisfy certain intuitive requirements. A new criterion based on decisions theoretic considerations is introduced. It is shown through examples that the judgement about the choice of density estimates is seriously dependent on the criterion chosen. Some other density estimates are introduced which look similar to Bayesian predictive density estimates without using a prior…

泊松过程发生率的贝叶斯序贯估计AI 解读

This paper provides numerical and analytical solutions to the problem of estimating the rate of a Poisson process. Optimal designs are obtained for various loss functions and the method of analysis is valid for any other loss function. The cost of sampling plays a fundamental role and since there are many practical situations where there is a time cost and an event cost, a sampling cost per observed event and a cost per unit time are both included.

泊松回归的贝叶斯与经典分析AI 解读

Summary This paper is concerned with the problem of testing the existence of a trend in the means θi of Poisson distributions. It is assumed that these means are changing exponentially, that is, log θi = α + βxi. A classical method is reviewed which is used for testing the hypothesis β = 0. The exact Bayesian distribution for β is derived and a Bayesian approximation suggested which proved to be very useful. Finally, a comparison of these three methods by means of numerical…

泊松过程发生率的贝叶斯序贯估计AI 解读

This paper provides numerical and analytical solutions to the problem of estimating the rate of a Poisson process. Optimal designs are obtained for various loss functions and the method of analysis is valid for any other loss function. The cost of sampling plays a fundamental role and since there are many practical situations where there is a time cost and an event cost, a sampling cost per observed event and a cost per unit time are both included.

泊松过程抽样方法的比较AI 解读

Summary Comparison of fixed sampling schemes from a Poisson process is discussed by means of minimum average risk. The best scheme depends upon the loss function, the prior distribution and the cost of sampling which plays a fundamental role in this problem. Also optimum schemes are considered.

线性函数关系的贝叶斯估计AI 解读

Summary The purpose of this note is twofold. First, to demonstrate by means of an example that a statistical approach based solely on the likelihood function can be misleading, whereas the Bayesian method yields sensible results. Second, to develop the Bayesian method and apply the results to the problem of estimating a linear functional relationship. In Section 1 we discuss the likelihood approach. Section 2 concerns the Bayesian method, which is applied to the functional…

指数分布参数的估计AI 解读

Summary Some new estimators, which are unbiased with respect to some loss functions, are derived for the parameter in the exponential distribution. The corresponding Bayes estimators are also obtained. The comparison between these two kinds of estimation is discussed.