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实时估计数百万个动态交易时点模式AI 解读

In some business applications, the transaction behavior of each customer is tracked separately with a customer signature. A customer's signature for buying behavior, for example, may contain information on the likely place of purchase, value of goods purchased, type of goods purchased, and timing of purchases. The signature may be updated whenever the customer makes a transaction, and, because of storage limitations, the updating may be able to use only the new transaction…

含无关数据与核验偏差样本的非参数极大似然估计AI 解读

Suppose that some measurements come from a distribution F that is of interest and others come from another, irrelevant distribution G. Some measurements from F are verified and known to be from F. The other, unverified measurements may be from F or from G. Not all measurements from F are equally likely to be verified, and no measurement from G is ever verified. This model applies to measurements of low concentrations obtained using gas chromatography/mass spectroscopy, for…

含无关数据与核验偏差样本的非参数最大似然估计AI 解读

Suppose that some measurements come from a distribution F that is of interest and others come from another, irrelevant distribution G. Some measurements from F are verified and known to be from F. The other, unverified measurements may be from F or from G. Not all measurements from F are equally likely to be verified, and no measurement from G is ever verified. This model applies to measurements of low concentrations obtained using gas chromatography/mass spectroscopy, for…

广义线性模型的过度离散诊断AI 解读

Generalized linear models (GLM's) are simple, convenient models for count data, but they assume that the variance is a specified function of the mean. Although overdispersed GLM's allow more flexible mean-variance relationships, they are often not as simple to interpret nor as easy to fit as standard GLM's. This article introduces a convexity plot, or C plot for short, that detects overdispersion and relative variance curves and relative variance tests that help to…

Statistical agencies that provide microdata for public use strive to keep the risk of disclosure of confidential information negligible. Assessing the magnitude of the risk of disclosure is not easy, however. Whether a data user or intruder attempts to obtain confidential information from a public-use file depends on the perceived costs of identifying a record, the perceived probability of success, and the information expected to be gained. In this article, a…

通过非参数混合推广逻辑回归AI 解读

Logistic regression is a common technique for analyzing the effect of a covariate vector x on the number of successes y in m trials when y has a binomial distribution. But at times either the logistic curve does not describe the probability of success p(x) adequately, or m is larger than 1 and y is more variable than the binomial distribution allows. Overdispersion relative to the binomial distribution is possible if the m trials in a set or “litter” are positively…

环境污染监测的统计方法AI 解读

Environmental pollution studies may be divided into the following broad and somewhat overlapping types.1. Monitoring.Data may be collected (a) to monitor or to characterize ambient concentrations in environmental media (air, water, soil, biota) or (b) to monitor concentrations in air and water effluents.The purpose may be to assess the adequacy of controls on the release or containment of pollutants, Overview of the Design and Analysis Process 3give misleading results when…

稳健两样本置换检验AI 解读

A new two-sample randomization test is proposed for testing that the joint distribution of two samples is invariant under permutations. The $p$-value of the test has a finite sample minimaxity property over neighborhoods of completely specified alternative distributions. Asymptotically, the test has minimax Bahadur slope against the neighborhoods, which remain fixed as the sample sizes increase. The proposed test also offers the best compromise between robustness against…

混合泊松模型中极大似然估计的渐近性质AI 解读

This paper considers the asymptotic behavior of the maximum likelihood estimators (mle's) of the probabilities of a mixed Poisson distribution with a nonparametric mixing distribution. The vector of estimated probabilities is shown to converge in probability to the vector of mixed probabilities at rate $n^{1/2-\varepsilon}$ for any $\varepsilon > 0$ under a generalized $\chi^2$ distance function. It is then shown that any finite set of the mle's has the same joint limiting…

混合分布泛函估计量的渐近效率AI 解读

Suppose $F$ is a mixture of a known parametric family of distributions with an unknown nonparametric mixing distribution. Consider the problem of estimating the value $T(dF)$ of a smooth functional $T$ at the mixed distribution $F$. One nonparametric estimator of $T(dF)$ is $T(dF_n)$ where $F_n$ denotes the empirical distribution. Under a differentiability condition on $T$ given in this note, $T(dF_n)$ is shown to be fully efficient asymptotically in the sense that the…

P值的渐近对数正态性AI 解读

Sufficient conditions for asymptotic lognormality of exact and approximate, unconditional and conditional $P$-values are established. It is pointed out that the mean, which is half the Bahadur slope, and the standard deviation of the asymptotic distribution of the log transformed $P$-value together, but not the mean alone, permit approximation of both the level and power of the test. This provides a method of discriminating between tests that have Bahadur efficiency one. The…