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气候模型集合中不确定性的贝叶斯建模AI 解读

Projections of future climate change caused by increasing greenhouse gases depend critically on numerical climate models coupling the ocean and atmosphere (global climate models [GCMs]). However, different models differ substantially in their projections, which raises the question of how the different models can best be combined into a probability distribution of future climate change. For this analysis, we have collected both current and future projected mean temperatures…

合同选择的决定因素：以认股权证支付增发承销报酬AI 解读

ABSTRACT The issuer's decision to include warrants as compensation to underwriters is studied for a sample of 1,991 negotiated firm commitment issues of seasoned equity. Using a two‐stage logit model to correct for self‐selection bias, we find direct evidence that warrant compensation functions as a bond, substituting for reputational capital and enabling the underwriter to certify the issue price. To a lesser degree, the decision also is affected by regulations on…

极值指数的估计AI 解读

SUMMARY The extremal index is an important parameter measuring the degree of clustering of extremes in a stationary process. If we consider the point process of exceedance times over a high threshold, then this can be shown to converge asymptotically to a clustered Poisson process. The extremal index, a parameter in the interval [0, 1], is the reciprocal of the mean cluster size. Apart from being of interest in its own right, it is a crucial parameter for determining the…

非正则回归AI 解读

In an earlier paper, the author has studied asymptotic properties of maximum likelihood estimates for a class of nonregular models in which the range of the distribution depends on unknown parameters. Examples include Weibull and extreme value distributions. The present paper is concerned with the extension of this theory to the case when covariates are present. The proposed solution involves solving a linear programming problem for the regression parameters, followed by…

SUMMARY An extension of the threshold method for extreme values is developed, to consider the joint distribution of extremes of two variables. The methodology is based on the point process representation of bivariate extremes. Both parametric and nonparametric models are considered. The simplest case to handle is that in which both marginal distributions are known. For the more realistic case in which the marginal distributions are unknown, a mixed parametric-nonparametric…

SUMMARY This paper is concerned with estimating the dimension of an attractor. The Grassberger–Procaccia procedure for estimating the correlation dimension is reviewed, and some alternative estimators considered. A particularly important problem is to estimate dimension in the presence of noise in the data. In pursuit of this, a modification of the Grassberger–Procaccia procedure is proposed, and illustrated on both artificial and real data sets.

平移幂变换模型的分组似然AI 解读

SUMMARY Estimation of parameters is considered in the shifted power transformation family of models. The ordinary likelihood function is shown to behave poorly, often having no local maximum. It is argued that a grouped likelihood approach avoids these difficulties, and the practical implementation of this approach is considered. Bayesian inference is also considered, though more briefly, and it is argued that there are again difficulties with an ungrouped likelihood…

利用最大似然预测纪录AI 解读

A maximum likelihood method of fitting a model to a series of records is proposed, using ideas from the analysis of censored data to construct a likelihood function based on observed records. This method is tried out by fitting several models to series of athletics records for mile and marathon races. A form of residual analysis is proposed for testing the models. Forecasting consequences are also considered. In the case of mile records, a steady linear improvement since…

用最大似然法预测纪录AI 解读

A maximum likelihood method of fitting a model to a series of records is proposed, using ideas from the analysis of censored data to construct a likelihood function based on observed records. This method is tried out by fitting several models to series of athletics records for mile and marathon races. A form of residual analysis is proposed for testing the models. Forecasting consequences are also considered. In the case of mile records, a steady linear improvement since…

概率分布尾部的估计AI 解读

We study the asymptotic properties of estimators of the tail of a distribution based on the excesses over a threshold. A key idea is the use of Pickands' generalised Pareto distribution and its fitting, in most cases, by the method of maximum likelihood. The results cover all three limiting types of extreme value theory. We propose a new estimator for an index of regular variation and show that it often performs better than Hill's estimator. We give new results for…

NEAR(2) 模型的最大似然估计AI 解读

SUMMARY The NEAR(2) model is a model for nonlinear time series with exponential marginals. It formed the subject of a recent discussion paper by Lawrance and Lewis. We explore the possibility of maximum likelihood estimation with particular reference to the difficulties created by discontinuities in the likelihood function. Two exploratory techniques are proposed for resolving those difficulties. This note is an expanded version of a contribution presented orrally at the…

概率分布下尾的最大似然估计AI 解读

SUMMARY We consider the estimation of the three parameters of the lower tail of a distribution function based on the k smallest out of n observations. The likelihood function has a singularity but it is argued that a local maximum, when it exists, should be taken as the m.l.e. Asymptotic results as k → ∞, n → ∞, k/n → 0 show that such a local maximum does exist, and provides consistent estimators whenever the shape parameter is greater than one; otherwise there is no local…

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序贯临床试验中偏置硬币设计的性质AI 解读

Martingale methods and the martingale invariance principle are used to derive central limit theorems and related results for biased coin designs of the kind previously studied by Efron, Wei and many others. The results are applied to the study of selection bias. The method is developed for the simplest two-treatment case and then extended, first to the case of several treatments, and secondly to the case of two treatments with prognostic factors.