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二阶 Fisher 信息AI 解读

The paper presents general second-order approximate formulae for the Fisher information of asymptotically normal statistics, and applies the formulae to a stationary time-series model as well as to an econometric simultaneous equation model. Also the second-order conditional information is evaluated for the exponential family and the location family. Conditioned on a second-order ancillary statistic, the second-order information loss of the maximum likelihood estimate is…

简单随机流行病模型中感染率最大似然估计的近似AI 解读

Hill & Severo (1969) and Kryscio (1972) present approximations to the maximum likelihood estimator of the infection rate of the simple stochastic epidemic model. These approximations, valid under some restrictions on the data set, use a table published by Hill & Severo (1969). We give here an algebraically simpler approximation, which does not use an auxiliary table and may be applied to all data sets.

鱼类标记实验中自然死亡率估计的比较AI 解读

Tagging experiments in which recaptures have to be made by professional fishermen are considered. The methods put forward are shown to be maximum likelihood solutions, and expressions are derived for the variances of the estimators. Optimal conditions for the experiment are found, and cases of questionable behaviour are identified.

左截断与右删失数据下失效率递增的生存函数估计AI 解读

The maximum conditional likelihood estimator of the survival function with increasing hazard rate is derived, based on left truncated and right censored data. This estimator always exists, whereas the fully nonparametric conditional maximum likelihood estimator may not exist. A strong consistency theorem is established based on the total time on test transformation.

单个统计泛函的经验似然比置信区间AI 解读

The empirical distribution function based on a sample is well known to be the maximum likelihood estimate of the distribution from which the sample was taken. In this paper the likelihood function for distributions is used to define a likelihood ratio function for distributions. It is shown that this empirical likelihood ratio function can be used to construct confidence intervals for the sample mean, for a class of M-estimates that includes quantiles, and for differentiable…

利用再捕获抽样估计总体规模AI 解读

A design called recapture debugging is proposed to get extra information to estimate the original number of faults, N, in a reliability system. The system is observed for a fixed amount of time τ and the failures are assumed to follow an exponential law with an unknown common parameter λ. The maximum likelihood and moment estimators of N and λ are derived and compared with the existing estimators. The recapture sampling provides substantially more information and improved…

非标准条件下非正则广义最大似然估计的渐近行为AI 解读

In this paper we generalize Huber's (1967) results to include the nonregular case. Resistant estimators which turn out to be asymptotically unbiased in a neighbourhood of the model are given for some univariate models. Their order of consistency achieves the rate of the maximum likelihood estimates. Moreover, some of the estimates are asymptotically efficient under the central model, in the sense that they have the same asymptotic distribution as the maximum likelihood…

有限封闭总体规模的精确极大似然估计札记AI 解读

Using data obtained by the general capture-recapture sequential sampling process, an analytical expression for the maximum likelihood estimate of the population size is introduced. It is shown that the bounded likelihood functions have at most two maxima. For the simple one-to-one case the estimate is unique.

平方误差加复杂度成本损失下的正态均值估计AI 解读

Estimating the mean of a $p$-variate normal distribution is considered when the loss is squared error plus a complexity cost. The complexity of estimates is defined using a partition of the parameter space into sets corresponding to models of different complexity. The model implied by the use of an estimate determines the estimate's complexity cost. Complete classes of estimators are developed which consist of preliminary-test estimators. As is the case when loss is just…

传染性事件过程的时间序列分析AI 解读

Between 1968 and 1972 there were 326 attempts to hijack aircraft worldwide, including 137 attempts in the United States. Those attempts were often attributed to imitation of previous hijacking incidents, and aircraft hijacking, like many other types of behavior, was described as a “contagious” phenomenon. In this article a general mathematical model is developed for serial dependence of rates at which events occur and is applied to data on the hijacking attempts in the U.S.…

总体规模未知的一般次序统计量模型：推断与预测AI 解读

Suppose that the first n order statistics from a random sample of N positive random variables are observed, where N is unknown. This, the general order statistic model, has been applied to the study of market penetration, capture—recapture, burn-in in repairable systems, software reliability growth, the estimation of the number of individuals exposed to radiation, and the estimation of the number of unseen species. Inference is to be made about the unknown parameters,…

多项逻辑回归相对于多组判别分析的效率AI 解读

Multinomial logistic regression (also referred to as polychotomous logistic regression) is frequently used for the analysis of categorical response data with continuous or categorical explanatory variables. Parameter estimates are usually obtained through direct maximum likelihood estimation. Normal discriminant analysis has been used as an alternative approach to this methodology, although it is strictly appropriate only when the usual normal discriminant assumptions…

椭圆分布下的协方差结构分析AI 解读

This article examines the adjustment of normal theory methods for the analysis of covariance structures to make them applicable under the class of elliptical distributions. It is shown that if the model satisfies a mild scale invariance condition and the data have an elliptical distribution, the asymptotic covariance matrix of sample covariances has a structure that results in the retention of many of the asymptotic properties of normal theory methods. If a scale adjustment…

摘要暂缺

自回归移动平均参数的稳健一致估计AI 解读

We aim at estimates of autoregressive-moving average parameters which are simultaneously consistent at the nominal Gaussian model and insensitive to outliers in the data. The estimates may be viewed as a robust version of maximum likelihood estimates of order r and, for purely autoregressive models, reduce to a special case of generalized M-estimates.

摘要暂缺

非正则问题中的修正最大似然法AI 解读

SUMMARY Maximum likelihood (ML) estimation can break down for distributions like the three-parameter Weibull or gamma where one of the parameters is a limit of the range of the distribution. It is suggested that use of the product of densities for the likelihood function is a misapplication of the ML method in such non-regular cases, and that this is the reason for its failure. It is shown that ML works quite satisfactorily if the likelihood is corrected in an appropriate…

参数正交性与近似条件推断AI 解读

SUMMARY We consider inference for a scalar parameter Ψ in the presence of one or more nuisance parameters. The nuisance parameters are required to be orthogonal to the parameter of interest, and the construction and interpretation of orthogonalized parameters is discussed in some detail. For purposes of inference we propose a likelihood ratio statistic constructed from the conditional distribution of the observations, given maximum likelihood estimates for the nuisance…

独立随机变量序列中变点极大似然估计量的分布近似AI 解读

The problem of estimating the change-point in a sequence of independent random variables is considered. As the sample sizes before and after the change-point tend to infinity, Hinkley (1970) showed that the maximum likelihood estimate of the change-point converges in distribution to that of the change-point based on an infinite sample. Letting the amount of change in distribution approach 0, it is shown that the distribution, suitably normalized, of the maximum likelihood…

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…

随机化估计与检验AI 解读

Stochastic procedures are randomized tests, estimates and confidence sets with two properties: (i) They are functions of an original sample and one or more artificially constructed auxiliary samples. (ii) They become nearly nonrandomized when the auxiliary samples increase in size. The stochastic procedures of this paper, which arise as approximations to numerically intractable procedures, involve iterated bootstrap techniques and random sampling schemes over abstract…

密度估计的半参数方法AI 解读

One method of fitting a parametric density function f(x, θ) is first to estimate θ by maximum likelihood, say, and then to estimate f(x, θ) by . On the other hand, when the parametric model does not hold, the true density f(x) may be estimated nonparametrically, as in the case of a kernel estimate . The key idea proposed is to fit a combination of the parametric and nonparametric estimates, namely where π (0 ≤ π ≤ 1) is unknown. The parameter π is estimated from the data,…

计数数据分析中的最小 Hellinger 距离估计AI 解读

Minimum Hellinger distance (MHD) estimation is studied in the context of discrete data. The MHD estimator is shown to provide an effective treatment of anomalous data points, and its properties are illustrated using short-term mutagenicity test data. Asymptotic normality for a discrete distribution with countable support is derived under a readily verified condition on the model. Breakdown properties of the MHD estimator and an outlier screen are compared. Count data occur…

Sichel 分布及其多元扩展的参数估计AI 解读

The Sichel distribution is a three-parameter compound Poisson distribution. It is a versatile model for highly skewed frequency distributions of observed counts and has proved useful in fields as diverse as mining engineering, linguistics, ecology, industrial psychology, and market research. We propose a reparameterization of the Sichel distribution and give an algorithm, which can be implemented on a typical desktop microcomputer, for computing the maximum likelihood…