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破纪录数据问题的参数似然推断AI 解读

In this paper we consider the analysis of record breaking data sets, where only observations that exceed, or only those that fall below, the current extreme value are recorded. Example application areas include industrial stress testing, meteorological analysis, sporting and athletic events, and oil and mining surveys. A closely related area is that of threshold modelling, where the observations are those that cross a certain threshold value. The inherent missing data…

共同优势比对数的偏差修正极大似然估计AI 解读

A bias-correction factor for the maximum likelihood estimator of the log common odds ratio for sparse data is derived, which is applicable when the design is balanced and/or when the number of strata is large. The corrected maximum likelihood estimator is practically unbiased and its mean squared error is smaller than that of the uncorrected maximum likelihood estimator. The correction factor for the maximum likelihood estimator approaches one as strata sizes increase.…

不确定性下的序贯劳动决策：西非农户的可估计家庭模型AI 解读

This paper reports estimates of the primitive parameters of a stochastic control model describing the labor decisions of West African small farmers. Maximum likelihood estimates are computed although optimal labor decision rules cannot be derived analytically. Vuong's non-nested model specification test shows that this method yields estimates superior to those derived by assuming that farmers solve a deterministic control problem. Low levels of labor effort are shown to be a…

摘要暂缺

渐近展开的符号计算工具AI 解读

SUMMARY This paper describes a collection of procedures for the systematic computation of asymptotic expansions that are common in statistical theory and practice: expansions of functions of sums of independent and identically distributed random variables. The procedures permit the expansion of maximum likelihood estimates, the associated deviance or drop in likelihood and more general functions of random variables with distributions involving one or more parameters. The…

从图像去模糊到最优投资：正性线性逆问题的极大似然解法AI 解读

SUMMARY The problem of recovering an input signal from a blurred output, in an input-output system with linear distortion, is ubiquitous in science and technology. When the blurred output is not degraded by statistical noise the problem is entirely deterministic and amounts to a mathematical inversion of a linear system with positive parameters, subject to positivity constraints on the solution. We show that all such linear inverse problems with positivity restrictions…

移动平均参数估计：经典估计的堆积现象与贝叶斯后验AI 解读

The authors analyze posterior distributions of the moving average parameter in the first-order case and sampling distributions of the corresponding maximum likelihood estimator. Sampling distributions 'pile up' at unity when the true parameter is near unity; hence, if one were to difference such a process, estimates of the moving average component of the resulting series would spuriously tend to indicate that the process was overdifferenced. Flat-prior posterior…

检验正态观测参数变化的最大似然方法AI 解读

We compute the asymptotic distribution of the maximum likelihood ratio test when we want to check whether the parameters of normal observations have changed at an unknown point. The proof is based on the limit distribution of the largest deviation between a $d$-dimensional Ornstein-Uhlenbeck process and the origin.

含随机趋势成分的回归模型极大似然估计AI 解读

This article is concerned with the estimation of a regression model with a stochastic trend component. It is shown that the probability of estimating the trend to be deterministic is very sensitive to the type of likelihood function used as the basis of inference.

参数比较的贝叶斯与经验贝叶斯方法AI 解读

The number of successes out of the total number of trials is observed for each of a set of N independent binomial experiment's and the associated success probabilities are compared. Ranking procedures for comparing these success probabilities are constructed under circumstances where the number of trials for each of the experiments may differ by a large amount. A loss function is constructed that represents an appropriate measure of distance between a given ranking of the…

二元与多类别响应数据的贝叶斯分析AI 解读

A vast literature in statistics, biometrics, and econometrics is concerned with the analysis of binary and polychotomous response data. The classical approach fits a categorical response regression model using maximum likelihood, and inferences about the model are based on the associated asymptotic theory. The accuracy of classical confidence statements is questionable for small sample sizes. In this article, exact Bayesian methods for modeling categorical response data are…

彩票热门号码的概率估计与均匀性检验AI 解读

We consider the problem of estimating probabilities for the different numbers in a lottery when the winning numbers are selected sequentially without replacement. Numerical methods are developed to compute maximum likelihood estimates of the probabilities and their variance-covariance matrix based on observed outcomes. The generalized likelihood ratio statistic –2 ln(λ) for testing equiprobable numbers is also given. The methods are applied to a data set from the Lotto…

相对效力的收缩估计量AI 解读

This article examines the finite and infinite sample properties of the shrinkage estimator, motivated by a Bayesian argument, for the log relative potency, proposed in an earlier paper by Kim, Carter, and Hubert. This estimator can be written in closed form and is shown to have finite mean and finite variance in finite samples. As a consequence, this shrinkage estimator has finite frequentist risk, which is an improvement over the usual maximum likelihood estimator, for all…

一致随机序约束下的生存曲线估计AI 解读

If F and G are cumulative distribution functions on [0, ∞) governing the lifetimes of specific systems under study, and if F and G are their corresponding survival functions, then F is said to be uniformly stochastically smaller than G, denoted by F <(+) G, if and only if the ratio l(x) = G (x)/ F (x) is nondecreasing for x ∈ [0, sup{t: [0, sup {(t: F (t) > 0}). When F and G are absolutely continuous, F (+) G is equivalent to the assumption that the corresponding failure…

非线性实验：最优设计与基于似然的推断AI 解读

Nonlinear experiments involve response and regressors that are connected through a nonlinear regression-type structure. Examples of nonlinear models include standard nonlinear regression, logistic regression, probit regression. Poisson regression, gamma regression, inverse Gaussian regression, and so on. The Fisher information associated with a nonlinear experiment is typically a complex nonlinear function of the unknown parameter of interest. As a result, we face an awkward…

特定死因失效概率与条件失效概率的使用：临床肿瘤数据示例AI 解读

Nonparametric maximum likelihood estimation of the probability of failing from a particular cause by time t in the presence of other acting causes (i.e., the cause-specific failure probability) is discussed. A commonly used incorrect approach is to take 1 minus the Kaplan-Meier (KM) estimator (1 – KM), whereby patients who fail of extraneous causes are treated as censored observations. Examples showing the extent of bias in using the 1-KM approach are presented using…

项目反应理论：参数估计技术AI 解读

The Item Characteristic Curve: Dichotomous Response Estimating the Parameters of an Item Characteristic Curve Maximum Likelihood Estimation of Examinee Ability Maximum Likelihood Procedures for Estimating Both Ability and Item Parameters The Rasch Model Marginal Maximum Likelihood Estimation and an EM Algorithm Bayesian Parameter Estimation Procedures The Graded Item Response Nominally Scored Items Markov Chain Monte Carlo Methods Parameter Estimation with Multiple Groups…

参数比较的贝叶斯与经验贝叶斯程序AI 解读

The number of successes out of the total number of trials is observed for each of a set of N independent binomial experiment's and the associated success probabilities are compared. Ranking procedures for comparing these success probabilities are constructed under circumstances where the number of trials for each of the experiments may differ by a large amount. A loss function is constructed that represents an appropriate measure of distance between a given ranking of the…

相对效力的收缩估计量AI 解读

This article examines the finite and infinite sample properties of the shrinkage estimator, motivated by a Bayesian argument, for the log relative potency, proposed in an earlier paper by Kim, Carter, and Hubert. This estimator can be written in closed form and is shown to have finite mean and finite variance in finite samples. As a consequence, this shrinkage estimator has finite frequentist risk, which is an improvement over the usual maximum likelihood estimator, for all…

含随机趋势成分回归模型的最大似然估计AI 解读

This article is concerned with the estimation of a regression model with a stochastic trend component. It is shown that the probability of estimating the trend to be deterministic is very sensitive to the type of likelihood function used as the basis of inference.

统计理论与建模：纪念 David Cox 爵士AI 解读

Part 1 Statistical theory - theoretical concepts significance tests theory of optimal tests estimation asymptotic theory. Part 2 Applied statistics - preliminary considerations statistical models statistical inference model adequancy exploratory and robust methods multi-variate methods use of computers. Part 3 Generalized linear models - a class of non-linear regression models likelihood functions estimation analysis of deviance checking the model. Part 4 Residuals and…

用于多项数据额外变异建模的有限混合分布AI 解读

We propose a new distribution to model categorical data exhibiting overdispersion when the overdispersion is believed to be caused by clumped sampling. The proposed distribution is a finite mixture of multinomial random variables. The finite mixture representation facilitates computation of the maximum likelihood estimator. For large cluster sizes, we derive an approximation for the Fisher information matrix of the model, and an explicit expression for the joint asymptotic…

分类协变量观测不完整时的logistic回归：三种方法比较AI 解读

A logistic regression analysis based on the complete cases neglects the information due to subjects with missing values in at least one but not in all covariates. Three different approaches allowing the use of this information are compared: maximum likelihood estimation, pseudo maximum likelihood estimation, and probability imputation. The first two yield consistent estimates of the regression coefficients and asymptotic normality allows the construction of asymptotically…

迭代定义统计量的影响函数AI 解读

SUMMARY Hampel's influence function and its finite-sample counterparts are the basis for a number of diagnostic statistics. These diagnostics can be expensive to compute in the natural way when the estimation calculations are iterative, as they frequently are when maximum likelihood or robust methods are used. We show how the influence function can be calculated in these situations by implicit differentiation of the fixed-point equation satisfied by the limit of the…