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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…

基于正态近似的两二项概率之差置信区间新方法AI 解读

Using a general method for obtaining confidence intervals from samples from discrete distributions, this article introduces a new confidence interval method for estimating the difference of two binomial probabilities and compares it to three other confidence interval methods, one of which is the usual method with no continuity correction. Each of the other two confidence interval methods uses its own continuity correction; one combines it with an estimate of the standard…

复杂调查数据的假设检验：经典二次型统计量及回归应用AI 解读

Sample surveys often have complex sample designs with multistage cluster sampling, stratification, and differential selection probabilities. This article is concerned with testing the null hypothesis H 0: θ = θ, where the p-dimensional parameter θ = g( μ ) and μ is a q-dimensional vector of means. The asymptotic framework that consists of a sequence of increasing finite populations is used to define μ as the limit of finite population means. As part of the inference, we use…

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…

ARIMA模型中移动平均单位根的检验AI 解读

Test procedures for detecting overdifferencing or a moving average unit root in Gaussian autoregressive integrated moving average (ARIMA) models are proposed. The tests can be used when an autoregressive unit root is a serious alternative but the hypothesis of primary interest implies stationarity of the observed time series. This is the case, for example, if one wishes to test the null hypothesis that a multivariate time series is cointegrated with a given theoretical…

回归中最小可估子集近似的精度AI 解读

The elemental set algorithm involves performing many fits to a data set, each fit made to a subsample of size just large enough to estimate the parameters in the model. Elemental sets have been proposed as a computational device to approximate estimators in the areas of high breakdown regression and multivariate location/scale estimation, where exact optimization of the criterion function is computationally intractable. Although elemental set algorithms are used widely and…

删失数据中二元生存曲线的可识别性AI 解读

We show that the survival curve is identifiable in bivariate censored data problems under weaker independence assumptions than have commonly been made. The common assumption has been mutual independence of (T 1, T 2) and (Z 1, Z 2), where (T 1, T 2) is the true survival vector, (Z 1, Z 2) is a nuisance censoring vector, and bivariate right-censored data is observed. We show that the distribution of (T 1, T 2) is identifiable under weaker, conditional independence assumptions…

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…

变量选择问题中的观测影响评估AI 解读

Variable selection techniques are often used in combination with multiple linear regression to produce a parsimonious model that fits the data well. It is clearly undesirable for the final model to depend strongly on the inclusion of a few influential cases in the data set. This article discusses a measure of influence of single cases on the final model, based on a similar measure used in ordinary multiple regression. When variables are selected objectively, deletion of…

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…

稳健奇异值分解：投影寻踪的新方法AI 解读

Robust location and covariance estimators are developed via general M estimation for covariance matrix eigenvectors and eigenvalues. The solution to this GM estimation problem is obtained by transforming it into a series of robust regression problems based on a new algorithm for the singular value decomposition. It is shown here that the singular value decomposition can be represented as an iteration of two steps: a least squares regression fit of the data matrix followed by…

平滑样条密度估计：无量纲自动算法AI 解读

As a sequel to an earlier article by Gu and Qiu, this article describes and illustrates a dimensionless automatic algorithm for nonparametric probability density estimation using smoothing splines. The algorithm is designed to calculate an adaptive finite dimensional solution to the penalized likelihood problem, which was shown by Gu and Qiu to share the same asymptotic convergence rates as the nonadaptive infinite dimensional solution. The smoothing parameter is updated…

通过交叉验证选择线性模型AI 解读

We consider the problem of selecting a model having the best predictive ability among a class of linear models. The popular leave-one-out cross-validation method, which is asymptotically equivalent to many other model selection methods such as the Akaike information criterion (AIC), the C p , and the bootstrap, is asymptotically inconsistent in the sense that the probability of selecting the model with the best predictive ability does not converge to 1 as the total number of…

模拟极端次序统计量的半参数自助法AI 解读

We propose a technique for simulating the joint distribution of the j largest order statistics of a very large sample. We assume that the parent population is in the domain of attraction of the Type 1 (Gumbel) extreme value distribution. The bootstrap variates are generated by resampling the normalized spacings of the k largest observed values in the original data where k is larger than j. We compare the bootstrap distribution to the fitted extremal distribution of Weissman.…

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…

硫酸盐湿沉降的区域趋势AI 解读

I propose a multiple time series model for data from a network of monitoring stations that have both temporal and spatial correlation. The model includes a separate mean and trend for each monitoring station and obtains spatial estimates of mean and trend by smoothing the observed values over a rectangular grid using a discrete smoothing prior. Smoothing parameters and covariance estimates can be chosen subjectively or selected using indirect generalized cross-validation.…

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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…

利用动态回归模型进行预测AI 解读

A Primer on ARIMA Models. A Primer on Regression Models. Rational Distributed Lag Models. Building Dynamic Regression Models: Model Identification. Building Dynamic Regression Models: Model Checking, Reformulation, and Evaluation. Intervention Analysis. Intervention and Outlier Detection and Treatment. Estimation and Forecasting. Dynamic Regression Models in a Vector ARMA Framework. Appendices. References. Index.

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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…

复杂调查数据的假设检验：经典二次型统计量及回归应用AI 解读

Sample surveys often have complex sample designs with multistage cluster sampling, stratification, and differential selection probabilities. This article is concerned with testing the null hypothesis H 0: θ = θ, where the p-dimensional parameter θ = g( μ ) and μ is a q-dimensional vector of means. The asymptotic framework that consists of a sequence of increasing finite populations is used to define μ as the limit of finite population means. As part of the inference, we use…

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…