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顺序限制下多项式回归的经验贝叶斯方法AI 解读

An unknown polynomial is to be estimated over a finite interval from N independent, normally distributed observations. A prior distribution is placed on the polynomial coefficients expressing the opinion that the coefficients decrease in absolute value as the degree of the corresponding terms increase. The data are used to estimate the parameters in the prior distribution of the coefficients. A Monte Carlo study is presented which compares the proposed method with the…

摘要暂缺

序贯假设检验的完全类AI 解读

We consider problems of sequential testing when the loss function is the sum of a component due to an error in the terminal decision and a cost of observation component. In all cases we establish a characterization of a complete class or an essentially complete class. In order to obtain such results for testing a null hypothesis against an alternative hypothesis we establish complete class results for testing the closure of the null hypothesis against the closure of the…

Let $(X, Y)$ be an $\mathbb{R}^d \times \mathbb{R}$-valued random vector and let $(X_1, Y_1), \cdots, (X_n, Y_n)$ be a random sample drawn from its distribution. We study the consistency properties of the kernel estimate $m_n(x)$ of the regression function $m(x) = E\{Y\mid X = x\}$ that is defined by $m_n(x) = \Sigma^n_{i=1} Y_ik((X_i - x)/h_n)/\Sigma^n_{i=1}k((X_i - x)/h_n)$ where $k$ is a bounded nonnegative function on $\mathbb{R}^d$ with compact support and $\{h_n\}$ is…

非线性回归中参数函数的显式估计量AI 解读

Abstract When repetitive estimations are to be made under field conditions using data that follow a nonlinear regression law, a simple polynomial function of the observations has considerable appeal as an estimator. The polynomial estimator of finite degree with smallest average mean squared error is found. Conditions are given such that as degree increases it converges in probability to the Bayes estimator and its average mean squared error converges to the lower bound of…

惩罚似然密度估计与峰值识别：散射及陨石数据示例AI 解读

The (maximum) penalized-likelihood method of probability density estimation and bump-hunting is improved and exemplified by applications to scattering and chondrite data. We show how the hyperparameter in the method can be satisfactorily estimated by using statistics of goodness of fit. A Fourier expansion is found to be usually more expeditious than a Hermite expansion but a compromise is useful. The best fit to the scattering data has 13 bumps, all of which are evaluated…

非线性回归中参数函数的显式估计量AI 解读

When repetitive estimations are to be made under field conditions using data that follow a nonlinear regression law, a simple polynomial function of the observations has considerable appeal as an estimator. The polynomial estimator of finite degree with smallest average mean squared error is found. Conditions are given such that as degree increases it converges in probability to the Bayes estimator and its average mean squared error converges to the lower bound of all square…

线性模型的贝叶斯因子与选择准则AI 解读

Summary Global and local Bayes factors are defined and their respective roles examined as choice criteria among alternative linear models. The global Bayes factor is seen to function, in appropriate contexts, as a fully automatic Occam's razor and to be closely related to the Schwarz model choice criterion. The local Bayes factor is shown to have a close relationship with the Akaike Information Criterion.

基于删失数据的分布函数经验贝叶斯估计札记AI 解读

Susarla and Van Ryzin exhibited an empirical Bayes estimator of a distribution function $F$ based on randomly right-censored observations. In a later paper they obtained a different estimator which alleviates the weaknesses of their earlier estimator and showed that it is asymptotically optimal with rate of convergence $n^{-1}$. The purpose of this note is to present a slightly different estimator which is simpler and is also asymptotically optimal with the same rate of…

Dynkin恒等式在泊松过程速率的贝叶斯序贯估计中的应用AI 解读

Conditional on the value of $\theta, \theta > 0$, let $X(t), t \geqslant 0$, be a homogeneous Poisson process. Sequential estimation procedures of the form $(\sigma, \theta(\sigma))$ are considered. To measure loss due to estimation, a family of functions, indexed by $p$, is used: $L(\theta, \hat{\theta}) = \theta^{-p}(\theta - \hat{\theta})^2$, and the cost of sampling involves cost per arrival and cost per unit time. The notion of "monotone case" for total cost functions…

自适应多元岭回归AI 解读

A multivariate version of the Hoerl-Kennard ridge regression rule is introduced. The choice from among a large class of possible generalizations is guided by Bayesian considerations; the result is implicitly in the work of Lindley and Smith although not actually derived there. The proposed rule, in a variety of equivalent forms is discussed and the choice of its ridge matrix considered. As well, adaptive multivariate ridge rules and closely related empirical Bayes procedures…

弱先验假设下的线性贝叶斯回归估计量AI 解读

A simple set of prior assumptions is given with respect to which the linear Bayes regression estimator, in the case of univariate regression, is determined explicitly. The risk, also determined explicitly, is shown to decrease,at rate 0 ( n-1 ), to the minimum risk attainable by any linear fitting procedure.

层次线性模型推断的贝叶斯设计札记AI 解读

Some simple cases of optimal Bayes designs are investigated for linear models with prior information represented in hierarchical form.

有界损失下的贝叶斯估计AI 解读

Regions containing all possible Bayes estimates under certain classes of bounded loss functions are given for many standard distributions. The properties of such regions are studied in depth for general classes of posterior distributions. Estimators are proposed that replace the posterior mean.

平行线生物测定的贝叶斯方法AI 解读

This paper considers parallel line bioassay from a Bayesian point of view. The mathematical formulation considered is a nonlinear one in which the log potency ratio appears explicitly as a parameter. Models for estimating log potency ratio from a single assay, and also for combining information from several assays are discussed. The method of analysis follows closely the ideas of Lindley & Smith (1972) for the linear model.

面向小样本的综合正态性检验AI 解读

An extension of the test statistic of Spiegelhalter (1977) is investigated. The Bayesian background to the test is discussed, and numerical examples display the adaptive nature of the statistic. A small simulation study indicates good power properties against all alternatives for n = 20, and symmetric alternatives for n = 50.

利用似然比解释法庭科学证据AI 解读

Forensic scientists often have to interpret refractive index measurements made on fragments of window glass, some taken from the scene of a crime and some found on a suspect. Adopting a model used recently by Lindley (1977) and Seheult (1978) this contribution proposes a non-Bayesian solution based on a likelihood ratio. The problem of deciding whether the fragments have come from a common source is distinguished from the problem of deciding the guilt or innocence of the…

次序约束下多项式回归的经验贝叶斯方法AI 解读

An unknown polynomial is to be estimated over a finite interval from N independent, normally distributed observations. A prior distribution is placed on the polynomial coefficients expressing the opinion that the coefficients decrease in absolute value as the degree of the corresponding terms increase. The data are used to estimate the parameters in the prior distribution of the coefficients. A Monte Carlo study is presented which compares the proposed method with the…

含伴随变量的单臂老虎机问题AI 解读

We consider a Bayesian sequential allocation problem that incorporates a concomitant variable in the model. Although the model is highly simplified, our results do have some mildly surprising aspects: (a) the approximate solution to the allocation problem is simpler in the presence of concomitant information than in its absence, (b) the exact value of the discount factor is less important than in previous work, and (c) the myopic procedure is asymptotically optimal.

非参数贝叶斯区间估计AI 解读

Bayesian confidence bands for a distribution function are converted into confidence intervals for specified population quantilea and also for the mean. Bayesian tolerance limits are similarly constructed.

摘要暂缺

方差修正的线性贝叶斯估计量AI 解读

Summary A modification of the linear Bayes estimator of the mean of a distribution of unknown form is proposed, involving a linear estimate for the variance of the distribution. The risk properties of the estimator are discussed and an example is given.

复合决策问题的可容许规则：两行动两状态情形AI 解读

For the two-action two-state compound decision problem, a class of decision rules is found that are both asymptotically optimal and admissible at each stage $n$. These rules are Bayes rules with respect to appropriate exchangeable prior distributions.

渐近最优序贯估计：泊松情形AI 解读

The problems of estimating sequentially the intensity parameter of a homogeneous Poisson process and of estimating sequentially the mean of a sequence of i.i.d. Poisson rv's, are considered. The procedures suggested are shown to perform well for large values of the parameter and/or for small sampling cost. Having bounded regret, the procedure for estimating the mean of the Poisson sequence is asymptotically Bayes w.r.t. any sequence of a priori densities, which spread mass…