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扩散过程及其样本路径AI 解读

Prerequisites.- 1. The standard BRownian motion.- 1.1. The standard random walk.- 1.2. Passage times for the standard random walk.- 1.3. Hin?in's proof of the de Moivre-laplace limit theorem.- 1.4. The standard Brownian motion.- 1.5. P. Levy's construction.- 1.6. Strict Markov character.- 1.7. Passage times for the standard Brownian motion.- Note l: Homogeneous differential processes with increasing paths.- 1.8. Kolmogorov's test and the law of the iterated logarithm.- 1.9.…

F. Y. Edgeworth：概率、统计与经济学著作AI 解读

Volume 1: probability the law of error. Volume 2. Volume 3: applications of probability and statistical theory to economics and the social sciences applications of probability and statistical theory to physics, chemistry and biology applications of probability and statistical theory to education applications of probability and statistical theory to psychial research.

行为科学的简明统计学AI 解读

Getting started: why study satistics? basic concepts and ideas. Descriptive statistics: frequency distributions and graphs summary measures relative measures and the normal curve linear correlation linear regression. Concepts of inferential statistics: sampling distributions logic of hypothesis testing. Methods of inferential statistics: one-sample t statistic - when a t ratio is not practical two-sample t tests analysis of variance two-way analysis of variance…

存在干扰参数时的一种检验方法AI 解读

We are interested in testing Ψ = 0 against an alternative in the presence of some nuisance parameter λ. The usual procedure for such problems is to use a test statistic that is a function of the data only. Let q(λ) denote the p-value at a given value λ. If q(λ) does not depend on λ, then in principle we can apply this procedure. However, a major difficulty that arises in many situations is that q(λ) depends on λ and therefore cannot be used as a p-value. In such cases, the…

针对 ARMA(1,1) 备择的序列相关检验AI 解读

This article is concerned with tests for serial correlation in time series and in the errors of regression models. In particular, the nonstandard problem of testing for white noise against autoregressive moving average model ARMA(1, 1) alternatives is considered. The likelihood ratio (LR), sup Lagrange multiplier (LM), and exponential average LM and LR tests are shown to be asymptotically admissible for ARMA(1, 1) alternatives. In addition, they are shown to be consistent…

全信息项目因子模型的拟合与桥接抽样的实证考察AI 解读

Based on item response theory, Bock and Aitken introduced a method of item factor analysis, termed full-information item factor (FIIF) analysis by Bartholomew because it uses all distinct item response vectors as data. But a limitation of their fitting algorithm is its reliance on fixed-point Gauss—Hermite quadrature, which can produce appreciable numerical errors, especially in high-dimension problems. The first purpose of this article is to offer more reliable methods by…

不完整数据下稳健多元线性回归的贝叶斯分析AI 解读

The multivariate t distribution and other normal/independent multivariate distributions, such as the multivariate slash distribution and the multivariate contaminated distribution, are used for robust regression with complete or incomplete data. Most previous work focused on the method of maximum likelihood estimation for linear regression using normal/independent distributions. This article considers Bayesian estimation of multivariate linear regression models using…

地震时间演化的贝叶斯分析AI 解读

We adopt a Bayesian approach to analyze the occurrence times of seismic events and their magnitudes. We choose an epidemic model for the process of occurrence times conditional on the observed magnitude values. The locations of, and dependencies between, the model parameters are determined on the basis of historical and physical information. The overall prior variability is deliberately made diffuse. We generate samples from the joint posterior distribution of the model…

截断数据的积矩相关系数与线性回归AI 解读

The random truncation model has been considered extensively in the literature. Tsai has noted that many previous results hold under the weaker assumption of quasi-independence between the failure time and the truncation time in the observable region of truncated data. We generalize the Pearson product-moment correlation coefficient to measure the association between both time variables in the observable region. We show that if the failure time and the truncation time follow…

非参数风险率估计中平滑参数的 Bootstrap 选择AI 解读

An asymptotic representation of the mean weighted integrated squared error for the kernel-based estimator of the hazard rate in the presence of right-censored samples is obtained for different bootstrap resampling methods. As a consequence, a new bandwidth selector based on the bootstrap is introduced. Very satisfactory simulations results are obtained in comparison to the cross-validation selector for different models, using WARPed (i.e., binned) versions of the estimators.

单调剂量—响应曲线的估计AI 解读

Estimating monotone dose—response curves with independent, normal errors has been studied in detail in the literature. A simple procedure using a generalization of the studentized maximum modulus technique is proposed for constructing confidence bands for monotone regression functions. This procedure is shown to compare well with its predecessors. The center of this smooth and efficient confidence band is then used to estimate a smooth monotone regression function. Its…

由蒙特卡洛检验构造置信区间AI 解读

Monte Carlo tests have exact level when the distribution of the test statistic is free of nuisance parameters. Confidence sets obtained by inverting such tests are also exact but may have a complicated structure. The sets reduce to intervals if the sampling can be organized in a special way. A sufficient condition is that the test statistic is monotone in the parameter of interest when all random drawings are kept fixed. Examples given include models from the one-parameter…

方向数据置信域的改进枢轴方法AI 解读

The importance of pivoting is well established in the context of nonparametric confidence regions. It ensures enhanced coverage accuracy. However, pivoting for directional data cannot be achieved simply by rescaling. A somewhat cumbersome pivotal method, which involves passing first into a space of higher dimension, has been developed by Fisher and Hall for samples of unit vectors. Although that method has some advantages over nonpivotal techniques, it does suffer from…

聚类有序测量的边际回归模型AI 解读

This article constructs statistical models for clustered ordinal measurements. We specify two regression models: one for the marginal means and one for the marginal pairwise global odds ratios. Of particular interest are problems in which the odds ratio regression is a focus. Simple assumptions about higher-order conditional moments give a quadratic exponential likelihood function with second-order estimating equations (GEE2) as score equations. But computational difficulty…

广义线性测量误差模型中的工具变量估计AI 解读

Instrumental variable estimation in generalized linear measurement error models are studied. For models with canonical link functions, unbiased estimating equations are derived. The maximum likelihood estimator for the normal theory, structural linear instrumental variable model is shown to be a solution to the estimating equations derived herein. Logistic regression is studied in detail. An example is given and a simulation study described for the logistic model based on…

儿童成长结果研究中的“观察窗口问题”AI 解读

Numerous statistical studies of the determinants of children's attainments measure the circumstances or events occurring over the childhood period by observations of these variables for a single year or a short duration during childhood. These variables are accepted as proxies for information over the entire childhood period. We explore the reliability of estimated results from studies that use such “window” variables. Because window variables describing intermittent events…

专家混合与层级专家混合模型的贝叶斯推断：语音识别应用AI 解读

Machine classification of acoustic waveforms as speech events is often difficult due to context dependencies. Here a vowel recognition task with multiple speakers is studied via the use of a class of modular and hierarchical systems referred to as mixtures-of-experts and hierarchical mixtures-of-experts models. The statistical model underlying the systems is a mixture model in which both the mixture coefficients and the mixture components are generalized linear models. A…

利用前瞻性数据估计HIV母婴传播率与儿童艾滋病潜伏期AI 解读

This article considers the estimation of the rate of vertical human immunodeficiency virus (HIV) transmission and the pediatric acquired immune deficiency syndrome (AIDS) incubation period using data from birth cohort studies. Standard methods of analysis, which ignore children whose infection status is not established, may lead to biased estimates. Methods based on modeling the disappearance of HIV antibody or appearance of virus are inefficient, as they essentially rely on…

群体药代动力学模型中协变量的贝叶斯建模AI 解读

Pharmacokinetic (PK) models describe how the concentrations of a drug and its metabolite vary with time. Population PK models identify and quantify sources of between-individual variability in observed concentrations. Crucial to this aim is the identification of those covariates (i.e., individual-specific characteristics) responsible for explaining the variability. In this article we discuss how covariate modeling can be carried out for population PK models. We argue that…

纵向数据一阶条件自回归模型的 EM 拟合AI 解读

An EM algorithm fits a state-space formulation of the longitudinal regression model in which a continuous response depends on the lagged response and both time-dependent and time-independent covariates. The baseline response depends only on covariates. The model handles both missing data and Gaussian measurement error on both response and continuous covariates. The E step uses the Kalman filter and associated filtering algorithms to update the unknown true response and…

环境时间序列的非线性加性模型及地面臭氧应用AI 解读

Environmental time series usually vary systematically in response to meteorological conditions and thus often are not stationary. In this article a class of additive models are introduced for environmental time series, in which both mean levels and variances of the series are nonlinear functions of relevant meteorological variables. Backfitting algorithms in nonlinear regression are adopted to estimate the unknown functions in the model, and the maximum likelihood method is…

基于 LDU 分解的矩阵秩检验的渐近性质AI 解读

Gill and Lewbel recently introduced a test for the rank of a matrix based on the LDU decomposition. Unfortunately, the asymptotic distribution suggested by them is incorrect except in a very limited problem. In general, the asymptotic distribution is that of a highly complicated nonlinear function of a normally distributed random vector that appears to defy useful characterization. The LDU decomposition can be used to produce a valid test asymptotically equivalent to the…

不等概率抽样中方差计算简便的高效估计量AI 解读

For unequal probability sampling designs, design-based variance estimation is cumbersome because it requires second-order inclusion probabilities. For most fixed sample size probability proportional-to-size (φPS) schemes, these probabilities are difficult to compute, and the variance estimation depends on them for a tedious double-sum calculation. We show how to replace the traditional φPS scenario with simpler design/estimator alternatives that preserve the high efficiency…