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马尔可夫过程与微分方程：渐近问题AI 解读

1 Stochastic Processes Defined by ODE's.- 2 Small Parameter in Higher Derivatives: Levinson's Case.- 3 The Large Deviation Case.- 4 Averaging Principle for Stochastic Processes and for Partial Differential Equations.- 5 Averaging Principle: Continuation.- 6 Remarks and Generalizations.- 7 Diffusion Processes and PDE's in Narrow Branching Tubes.- 8 Wave Fronts in Reaction-Diffusion Equations.- 9 Wave Fronts in Slowly Changing Media.- 10 Large Scale Approximation for…

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多项分布数据的拟合优度检验AI 解读

Several new test procedures are proposed for assessing the goodness of fit of a postulated multinomial distribution. The new tests are Neyman smooth-type tests with orders selected adaptively from the data. They are shown, through Fourier and large-sample analyses, to provide potential improvements over classical methods in terms of their ability to detect certain types of alternatives. Simulation results and a real example illustrate the finite-sample validity of the…

纵向数据的部分条件均值建模AI 解读

We propose a general modeling approach to longitudinal data that is a hybrid of the marginal regression models of Zeger and Liang and of the classical transition models such as used in time series analyses. Rather than conditioning at time t only on covariate values, as is typical with the marginal approach, or on the entire history of the process up to t, as is typical with the transition model approach, we suggest models that condition on a subset of the process history.…

含无关数据与核验偏差样本的非参数最大似然估计AI 解读

Suppose that some measurements come from a distribution F that is of interest and others come from another, irrelevant distribution G. Some measurements from F are verified and known to be from F. The other, unverified measurements may be from F or from G. Not all measurements from F are equally likely to be verified, and no measurement from G is ever verified. This model applies to measurements of low concentrations obtained using gas chromatography/mass spectroscopy, for…

两阶段抽样中回归估计量的方差估计AI 解读

Many techniques in survey sampling depend on the possession of information about an auxiliary variable x, or a vector of auxiliary variables, available for the entire population. Regression estimates require , the population mean. If such information is unavailable, then one can sometimes obtain a large preliminary sample of xi relatively cheaply and use this to obtain a good estimate, say , of A smaller subsample can then be taken and the characteristic of interest, yi ,…

允许数据缺失的多特征随机效应模型AI 解读

The use of random-effects models for the analysis of longitudinal data with missing responses has been discussed by several authors. This article extends the random-effects model for a single characteristic to the case of multiple characteristics, allowing for arbitrary patterns of observed data. Two different structures for the covariance matrix of measurement error are considered: uncorrelated error between responses and correlation of error terms at the same measurement…

均值与协方差结构分析的理论和实践改进AI 解读

The most widely used multivariate statistical models in the social and behavioral sciences involve linear structural relations among observed and latent variables. In practice, these variables are generally nonnormally distributed; hence classical multivariate analysis, based on multinomial error-free variables having no simultaneous interrelations, is not adequate to deal with such data. A promising alternative, based on asymptotically distribution-free (ADF) covariance…

人工神经网络的预测区间AI 解读

The artificial neural network (ANN) is becoming a very popular model for engineering and scientific applications. Inspired by brain architecture, artificial neural networks represent a class of nonlinear models capable of learning from data. Neural networks have been applied in many areas, including pattern matching, classification, prediction, and process control. This article focuses on the construction of prediction intervals. Previous statistical theory for constructing…

ARIMA模型中季节移动平均单位根的检验AI 解读

Procedures to test for a unit root in the seasonal moving average (MA) operator for seasonal autoregressive integrated moving average (ARIMA) models are examined. Such procedures are useful to distinguish deterministic from stochastic seasonal patterns. The simple (integrated) seasonal MA(1) model Z t ≡ Y t - Yt-s = (1 - θB s)ϵt, where {Y t} is the observed seasonal series and {ϵt} is a white noise sequence, is considered, and tests for H 0: θ = 1 versus H 1: θ < 1 are…

众数位于边界时贝叶斯因子的近似AI 解读

Bayes factors, measuring the strength of evidence in favor of the null, are often used in the Bayesian approach to testing hypotheses. Laplace approximations to Bayes factors are convenient and quite accurate in many contexts. However, one usual assumption—the existence of an interior mode—does not always hold. The posterior mode can occur at the boundary of the parameter space. This article discusses the boundary mode Laplace's method for boundary modes, uses it to…

利用后验模拟与Laplace–Metropolis估计量估计贝叶斯因子AI 解读

The key quantity needed for Bayesian hypothesis testing and model selection is the integrated, or marginal, likelihood of a model. We describe a way to use posterior simulation output to estimate integrated likelihoods. We describe the basic Laplace—Metropolis estimator for models without random effects. For models with random effects, we introduce the compound Laplace-Metropolis estimator. We apply this estimator to data from the World Fertility Survey and show it to give…

通过条件高斯动态模型进行多项时间序列的贝叶斯预测AI 解读

We consider inference in the class of conditionally Gaussian dynamic models for nonnormal multivariate time series. In such models, data are represented as drawn from nonnormal sampling distributions whose parameters are related both through time and hierarchically across several multivariate series. A key example—the main focus here—is time series of multinomial observations, a common occurrence in sociological and demographic studies involving categorical count data.…

层级泊松回归建模AI 解读

The Poisson model and analyses here feature nonexchangeable gamma distributions (although exchangeable following a scale transformation) for individual parameters, with standard deviations proportional to means. A relatively uninformative prior distribution for the shrinkage values eliminates the ill behavior of maximum likelihood estimators of the variance components. When tested in simulation studies, the resulting procedure provides better coverage probabilities and…

神经传递分析中的层级混合模型AI 解读

Hierarchically structured mixture models are studied in the context of data analysis and inference on neural synaptic transmission characteristics in mammalian, and other, central nervous systems. Mixture structures arise due to uncertainties about the stochastic mechanisms governing the responses to electrochemical stimulation of individual neurotransmitter release sites at nerve junctions. Models attempt to capture such scientific features as the sensitivity of individual…

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删失数据析因设计的非参数方法AI 解读

Nonparametric hypotheses of no main effects, no simple effects, and no interaction effects are considered in the context of factorial designs with censored observations. To test these hypotheses, the asymptotic distribution of quadratic forms of rank statistics is derived using the methodology of martingales for counting processes. The weights used reduce to the usual logistic scores with uncensored data but are different from the weights commonly used for testing the…

为回归曲线检验获得最优功效的平滑参数选择AI 解读

We consider selection of smoothing parameters to obtain optimal power in tests of regression curves. We examine three tests and propose empirical smoothing parameters to maximize the power in each test. We also show that the data-based smoothing parameters converge to the optimal smoothing parameters as sample sizes get larger. We conduct a simulation study for various classes of alternative showing the effectiveness of the proposed procedures.

评估回归模型适切性的图形方法AI 解读

Graphical paradigms for assessing the adequacy of nearly any regression model are discussed. The fundamental idea is to examine the fit of a model using a sequence of marginal model plots. On each plot, nonparametric estimates of fit derived from the model are compared to nonparametric fits based on the observed data. Several examples are given.

广义部分线性单指标模型AI 解读

The typical generalized linear model for a regression of a response Y on predictors (X, Z) has conditional mean function based on a linear combination of (X, Z). We generalize these models to have a nonparametric component, replacing the linear combination α T 0X + β T 0Z by η0(α T 0X) + β T 0Z, where η0(·) is an unknown function. We call these generalized partially linear single-index models (GPLSIM). The models include the “single-index” models, which have β0 = 0. Using…

非参数回归中适应稀疏设计的插值方法AI 解读

We suggest interpolation methods for overcoming the problem of sparse design in local linear smoothing. These methods are based on simple rules, determined by the kernel and bandwidth, for deciding when and where pseudo-design points should be added to augment the original design sequence. New ordinates for the added design points are computed by simple interpolation, then local linear smoothing is applied directly to the expanded dataset. The method is competitive with…