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Estimating Millions of Dynamic Timing Patterns in Real Time

实时估计数百万个动态交易时点模式

In some business applications, the transaction behavior of each customer is tracked separately with a customer signature. A customer's signature for buying behavior, for example, may contain information on the likely place of purchase, value of goods purchased, type of goods purchased, and timing of purchases. The signature may be updated whenever the customer makes a transaction, and, because of storage limitations, the updating may be able to use only the new transaction…

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Information and Posterior Probability Criteria for Model Selection in Local Likelihood Estimation

局部似然估计中模型选择的信息与后验概率准则

Local likelihood estimation has proven to be an effective method for obtaining estimates of parameters that vary with a covariate. To obtain useful estimates of such parameters, approximating models are used. In such cases it is useful to consider window based estimates. We may need to choose between competing approximating models. In this article, we propose a modification to the methods used to motivate many information and posterior probability criteria for the weighted…

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Likelihood-Based Methods for Missing Covariates in the Cox Proportional Hazards Model

Cox 比例风险模型中缺失协变量的似然方法

Problems associated with missing covariate data are well known but often ignored. We present a method for estimating the parameters in the Cox proportional hazards model when the missing data are missing at random (MAR) and censoring is noninformative. Due to the computational burden of this method, we introduce an approximation that allows us to use a weighted expectation-maximization (EM) algorithm to estimate the parameters more easily. When the missing covariates are…

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Generalized Least Squares, Taylor Series Linearization and Fisher's Scoring in Multivariate Nonlinear Regression

In this article, we consider a general multivariate nonlinear regression setting in which the marginal mean and variance–covariance structure share a common set of regression parameters. Estimation is carried out via iteratively reweighted generalized least squares (IRGLS) that entails repeated application of Taylor series linearization and estimated generalized least squares (EGLS). Under normality, this IRGLS procedure is equivalent to Fisher's method of scoring and hence…

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Marginal Likelihood From the Metropolis–Hastings Output

利用 Metropolis–Hastings 输出估计边际似然

This article provides a framework for estimating the marginal likelihood for the purpose of Bayesian model comparisons. The approach extends and completes the method presented in Chib (1995) by overcoming the problems associated with the presence of intractable full conditional densities. The proposed method is developed in the context of MCMC chains produced by the Metropolis–Hastings algorithm, whose building blocks are used both for sampling and marginal likelihood…

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Jackknife Variance Estimation for Nearest-Neighbor Imputation

最近邻插补的刀切法方差估计

Nearest-neighbor imputation is a popular hot deck imputation method used to compensate for nonresponse in sample surveys. Although this method has a long history of application, the problem of variance estimation after nearest-neighbor imputation has not been fully investigated. Because nearest-neighbor imputation is a nonparametric method, a nonparametric variance estimation technique, such as the jackknife, is desired. We show that the naive jackknife that treats imputed…

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Spatially Adaptive Regression Splines and Accurate Knot Selection Schemes

空间自适应回归样条与精确结点选择方案

Spline procedures have proven effective in estimating smooth functions. However, spline procedures based on stepwise addition and/or deletion have some drawbacks. They suffer from the knot compounding problem, making their performance suboptimal. Furthermore, due to computational complexity, spline procedures may not achieve their full potential. In this article, we propose a novel knot selection algorithm for regression spline estimation in nonparametric regression. The…

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Confidence Intervals for Nonparametric Curve Estimates

非参数曲线估计的置信区间

Numerous nonparametric regression methods exist that yield consistent estimators of function curves. Often, one is also interested in constructing confidence intervals for the unknown function. When a function estimate is based on a single global smoothing parameter the resulting confidence intervals may hold their desired confidence level 1 – α on average but because bias in nonparametric estimation is not uniform, they do not hold the desired level uniformly at all design…

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ANCOVA Methods for Heteroscedastic Nonparametric Regression Models

异方差非参数回归模型的协方差分析方法

We consider an ANCOVA design in which the relationship between the response Yi and the covariate Xi in cell (factor-level combination) i satisfies the model Yi = mi(Xi)+σi(Xi)ϵi, where the error term ϵi is assumed to be independent of Xi, and mi and σi are respectively a smooth (but unknown) regression and scale function. This model can be viewed as a generalization of the nonparametric ANCOVA model of Young and Bowman. As such it is a useful alternative for parametric or…

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Gibbs Sampling Methods for Stick-Breaking Priors

折棍先验的 Gibbs 抽样方法

A rich and flexible class of random probability measures, which we call stick-breaking priors, can be constructed using a sequence of independent beta random variables. Examples of random measures that have this characterization include the Dirichlet process, its two-parameter extension, the two-parameter Poisson–Dirichlet process, finite dimensional Dirichlet priors, and beta two-parameter processes. The rich nature of stick-breaking priors offers Bayesians a useful class…

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Smoothing Spline ANOVA for Multivariate Bernoulli Observations With Application to Ophthalmology Data

多元伯努利观测的平滑样条方差分析及眼科应用

We combine a smoothing spline analysis of variance (SS-ANOVA) model and a log-linear model to build a partly flexible model for multivariate Bernoulli data. The joint distribution conditioning on the predictor variables is estimated. The log odds ratio is used to measure the association between outcome variables. A numerical scheme based on the block one-step successive over relaxation SOR–Newton-Ralphson algorithm is proposed to obtain an approximate solution for the…

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Investigating Child Mortality in Malawi Using Family and Community Random Effects

利用家庭和社区随机效应研究马拉维儿童死亡率

The Malawi Demographic and Health Survey conducted in 1992 collected the retrospective birth histories for a national sample of 4,878 women aged between 15 and 49 years. The sample was randomly selected by a two-stage sampling design. The data consist of biological, demographic, and social variables collected for each birth. This article models the infant and early childhood survival using family and community random effect multipliers on the fixed effect proportional…

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Poststratification Without Population Level Information on the Poststratifying Variable With Application to Political Polling

缺少总体分层变量信息时的后分层:政治民调应用

We investigate the construction of more precise estimates of a collection of population means using information about a related variable in the context of repeated sample surveys. The method is illustrated using poll results concerning presidential approval rating (our related variable is political party identification). We use poststratification to construct these improved estimates, but because we do not have population level information on the poststratifying variable, we…

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Markov chain Monte Carlo Estimation of Classical and Dynamic Switching and Mixture Models

经典与动态切换及混合模型的马尔可夫链蒙特卡洛估计

Bayesian estimation of a very general model class, where the distribution of the observations depends on a latent process taking values in a discrete state space, is discussed in this article. This model class covers finite mixture modeling, Markov switching autoregressive modeling, and dynamic linear models with switching. The consequences the unidentifiability of this type of model has on Markov chain Monte Carlo (MCMC) estimation are explicitly dealt with. Joint Bayesian…

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A Model-Calibration Approach to Using Complete Auxiliary Information From Survey Data

利用调查数据完整辅助信息的模型校准方法

Suppose that the finite population consists of N identifiable units. Associated with the ith unit are the study variable, yi, and a vector of auxiliary variables, xi. The values x1, x2,…, xN are known for the entire population (i.e., complete) but yi is known only if the ith unit is selected in the sample. One of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage. In this article, a unified model-assisted framework…

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The Distribution of Realized Exchange Rate Volatility

汇率已实现波动率的分布

Using high-frequency data on deutschemark and yen returns against the dollar, we construct model-free estimates of daily exchange rate volatility and correlation that cover an entire decade. Our estimates, termed realized volatilities and correlations, are not only model-free, but also approximately free of measurement error under general conditions, which we discuss in detail. Hence, for practical purposes, we may treat the exchange rate volatilities and correlations as…

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Driving Fast in Reverse

倒车疾驰

Structural equation modeling is one of the most widely used statistical techniques in the social sciences, especially psychology. Its popularity and complexity have spawned a large number of “user-friendly” computer programs, training seminars, introductory textbooks, edited volumes, and an internet discussion group (SEMNET). A review of several introductory textbooks and an edited volume raises disturbing questions about the interplay between commercial development,…

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Missing Data: Dial M for ???

缺失数据:拨 M 找寻什么?

The question mark is common notation for the missing data that occur in most applied statistical analyses. Over the past century, statisticians and other scientists not only have invented numerous methods for handling missing/incomplete data, but also have invented many forms of missing data, including data augmentation, hidden states, latent variables, potential outcome, and auxiliary variables. Purposely constructing unobserved/unobservable variables offers an…

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