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通过限制极大似然减少时间序列回归中自回归估计的偏差AI 解读

This article considers maximum likelihood (ML) and restricted maximum likelihood (REML) estimation of time series regression models with autoregressive AR(p) noise. Approximate biases of the ML and REML estimators of the AR parameters, based on their approximate representations, are derived. In addition, a bias result for the ML estimator (MLE) of the error variance is established. Numerical results are presented to illustrate the biases of the MLE and REML estimator for the…

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预防 HIV-1 母婴传播随机试验的分析AI 解读

We analyze data from a randomized trial of breastfeeding versus formula feeding in HIV-1-infected mothers and their infants. Estimates of infant HIV-1-free survival and the timing of vertical transmission of HIV-1 are complicated by the fact that the infants' HIV-1 status at death may be unknown, the time of HIV-1 infection may be interval censored, and the tests used to detect HIV-1 infection in the infants may be less than 100% sensitive or specific. To address these…

非线性时间序列的函数系数回归模型AI 解读

The local linear regression technique is applied to estimation of functional-coefficient regression models for time series data. The models include threshold autoregressive models and functional-coefficient autoregressive models as special cases but with the added advantages such as depicting finer structure of the underlying dynamics and better postsample forecasting performance. Also proposed are a new bootstrap test for the goodness of fit of models and a bandwidth…

空间边界不对齐数据的完全模型化方法AI 解读

We consider inference using multivariate data that are spatially misaligned; that is, involving variables (typically counts or rates) that are aggregated over differing sets of regional boundaries. Geographic information systems enable the simultaneous display of such datasets, but their current capabilities are essentially only descriptive, not inferential. We describe a hierarchical modeling approach that provides a natural solution to this problem through its ability to…

似然比统计量的几何理解AI 解读

It is well known that twice a log-likelihood ratio statistic follows asymptotically a chi-square distribution. The result is usually understood and proved via Taylor's expansions of likelihood functions and by assuming asymptotic normality of maximum likelihood estimators (MLEs). We obtain more general results by using a different approach: The Wilks type of results hold as long as likelihood contour sets are fan-shaped. The classical Wilks theorem corresponds to the…

用于拟合优度检验的阶数选择准则AI 解读

The classical problem of assessing the goodness of fit of a postulated parametric distribution is investigated using techniques from nonparametric density estimation. A new test is proposed based on the data-selected order of a Fourier series density estimator. This test has the novel feature of providing an associated nonparametric estimator that can be used to estimate the unknown density when the null hypothesis is rejected. The limiting null distribution of the proposed…

包含交互项与平滑效应的贝叶斯回归建模AI 解读

There have been many recent suggestions as to how to build and estimate flexible Bayesian regression models, using constructs such as trees, neural networks, and Gaussian processes. Although there is much to commend these methods, their implementation and interpretation can be daunting for practitioners. This article presents a spline-based methodology for flexible Bayesian regression that is quite simple in terms of computation and interpretation. Smooth bivariate…

非经典测量误差下参数估计的界限AI 解读

The bias introduced by errors in the measurement of independent variables has increasingly been a topic of interest among researchers estimating economic parameters. However, studies typically use the assumption of classical measurement error; that is, the variable of interest and its measurement error are uncorrelated, and the expected value of the mismeasured variable is equal to the expected value of the true measure. These assumptions often arise from convenience rather…

功能磁共振成像数据的贝叶斯时间过程模型AI 解读

Functional magnetic resonance imaging (fMRI) is a new technique for studying the workings of the active human brain. During an fMRI experiment, a sequence of magnetic resonance images is acquired while the subject performs specific behavioral tasks. Changes in the measured signal can be used to identify and characterize the brain activity resulting from task performance. The data obtained from an fMRI experiment are a realization of a complex spatiotemporal process with many…

互联网流量数据AI 解读

Internet engineering and management depend on an understanding of the characteristics of network traffic. Statistical models are needed that can generate traffic that mimics closely the observed behavior on live Internet wires. Models can be used on their own for some tasks and combined with network simulators for others. But the challenge of model development is immense. Internet traffic data are ferocious. Their statistical properties are complex, databases are very large,…

混合模型后验分布的计算与推断困难AI 解读

This article deals with both exploration and interpretation problems related to posterior distributions for mixture models. The specification of mixture posterior distributions means that the presence of k! modes is known immediately. Standard Markov chain Monte Carlo (MCMC) techniques usually have difficulties with well-separated modes such as occur here; the MCMC sampler stays within a neighborhood of a local mode and fails to visit other equally important modes. We show…

多项式结构方程模型的估计AI 解读

Structural equation analysis is one of the most widely used statistical methods in social and behavioral science research and has become a popular tool in marketing. Subject matter needs for considering nonlinear structural models have been well documented. But current fitting procedures are available only for a limited class of models. In this article a systematic statistical approach is developed for the general polynomial structural equation model. The new procedure…

使用后分层信息的估计量在插补下的刀切方差估计AI 解读

Poststratified estimators are commonly used in sample surveys to improve the efficiency of estimators and to ensure calibration to known poststrata counts. Similarly, generalized regression estimators are used to handle two or more poststratifiers with known marginal counts. In addition, weighting adjustment within weighting classes is used to handle unit nonresponse, and imputation within imputation classes is used to handle item nonresponse. For the full response case,…

变系数模型的高效估计与推断AI 解读

This article deals with statistical inferences based on the varying-coefficient models proposed by Hastie and Tibshirani. Local polynomial regression techniques are used to estimate coefficient functions, and the asymptotic normality of the resulting estimators is established. The standard error formulas for estimated coefficients are derived and are empirically tested. A goodness-of-fit test technique, based on a nonparametric maximum likelihood ratio type of test, is also…

偏倚函数未知时基于有偏样本的非参数密度估计AI 解读

We present a kernel estimator for the density of a variable when sampling probabilities depend on that variable. Both the density and sampling bias weight functions are unknown and are estimated nonparametrically. To achieve this, the method requires that two independent samples be taken from a fixed finite population. An estimator of population size follows simply from our density estimator. Asymptotic bias and standard errors for these estimators are provided, and the…

最小修剪差分回归估计量及其替代方法AI 解读

This article proposes and studies the performance in theory and practice of the least trimmed differences (LTD) linear regression estimator. The estimator minimizes the sum of the smallest quartile of the squares of the differences in each pair of residuals. We obtain the breakdown point, maxbias curve, and large-sample properties of a class of estimators including the LTD as special case. The LTD estimator has a 50% breakdown point and Gaussian efficiency of…

当前状态数据下的线性回归AI 解读

In survival analysis, a linear model often provides an adequate approximation after a suitable transformation of the survival times and possibly of the covariates. This article proposes a semiparametric regression method for estimating the regression parameter in the linear model without specifying the distribution of the random error, where the response variable is subject to so-called case 1 interval censoring. The method uses a constructed random-sieve likelihood and…

动态混合模型的高效贝叶斯推断AI 解读

A Bayesian approach is presented for estimating a mixture of linear Gaussian state-space models. Such models are used to model interventions in time series and nonparametric regression. Markov chain Monte Carlo sampling is usually necessary to obtain the posterior distributions of such mixture models, because it is difficult to obtain them analytically. The methodological contribution of the article is to derive a set of recursions for dynamic mixture models that efficiently…

异方差近似线性模型中用于估计与外推的整数值极小极大稳健设计AI 解读

We present our findings on a new approach to robust regression design. This approach differs from previous investigations into this area in three respects: The use of a finite design space, the use of simulated annealing to carry out the numerical minimization problems, and in our search for integer-valued, rather than continuous, designs. We present designs for the situation in which the response is thought to be approximately polynomial. We also discuss the cases of…