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协变量存在测量误差时匹配病例对照研究的优势比回归估计AI 解读

This article studies estimators of the odds ratio and odds ratio regression parameters in finely matched case-control studies containing a binary exposure of primary interest and subject-specific covariates that are subject to measurement error. A retrospective logistic regression model for the binary exposure variable is used. The effect of measurement errors on the conditional maximum likelihood estimator is determined. Three alternatives are considered: bias-corrected,…

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一般估计函数的近似似然比AI 解读

The method of estimating functions (Godambe, 1991) is commonly used when one desires to conduct inference about some parameters of interest but the full distribution of the observations is unknown. However, this approach may have limited utility, due to multiple roots for the estimating function, a poorly behaved Wald test, or lack of a goodness-of-fit test. This paper presents approximate likelihood ratios that can be used along with estimating functions when any of these…

共同典型变量AI 解读

Canonical correlation analysis measures the linear relationship between two random vectors X1 and X2 as the maximum correlation between linear combinations of X1 and linear combinations of X2. Several generalisations of canonical correlation analysis to k2 random vectors X1 …, Xk have been proposed in the literature (Kettenring, 1971, 1985), based on the principle of maximising some generalised measure of correlation. In this paper we propose an alternative generalisation,…

正电子发射断层成像重建中的最小二乘与最大似然比较AI 解读

Positron emission tomography (PET) is a radiologic tool offering a unique capability for measuring tissue metabolism in vivo. A number of biological and physical factors limit the resolution of PET so often the statistical aspects of image reconstruction have an appreciable effect on the quality of information obtained from a study. To a first approximation, reconstruction involves the solution of a linear inverse problem with a line-integral Radon-type transform. Standard…

半参数广义线性模型中的渐近有效估计AI 解读

We use the method of maximum likelihood and regression splines to derive estimates of the parametric and nonparametric components of semiparametric generalized linear models. The resulting estimators of both components are shown to be consistent. Also, the asymptotic theory for the estimator of the parametric component is derived, indicating that the parametric component can be estimated efficiently without under-smoothing the nonparametric component.

若干马尔可夫过程的极小充分统计量与极大似然估计量的显式极限结果：指数族方法AI 解读

Finite-state Markov chains with either a discrete or continuous time parameter, Markov renewal processes and Markov-additive processes are considered. We prove that their likelihood functions, in the nonsequential as well as in various sequential cases, belong to special $(n + k, n)$-curved exponential families in general, for which limit results are easily established. Subsequently, asymptotic normality of the corresponding nonsequential and sequential maximum likelihood…

伪结构突变AI 解读

A quasi-maximum likelihood estimator of the break date is analyzed. Consistency of the estimator is demonstrated under very general conditions, provided that the data-generating process is not integrated. However, the asymptotic distribution of the estimator is quite different for time series that are integrated of order one. In that case, when there is no break, the analyst can be spuriously led to the estimation of a break near the middle of the time series.

不规则采样、控制变量与缺失值下连续时间随机过程的解析得分函数AI 解读

The unknown structural parameters of a continuous/discrete state space model are estimated by maximum likelihood in the presence of irregular sampling, missing values, and cross-sections of time series (panel data). Exogenous (control) variables are included, and the sampling scheme and missing data pattern can be different for each variable and system. Furthermore, the derived non-linear optimization algorithm with analytical score function can be used for the discrete time…

GARCH 稳定分布模型的极大似然估计AI 解读

Abstract Maximum likelihood is used to estimate a generalized autoregressive conditional heteroskedastic (GARCH) process where the residuals have a conditional stable distribution (GARCH‐stable). The scale parameter is modelled such that a GARCH process with normally distributed residuals is a special case. The usual methods of estimating the parameters of the stable distribution assume constant scale and will underestimate the characteristic exponent when the scale…

高斯白噪声中不连续信号最大似然估计渐近效率的精确计算AI 解读

In this paper, the problem of computing the exact value of the asymptotic efficiency of maximum likelihood estimators of a discontinuous signal in a Gaussian white noise is considered. A method based on constructing difference equations for the appropriate moments is presented and used to show that the exact variance of the Pitman estimator is $16\zeta(3)$, where $\zeta$ is the Riemann zeta function.

参数线性约束下最大似然估计的受限 EM 算法AI 解读

The EM algorithm is one of the most powerful algorithms for obtaining maximum likelihood estimates for many incomplete-data problems. But when the parameters must satisfy a set of linear restrictions, the EM algorithm may be too complicated to apply directly. In this article we propose maximum likelihood estimation procedures under a set of linear restrictions for situations in which the EM algorithm could be used if there were no such restrictions on the parameters. We…

多响应回归模型的曲率度量AI 解读

The Bates & Watts (1981) curvature measures developed for single response nonlinear least squares problems are extended to multiresponse parameter estimation problems based on the Box-Draper estimation criterion. Exact determination contours are approximated by contours of the generalised least squares model conditioned on the maximum likelihood estimate of the covariance matrix for the responses. By this approximation, curvature measures calculated for the generalised least…

离散选择模型模拟极大似然估计的渐近偏差AI 解读

In this article, we investigate a bias in an asymptotic expansion of the simulated maximum likelihood estimator introduced by Lerman and Manski (pp. 305–319 in C. Manski and D. McFadden (eds.), Structural Analysis of Discrete Data with Econometric Applications , Cambridge: MIT Press, 1981) for the estimation of discrete choice models. This bias occurs due to the nonlinearity of the derivatives of the log likelihood function and the statistically independent simulation errors…

参数生存模型的序贯方法AI 解读

SUMMARY The asymptotic sequential distribution is derived for score tests and maximum likelihood estimates in parametric survival models in the presence of nuisance parameters where individuals enter over time and the data are subject to right censoring. It is shown that these sequential tests and estimates have an independent increments structure. This allows the use of standard group sequential methods for early stopping.

单一离散分量广义线性混合模型的偏差校正AI 解读

General expressions are derived for the asymptotic biases in three approximate estimators of regression coefficients and variance component, for small values of the variance component, in generalised linear mixed models with canonical link function and a single source of extraneous variation. The estimators involve first and second order Laplace expansions of the integrated likelihood and a related procedure known as penalised quasi-likelihood. Numerical studies of a series…

失效时间回归中的辅助协变量数据AI 解读

SUMMARY We consider the problem of missing covariate data in the context of censored failure time relative risk regression. Auxiliary covariate data, which are considered informative about the missing data but which are not explicitly part of the relative risk regression model, may be available. Full covariate information is available for a validation set. An estimated partial likelihood method is proposed for estimating relative risk parameters. This method is an extension…

平稳向量 ARMA 模型的精确最大似然估计AI 解读

The problems of evaluating and subsequently maximizing the exact likelihood function of vector autoregressive moving average (ARMA) models are considered separately. A new and efficient procedure for evaluating the exact likelihood function is presented. This method puts together a set of useful features that can only be found separately in currently available algorithms. A procedure for maximizing the exact likelihood function, which takes full advantage of the properties…

补充意向治疗分析：处理临床试验中随机化后观测的协变量AI 解读

A problem that arises frequently in the analysis of clinical trials is accounting for covariates observed postrandomization. Two examples are patient compliance measured through pill counts and the dose of a concomitant medication. Typically these are measured concurrently with the primary endpoint at the regularly scheduled follow-ups during the course of the study. To account for these effects, the confounders are sometimes introduced as time-dependent covariates into the…

广义线性模型与拟似然中的局部多项式核回归AI 解读

We investigate the extension of the nonparametric regression technique of local polynomial fitting with a kernel weight to generalized linear models and quasi-likelihood contexts. In the ordinary regression case, local polynomial fitting has been seen to have several appealing features in terms of intuitive and mathematical simplicity. One noteworthy feature is the better performance near the boundaries compared to the traditional kernel regression estimators. These…

风险率回归AI 解读

Linear splines and their tensor products are used to estimate the conditional log-hazard function based on possibly censored, positive response data and one or more covariates. An automatic procedure involving the maximum likelihood method, stepwise addition, stepwise deletion, and the Bayes Information Criterion is used to select the final model. The possible models contain proportional hazards models as a subclass, which makes it possible to diagnose departures from…

补充意向治疗分析：处理临床试验中随机化后观测的协变量AI 解读

A problem that arises frequently in the analysis of clinical trials is accounting for covariates observed postrandomization. Two examples are patient compliance measured through pill counts and the dose of a concomitant medication. Typically these are measured concurrently with the primary endpoint at the regularly scheduled follow-ups during the course of the study. To account for these effects, the confounders are sometimes introduced as time-dependent covariates into the…

单一离散度分量广义线性混合模型的偏差校正AI 解读

General expressions are derived for the asymptotic biases in three approximate estimators of regression coefficients and variance component, for small values of the variance component, in generalised linear mixed models with canonical link function and a single source of extraneous variation. The estimators involve first and second order Laplace expansions of the integrated likelihood and a related procedure known as penalised quasi-likelihood. Numerical studies of a series…

无限方差创新下 ARMA 模型的参数估计AI 解读

We consider a standard ARMA process of the form $\phi(B)X_t = \theta(B)Z_t$, where the innovations $Z_t$ belong to the domain of attraction of a stable law, so that neither the $Z_t$ nor the $X_t$ have a finite variance. Our aim is to estimate the coefficients of $\phi$ and $\theta$. Since maximum likelihood estimation is not a viable possibility (due to the unknown form of the marginal density of the innovation sequence), we adopt the so-called Whittle estimator, based on…