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近似贝叶斯推断中的 Bartlett 调整AI 解读

In wide generality, the posterior distributions of the likehood ratio statistic and the posterior ratio statistic are chi-squared to error of order O(n−1), where n is sample size. The error in the chi-squared approximation can be reduced to order O(n−2) by Bartlett correction. In this paper, explicit formulae are derived for the Bartlett adjustment factors of both statistics, and the derivations are based on the Tierney. Kass & Kadane (1989) asymptotic approximation for…

随机效应对无条件风险率与生存函数的影响AI 解读

The consequences of introducing random effects have been a major issue in models for survival analysis. A general result is derived to establish the underestimation of the unconditional hazard rate when a random effect is present. Also, the survival time is shown to be underestimated. No distributional assumption regarding the random effect is required.

This paper offers an approach to detecting outliers in multiple time series by studying transfer functions with one input where outliers in the input may or may not be passed to the output.

评估广义线性模型遗漏协变量偏误的几何方法AI 解读

Misspecifying generalized linear models by omitting covariates associated with the response can result in seriously biased estimates of the effects of the included covariates. For certain models, such bias can occur even when the omitted covariate is independent of the included covariates, as in studies with randomized treatment assignment. This paper presents a geometric approach to assess the direction of the bias resulting from omitted covariates and develop intuition…

有偏处理分配下的最优估计AI 解读

This paper provides a semi-parametric solution to a problem proposed by Robbins & Zhang (1991). The solution is obtained utilizing the theory of optimum estimating functions (Godambe & Thompson, 1989). Our solution coincides with maximum likelihood estimation for the parametric model suggested by Robbins & Zhang (1991). Even for alternative models investigated in this paper, the efficiency of our estimation appears very close to that of maximum likelihood estimation.

非参数 Neyman–Scott 问题：望远镜乘积方法AI 解读

In this paper, we consider some generalizations of the Neyman-Scott problem of estimating a common variance in the presence of infinitely many mean nuisance parameters. For example, suppose observations are independent and stratified such that they have common distribution of the form F(x-μk) within the kth stratum. If both F and the location parameters μk are unknown, then estimates for F, obtained by centring the samples in each stratum and constructing an estimate…

受约束的拟似然估计AI 解读

For maximum likelihood or least squares parameter estimation subject to a constrained parameter, the standard approach is to use the method of Lagrange multipliers. In this paper it is shown that the same formal procedure applies very generally for constrained quasi-likelihood estimation even though there is ordinarily no objective function to maximize or minimize. This allows for optimal estimation in a wide range of problems where maximum likelihood cannot be used, such as…

研究剖面似然调整的符号算法AI 解读

A symbolic algorithm for the derivation of the asymptotic expansion of the maximum likelihood estimate was first introduced by Andrews & Stafford (1993). This algorithm is quite general and can be modified to give asymptotic expansions for the maximum likelihood estimate based on either the conditional, modified or adjusted profile likelihoods. Expansions are obtained quickly with no chance for human clerical error. As a result, these three adjustments can be easily studied…

分数差分 ARIMA 过程的可逆性AI 解读

To evaluate how the condition for invertibility of fractional ARIMA (p, d, q) processes can be achieved, we formulate a measure based on the prediction error related to the autoregressive inversion. Some results are obtained by investigating the behaviour of the measure. A conclusion is that the condition for invertibility is satisfied when the degree of fractionally differencing d exceeds −1. As another one, it is pointed out that invertibility is not so easily achieved…

分数噪声样本自相关的偏差AI 解读

The autocorrelation function of fractional noise, when the difference parameter is positive, is quite distinctive. However, for time series of moderate length, this pattern is unlikely to be seen in the sample autocorrelations, which are severely biased when the process mean is unknown.

利用对比型检验区分回归函数的线性与凸性AI 解读

The best linear test is obtained for testing linearity against convexity of a regression function. Some power comparisons are made with the likelihood ratio test.

共同对数优势比的偏差校正最大似然估计AI 解读

A bias-correction factor for the maximum likelihood estimator of the log common odds ratio for sparse data is derived, which is applicable when the design is balanced and/or when the number of strata is large. The corrected maximum likelihood estimator is practically unbiased and its mean squared error is smaller than that of the uncorrected maximum likelihood estimator. The correction factor for the maximum likelihood estimator approaches one as strata sizes increase.…

类别时间序列的谱分析：数值赋值与谱包络AI 解读

Many studies produce categorical time series in which harmonic analysis is of interest. Although there exist time domain approaches for the analysis of categorical time series such as Markov chains or link function based regression models, there is apparently little statistical theory or methodology for analyzing qualitative-valued time series in the frequency domain. The purpose of this paper is to initiate the development of a general framework for the frequency domain…

线性模型异常值检测概率方法的比较AI 解读

This paper compares the use of two posterior probability methods to deal with outliers in linear models. We show that putting together diagnostics that come from the mean-shift and variance-shift models yields a procedure that seems to be more effective than the use of probabilities computed from the posterior distributions of actual realized residuals. The relation of the suggested procedure to the use of a certain predictive distribution for diagnostics is derived.

有限总体问题中的鞍点展开AI 解读

Saddlepoint approximations are derived for the sample mean in the case where samples are obtained randomly without replacement from a finite population. Asymptotic properties are investigated. The great accuracy is demonstrated by numerical examples. Extensions to more general statistics are discussed.

单变量删失下二元生存函数的简单非参数估计AI 解读

In the presence of univariate censoring, the bivariate survival function of paired failure times can be expressed as the ratio of the bivariate at-risk probability to the survival function of the censoring time. The use of this natural representation yields a very simple nonparametric estimator for the bivariate survival curve. The estimator is strongly consistent and, upon proper normalization, converges weakly to a zero-mean Gaussian process with an easily estimated…

癌症临床试验中生活质量分布函数的估计AI 解读

The analysis of quality-of-life data collected at periodic intervals in a cancer clinical trial must account for those patients' data that are ‘missing’ because of death or administrative censoring. We examine estimates of the cumulative distribution function of an interpolated area under a quality-of-life curve as summaries of the quality-of-life experience of a treatment group. A proposed estimator, although biased, offers an improvement over a Kaplan-Meier estimator that…

含个体特定效应的重复有序类别响应比例优势模型AI 解读

Suppose subjects make repeated responses on the same ordered categorical scale. We propose a generalization of the Rasch model that expresses the cumulative logit of the response distribution using subject parameters and a proportional odds structure for item effects. Parameters in the model describe subject-specific, rather than population averaged, effects. Consistent estimation of the effects requires eliminating the subject parameters. We accomplish this by simultaneous…

破纪录数据问题的参数似然推断AI 解读

In this paper we consider the analysis of record breaking data sets, where only observations that exceed, or only those that fall below, the current extreme value are recorded. Example application areas include industrial stress testing, meteorological analysis, sporting and athletic events, and oil and mining surveys. A closely related area is that of threshold modelling, where the observations are those that cross a certain threshold value. The inherent missing data…

具有光滑随机效应密度的非线性混合效应模型AI 解读

The fixed parameters of the nonlinear mixed effects model and the density of the random effects are estimated jointly by maximum likelihood. The density of the random effects is assumed to be smooth but is otherwise unrestricted. The method uses a series expansion that follows from the smoothness assumption to represent the density and quadrature to compute the likelihood. Standard algorithms are used for optimization. Empirical Bayes estimates of random coefficients are…

多步预测中最大似然估计的稳健性：指数平滑情形AI 解读

We extend the argument initiated by Cox (1961) that the exponential smoothing formula can be made more robust for multi-step forecasts if the smoothing parameter is adjusted as a function of the forecast horizon l. The consistency property of the estimator which minimizes the sum of squares of the sample l-step ahead forecast errors makes the robustness result useful in practice. We also generalize the consistency result to some other parsimonious nonstationary models which…

基于经验分布函数的序列独立性非参数检验AI 解读

The Blum, Kiefer & Rosenblatt (1961) statistic for testing independence is considered in a time series setting. This test is, under mild conditions, shown to be consistent against lag one dependent alternatives. The null distribution of the test statistic is established, both when the marginal distribution is continuous and when it is discrete. Simulation results giving information on the size and the power of the test are provided, and comparisons are made with other tests…

利用鞅残差累积和检验 Cox 模型AI 解读

This paper presents a new class of graphical and numerical methods for checking the adequacy of the Cox regression model. The procedures are derived from cumulative sums of martingale-based residuals over follow-up time and/or covariate values. The distributions of these stochastic processes under the assumed model can be approximated by zero-mean Gaussian processes. Each observed process can then be compared, both visually and analytically, with a number of simulated…

用交替逻辑回归建模多元二元数据AI 解读

Marginal models for multivariate binary data permit separate modelling of the relationship of the response with explanatory variables, and the association between pairs of responses. When the former is the scientific focus, a first-order generalized estimating equation method (Liang & Zeger, 1986) is easy to implement and gives efficient estimates of regression coefficients, although estimates of the association among the binary outcomes can be inefficient. When the…