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二项可探测性模型中的种群规模推断AI 解读

Many models for biological populations, including simple mark-recapture models and distance sampling models, involve a binomially distributed number, n, of observations x1, …, xn on members of a population of size N. Two popular estimators of (N, θ), where θ is a vector parameter, are the maximum likelihood estimator and the conditional maximum likelihood estimator based on the conditional distribution of x1, …, xn given n. We derive the large-N asymptotic distributions of…

指数族非线性模型中的偏差缩减AI 解读

In Firth (1993, Biometrika) it was shown how the leading term in the asymptotic bias of the maximum likelihood estimator is removed by adjusting the score vector, and that in canonical-link generalized linear models the method is equivalent to maximizing a penalized likelihood that is easily implemented via iterative adjustment of the data. Here a more general family of bias-reducing adjustments is developed for a broad class of univariate and multivariate generalized…

闭合指数族中利用复合似然进行最大似然估计AI 解读

In certain multivariate problems the full probability density has an awkward normalizing constant, but the conditional and/or marginal distributions may be much more tractable. In this paper we investigate the use of composite likelihoods instead of the full likelihood. For closed exponential families, both are shown to be maximized by the same parameter values for any number of observations. Examples include log-linear models and multivariate normal models. In other cases…

双曲正弦—反双曲正弦分布族AI 解读

We introduce the sinh-arcsinh transformation and hence, by applying it to a generating distribution with no parameters other than location and scale, usually the normal, a new family of sinh-arcsinh distributions. This four-parameter family has symmetric and skewed members and allows for tailweights that are both heavier and lighter than those of the generating distribution. The central place of the normal distribution in this family affords likelihood ratio tests of…

自适应近似贝叶斯计算AI 解读

Sequential techniques can enhance the efficiency of the approximate Bayesian computation algorithm, as in Sisson et al.’s (2007) partial rejection control version. While this method is based upon the theoretical works of Del Moral et al. (2006), the application to approximate Bayesian computation results in a bias in the approximation to the posterior. An alternative version based on genuine importance sampling arguments bypasses this difficulty, in connection with the…

依赖情形下自适应 Bonferroni 与 Holm 程序的一则说明AI 解读

Hochberg & Benjamini (1990) first presented adaptive procedures for controlling familywise error rate. However, until now, it has not been proved that these procedures control the familywise error rate. We introduce a simplified version of Hochberg & Benjamini’s adaptive Bonferroni and Holm procedures. Assuming a conditional dependence model, we prove that the former procedure controls the familywise error rate in finite samples while the latter controls it approximately.

病例对照研究中风险预测标志物评价的半参数方法AI 解读

The performance of a well-calibrated risk model for a binary disease outcome can be characterized by the population distribution of risk and displayed with the predictiveness curve. Better performance is characterized by a wider distribution of risk, since this corresponds to better risk stratification in the sense that more subjects are identified at low and high risk for the disease outcome. Although methods have been developed to estimate predictiveness curves from cohort…

矩阵正态图模型的贝叶斯分析AI 解读

We present Bayesian analyses of matrix-variate normal data with conditional independencies induced by graphical model structuring of the characterizing covariance matrix parameters. This framework of matrix normal graphical models includes prior specifications, posterior computation using Markov chain Monte Carlo methods, evaluation of graphical model uncertainty and model structure search. Extensions to matrix-variate time series embed matrix normal graphs in dynamic…

小波回归的广义 fiducial 推断AI 解读

We apply Fisher’s fiducial idea to wavelet regression, first developing a general methodology for handling model selection problems within the fiducial framework. We propose fiducial-based methods for wavelet curve estimation and the construction of pointwise confidence intervals. We show that these confidence intervals have asymptotically correct coverage. Simulations demonstrate that they possess promising empirical properties.

双重稳健 G 估计量方差的一则说明AI 解读

A recursive variance calculation is derived for doubly-robust G-estimators for dynamic treatment regimes in a multi-interval setting. Treatment decision parameters are not assumed to be shared across treatment intervals; this independence of parameters permits sequential estimation of the G-estimators’ variance when G-estimation is performed in a sequential fashion. The recursive variance calculation is both natural and computationally feasible. This development can easily…

横截面抽样下疾病—死亡模型患病概率的非参数估计AI 解读

Cross-sectional sampling is an attractive design that saves resources but results in biased data. For proper inference, one should first discover the bias function and then weigh observations appropriately. We consider cross-sectioning of the illness-death model with the aim of estimating the probability of visiting the illness state before death. We develop simple consistent and asymptotically normal estimators under various assumptions on the model and data collection and,…

贝叶斯 lasso 回归AI 解读

The lasso estimate for linear regression corresponds to a posterior mode when independent, double-exponential prior distributions are placed on the regression coefficients. This paper introduces new aspects of the broader Bayesian treatment of lasso regression. A direct characterization of the regression coefficients’ posterior distribution is provided, and computation and inference under this characterization is shown to be straightforward. Emphasis is placed on point…

嵌套拉丁超立方设计AI 解读

We propose an approach to constructing nested Latin hypercube designs. Such designs are useful for conducting multiple computer experiments with different levels of accuracy. A nested Latin hypercube design with two layers is defined to be a special Latin hypercube design that contains a smaller Latin hypercube design as a subset. Our method is easy to implement and can accommodate any number of factors. We also extend this method to construct nested Latin hypercube designs…

调查数据项目无应答插补后的线性化方差估计统一方法AI 解读

Variance estimation after imputation is an important practical problem in survey sampling. When deterministic imputation or stochastic imputation is used, we show that the variance of the imputed estimator can be consistently estimated by a unifying linearize and reverse approach. We provide some applications of the approach to regression imputation, fractional categorical imputation, multiple imputation and composite imputation. Results from a simulation study, under a…

泛函在双样本调查线性化与复合估计中的应用AI 解读

An important problem associated with two-sample surveys is the estimation of nonlinear functions of finite population totals such as ratios, correlation coefficients or measures of income inequality. Computation and estimation of the variance of such complex statistics are made more difficult by the existence of overlapping units. In one-sample surveys, the linearization method based on the influence function approach is a powerful tool for variance estimation. We introduce…

利用完整解曲面进行自适应正则化AI 解读

Several sparseness penalties have been suggested for delivery of good predictive performance in automatic variable selection within the framework of regularization. All assume that the true model is sparse. We propose a penalty, a convex combination of the L1- and L∞-norms, that adapts to a variety of situations including sparseness and nonsparseness, grouping and nongrouping. The proposed penalty performs grouping and adaptive regularization. In addition, we introduce a…

Student t 混合自回归模型及其在厚尾金融数据中的应用AI 解读

We introduce the class of Student t-mixture autoregressive models, which is promising for financial time series modelling. The model is able to capture serial correlations, time-varying means and volatilities, and the shape of the conditional distributions can be time varied from short-tailed to long-tailed, or from unimodal to multimodal. The use of t-distributed errors in each component of the model allows conditional leptokurtic distributions that account for the commonly…

惩罚样条估计量的渐近性质AI 解读

We study the class of penalized spline estimators, which enjoy similarities to both regression splines, without penalty and with fewer knots than data points, and smoothing splines, with knots equal to the data points and a penalty controlling the roughness of the fit. Depending on the number of knots, sample size and penalty, we show that the theoretical properties of penalized regression spline estimators are either similar to those of regression splines or to those of…

α-积和式的近似计算AI 解读

The standard matrix permanent is the solution to a number of combinatorial and graph-theoretic problems, and the α-weighted permanent is the density function for a class of Cox processes called boson processes. The exact computation of the ordinary permanent is known to be #P-complete, and the same appears to be the case for the α-permanent for most values of α. At present, the lack of a satisfactory algorithm for approximating the α-permanent is a formidable obstacle to the…

数据维度对经验似然的影响AI 解读

We evaluate the effects of data dimension on the asymptotic normality of the empirical likelihood ratio for high-dimensional data under a general multivariate model. Data dimension and dependence among components of the multivariate random vector affect the empirical likelihood directly through the trace and the eigenvalues of the covariance matrix. The growth rates to infinity we obtain for the data dimension improve the rates of Hjort et al. (2008).

改进不完整数据下总体均值双重稳健估计的效率与稳健性AI 解读

Abstract Considerable recent interest has focused on doubly robust estimators for a population mean response in the presence of incomplete data, which involve models for both the propensity score and the regression of outcome on covariates. The usual doubly robust estimator may yield severely biased inferences if neither of these models is correctly specified and can exhibit nonnegligible bias if the estimated propensity score is close to zero for some observations. We…

半参数变换模型中的加权 Breslow 型估计与最大似然估计AI 解读

A semiparametric transformation model comprises a parametric component for covariate effects and a nonparametric component for the baseline hazard/intensity. The Breslow-type estimator has been proposed for estimating the nonparametric component in some inefficient estimation procedures. We show that introducing weights into this estimator leads to nonparametric maximum likelihood estimation, with the weights depending on the martingale residuals. The weighted Breslow-type…

计数时间序列的负二项模型AI 解读

We study generalized linear models for time series of counts, where serial dependence is introduced through a dependent latent process in the link function. Conditional on the covariates and the latent process, the observation is modelled by a negative binomial distribution. To estimate the regression coefficients, we maximize the pseudolikelihood that is based on a generalized linear model with the latent process suppressed. We show the consistency and asymptotic normality…

动态计算机程序的高斯过程仿真代理AI 解读

Computer codes are used in scientific research to study and predict the behaviour of complex systems. Their run times often make uncertainty and sensitivity analyses impractical because of the thousands of runs that are conventionally required, so efficient techniques have been developed based on a statistical representation of the code. The approach is less straightforward for dynamic codes, which represent time-evolving systems. We develop a novel iterative system to build…