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有序单因素设计中基于惩罚基的混合收缩估计AI 解读

This paper constructs improved estimators of the means in the Gaussian saturated one-way layout with an ordinal factor. The least squares estimator for the mean vector in this saturated model is usually inadmissible. The hybrid shrinkage estimators of this paper exploit the possibility of slow variation in the dependence of the means on the ordered factor levels but do not assume it and respond well to faster variation if present. To motivate the development, candidate…

局部—全局神经网络AI 解读

We propose the local-global neural networks model within the context of time series models. This formulation encompasses some already existing nonlinear models and also admits the mixture of experts approach. We emphasize the linear expert case and extensively discuss the theoretical aspects of the model: stationarity conditions, existence, consistency and asymptotic normality of the parameter estimates, and model identifiability. The proposed model consists of a mixture of…

利用混合样条模型进行限制似然比失拟检验AI 解读

Summary Penalized regression spline models afford a simple mixed model representation in which variance components control the degree of non-linearity in the smooth function estimates. This motivates the study of lack-of-fit tests based on the restricted maximum likelihood ratio statistic which tests whether variance components are 0 against the alternative of taking on positive values. For this one-sided testing problem a further complication is that the variance component…

关于由边际密度构造伪似然的说明AI 解读

For likelihood‐based inference involving distributions in which high‐dimensional dependencies are present it may be useful to use approximate likelihoods based, for example, on the univariate or bivariate marginal distributions. The asymptotic properties of formal maximum likelihood estimators in such cases are outlined. In particular, applications in which only a single q×1 vector of observations is observed are examined. Conditions under which consistent estimators of…

纵向数据半参数建模的新估计与模型选择程序AI 解读

Semiparametric regression models are very useful for longitudinal data analysis. The complexity of semiparametric models and the structure of longitudinal data pose new challenges to parametric inferences and model selection that frequently arise from longitudinal data analysis. In this article, two new approaches are proposed for estimating the regression coefficients in a semiparametric model. The asymptotic normality of the resulting estimators is established. An…

通过似然基追踪进行变量选择与模型构建AI 解读

This article presents a nonparametric penalized likelihood approach for variable selection and model building, called likelihood basis pursuit (LBP). In the setting of a tensor product reproducing kernel Hilbert space, we decompose the log-likelihood into the sum of different functional components such as main effects and interactions, with each component represented by appropriate basis functions. Basis functions are chosen to be compatible with variable selection and model…

通过非齐次马尔可夫链模拟实现最优贝叶斯设计AI 解读

We consider decision problems defined by a utility function and an underlying probability model for all unknowns. The utility function quantifies the decision maker's preferences over consequences. The optimal decision maximizes the expected utility function where the expectation is taken with respect to all unknowns, that is, future data and parameters. In many problems, the solution is not analytically tractable. For example, the utility function might involve moments that…

广义加性模型中稳定高效的多重平滑参数估计AI 解读

Representation of generalized additive models (GAM's) using penalized regression splines allows GAM's to be employed in a straightforward manner using penalized regression methods. Not only is inference facilitated by this approach, but it is also possible to integrate model selection in the form of smoothing parameter selection into model fitting in a computationally efficient manner using well founded criteria such as generalized cross-validation. The current fitting and…

遥感高维反演的马尔可夫链蒙特卡洛方法AI 解读

Summary We discuss the inversion of the gas profiles (ozone, NO3, NO2, aerosols and neutral density) in the upper atmosphere from the spectral occultation measurements. The data are produced by the ‘Global ozone monitoring of occultation of stars’ instrument on board the Envisat satellite that was launched in March 2002. The instrument measures the attenuation of light spectra at various horizontal paths from about 100 km down to 10–20 km. The new feature is that these data…

时频曲面估计的贝叶斯变量选择与正则化AI 解读

Summary We describe novel Bayesian models for time–frequency inverse modelling of non-stationary signals. These models are based on the idea of a Gabor regression, in which a time series is represented as a superposition of translated, modulated versions of a window function exhibiting good time–frequency concentration. As a necessary consequence, the resultant set of potential predictors is in general overcomplete—constituting a frame rather than a basis—and hence the…

周期高斯再生核正则化方法的统计性质AI 解读

The method of regularization with the Gaussian reproducing kernel is popular in the machine learning literature and successful in many practical applications. In this paper we consider the periodic version of the Gaussian kernel regularization. We show in the white noise model setting, that in function spaces of very smooth functions, such as the infinite-order Sobolev space and the space of analytic functions, the method under consideration is asymptotically minimax; in…

通过局部随机惩罚进行复杂度正则化AI 解读

In this article, model selection via penalized empirical loss minimization in nonparametric classification problems is studied. Data-dependent penalties are constructed, which are based on estimates of the complexity of a small subclass of each model class, containing only those functions with small empirical loss. The penalties are novel since those considered in the literature are typically based on the entire model class. Oracle inequalities using these penalties are…

利用多协变量调整依赖删失的边际生存函数估计AI 解读

One goal in survival analysis of right-censored data is to estimate the marginal survival function in the presence of dependent censoring. When many auxiliary covariates are sufficient to explain the dependent censoring, estimation based on either a semiparametric model or a nonparametric model of the conditional survival function can be problematic due to the high dimensionality of the auxiliary information. In this paper, we use two working models to condense these…

利用广义谱与非线性时间序列模型推断汇率可预测性AI 解读

It is often documented, based on autocorrelation, variance ratio, and power spectrum, that exchange rates approximately follow a martingale process. Because these data check serial uncorrelatedness rather than martingale difference, they may deliver misleading conclusions in favor of the martingale hypothesis when the test statistics are insignificant. In this paper, we explore whether there exists a gap between serial uncorrelatedness and martingale difference for exchange…

This paper develops a new methodology that makes use of the factor structure of large dimensional panels to understand the nature of nonstationarity in the data. We refer to it as PANIC-Panel Analysis of Nonstationarity in Idiosyncratic and Common components. PANIC can detect whether the nonstationarity in a series is pervasive, or variable-specific, or both. It can determine the number of independent stochastic trends driving the common factors. PANIC also permits valid…

随机线性假设的非参数推断及高维应用AI 解读

The Mann–Whitney–Wilcoxon rank sum test is limited to comparison of two groups with univariate responses. In this paper, we introduce a class of stochastic linear hypotheses that addresses these limitations within a nonparametric setting. We formulate hypotheses for simultaneous comparisons of several, multivariate response groups, without modelling the response distributions. Inference is developed based on U‐statistics theory and an exchangeability assumption. The latter…

参数维度随样本量增长的非凹惩罚似然AI 解读

A class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed by Fan and Li to simultaneously estimate parameters and select important variables. They demonstrated that this class of procedures has an oracle property when the number of parameters is finite. However, in most model selection problems the number of parameters should be large and grow with the sample size. In this paper some asymptotic properties of the…

半参数回归中的一致协变量选择与模型选择后推断AI 解读

This paper presents a model selection technique of estimation in semiparametric regression models of the type $Y_{i}={\beta}^{\prime}\underline{X}_{i}+f(T_{i})+W_{i}$ , i=1,…,n. The parametric and nonparametric components are estimated simultaneously by this procedure. Estimation is based on a collection of finite-dimensional models, using a penalized least squares criterion for selection. We show that by tailoring the penalty terms developed for nonparametric regression to…

数据挖掘中的变量选择AI 解读

We predict the onset of personal bankruptcy using least squares regression. Although well publicized, only 2,244 bankruptcies occur in our dataset of 2.9 million months of credit-card activity. We use stepwise selection to find predictors of these from a mix of payment history, debt load, demographics, and their interactions. This combination of rare responses and over 67,000 possible predictors leads to a challenging modeling question: How does one separate coincidental…

广义线性混合模型的稳健分析AI 解读

The method of maximum likelihood (ML) is widely used for analyzing generalized linear mixed models (GLMM's). A full maximum likelihood analysis requires numerical integration techniques for calculation of the log-likelihood, and to avoid the computational problems involving irreducibly high-dimensional integrals, several maximum likelihood algorithms have been proposed in the literature to estimate the model parameters by approximating the log-likelihood function. Although…

平滑样条高斯回归：通过有效近似实现更可扩展的计算AI 解读

Summary Smoothing splines via the penalized least squares method provide versatile and effective nonparametric models for regression with Gaussian responses. The computation of smoothing splines is generally of the order O(n3), n being the sample size, which severely limits its practical applicability. We study more scalable computation of smoothing spline regression via certain low dimensional approximations that are asymptotically as efficient. A simple algorithm is…

脑成像中重复非均匀点模式的空间强度建模AI 解读

Summary Pharmacological experiments in brain microscopy study patterns of cellular activ- ation in response to psychotropic drugs for connected neuroanatomic regions. A typical ex- perimental design produces replicated point patterns having highly complex spatial variability. Modelling this variability hierarchically can enhance the inference for comparing treatments. We propose a semiparametric formulation that combines the robustness of a nonparametric kernel method with…

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多尺度似然分析与复杂度惩罚估计AI 解读

We describe here a framework for a certain class of multiscale likelihood factorizations wherein, in analogy to a wavelet decomposition of an L2 function, a given likelihood function has an alternative representation as a product of conditional densities reflecting information in both the data and the parameter vector localized in position and scale. The framework is developed as a set of sufficient conditions for the existence of such factorizations, formulated in analogy…