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局部多项式拟合的数据驱动带宽选择：可变带宽与空间适应AI 解读

SUMMARY When estimating a mean regression function and its derivatives, locally weighted least squares regression has proven to be a very attractive technique. The present paper focuses on the important issue of how to select the smoothing parameter or bandwidth. In the case of estimating curves with a complicated structure, a variable bandwidth is desirable. Furthermore, the bandwidth should be indicated by the data themselves. Recent developments in nonparametric smoothing…

协变量缺失或误测时条件密度的半参数有效估计AI 解读

SUMMARY Pepe and Fleming, and Carroll and Wand have recently proposed estimators in a parametric model for the density of a random variable Y conditional on a vector of covariates (X, V) when data on one of the regressors X is missing for some study subjects. We propose a new class of estimators that remains consistent and asymptotically normal even when the probability that X is missing depends on the observed V and Y, includes an estimator whose asymptotic variance attains…

小波收缩：渐近理想之境？AI 解读

SUMMARY Much recent effort has sought asymptotically minimax methods for recovering infinite dimensional objects—curves, densities, spectral densities, images—from noisy data. A now rich and complex body of work develops nearly or exactly minimax estimators for an array of interesting problems. Unfortunately, the results have rarely moved into practice, for a variety of reasons—among them being similarity to known methods, computational intractability and lack of spatial…

考虑短停留区间漏检的单离子通道两状态马尔可夫模型推断AI 解读

SUMMARY A two-state Markov model of a single ion channel, in which successive open and closed sojourns follow negative exponential distributions with respective means μO and μC, is considered. Estimation of (μO μC) when brief sojourns in the open and closed states fail to be detected is studied. The moment estimating equations for (μO, μC) have no, one or two solutions, with two being the most common situation. The asymptotic behaviour of method-of-moments estimators of (μO,…

Logistic 回归系数的可折叠性AI 解读

SUMMARY In this paper we discuss collapsibility of logistic regression coefficients over a background variable and present necessary and sufficient conditions for collapsibility.

线性高斯状态空间模型的贝叶斯模型判别与贝叶斯因子AI 解读

SUMMARY It is shown how to discriminate between different linear Gaussian state space models for a given time series by means of a Bayesian approach which chooses the model that minimizes the expected loss. A practical implementation of this procedure requires a fully Bayesian analysis for both the state vector and the unknown hyperparameters and is carried out by Markov chain Monte Carlo methods. An application to some non-standard situations such as testing hypotheses on…

基于核删失的局部似然AI 解读

SUMMARY By drawing an analogy with likelihood for censored data, a local likelihood function is proposed which gives more weight to observations near a region of interest in the sample space. Resulting methods can be used for assessing local departures from a parametric model, and for semiparametric density estimation. Some theory, and three examples, is given.

识别DNA序列中频率异常的词串AI 解读

SUMMARY Considering a Markov chain model for deoxyribonucleic acid sequences, this paper proposes two asymptotically normal statistics to test whether the frequency of a given word is concordant with the first-order Markov chain model or not. The problem is to choose estimates μ^(W) of the expectation of the frequency Mw of a word W in the observed sequence such that the asymptotic variance of MW−μ^(W) is easily computable. The first estimator is derived from the frequency…

生成并标记所有正规分数因子设计或区组的方法AI 解读

SUMMARY By exploiting the vector space structure of regular qn – m-designs we construct and demonstrate a method for generating all such designs, without repetition, along with their confounded interactions, resolution numbers, alias sets and a decodable design number.

回归中的删除影响与掩蔽AI 解读

SUMMARY The paper is concerned with masking of Cook's distance, the popular deletion measure of influence of individual data cases in linear regression. Masking is broadly concerned with the limitations imposed by the use of individual cases. Two specific views are drawn from quotations: the first is associated with the established idea of joint influence, i.e. the deletion of two or more cases simultaneously, and the second is conditional influence, i.e. the calculation of…

二元核回归的带宽选择器AI 解读

SUMMARY For two and higher dimensional kernel regression, currently available bandwidth selection procedures are based on cross-validation or related penalizing ideas. However, these techniques have been shown to suffer from high sample variability and, in addition, can sometimes be difficult to implement when a vector of bandwidths needs to be selected. In this paper we propose a selector based on an iterative plug-in approach for bivariate kernel regression. It is shown to…

不同扫描方式下 Gibbs 采样器的协方差结构与收敛速率AI 解读

SUMMARY This paper presents results on covariance structure and convergence for the Gibbs sampler with both systematic and random scans. It is shown that, under conditions that guarantee the compactness of the Markov forward operator and irreducibility of the corresponding chain, the Gibbs sampling scheme converges geometrically in terms of Pearson χ 2-distance. In particular, for the random scan, the autocovariance can be expressed as variances of iterative conditional…

利用影响矩阵识别线性回归中的高影响观测子集AI 解读

SUMMARY This paper presents a new method to identify influential subsets in linear regression problems. The procedure uses the eigenstructure of an influence matrix which is defined as the matrix of uncentred covariances of the effect on the whole data set of deleting each observation, normalized to include the univariate Cook statistics on the diagonal. It is shown that the eigenstructure of the influence matrix is useful to identify influential subsets and a procedure for…

相关误差下完全区组设计的主序与 D 最优性AI 解读

SUMMARY D-optimal designs are derived in the complete block design set-up for comparing treatments using ordinary least squares estimators when the experimental errors are correlated. It is shown that the D-optimal design is different from the weakly universally optimal design of Morgan and Chakravarti, and Kiefer and Wynn.

非正则最大似然问题AI 解读

SUMMARY Four non-regular estimation problems are reviewed and discussed. One (the unbounded likelihood problem) involves distributions with infinite spikes, for which maximum likelihood can fail to give consistent estimators. A comparison is made with modified likelihood and spacings methods which do give efficient estimators in this case. An application to the Box–Cox shifted power transform is given. The other three problems occur when the true parameter lies in some…

预测式模型选择AI 解读

SUMMARY We consider the problem of selecting one model from a large class of plausible models. A predictive Bayesian viewpoint is advocated to avoid the specification of prior probabilities for the candidate models and the detailed interpretation of the parameters in each model. Using criteria derived from a certain predictive density and a prior specification that emphasizes the observables, we implement the proposed methodology for three common problems arising in normal…

用于模型比较的分数贝叶斯因子AI 解读

SUMMARY Bayesian comparison of models is achieved simply by calculation of posterior probabilities of the models themselves. However, there are difficulties with this approach when prior information about the parameters of the various models is weak. Partial Bayes factors offer a resolution of the problem by setting aside part of the data as a training sample. The training sample is used to obtain an initial informative posterior distribution of the parameters in each model.…

模型不确定性的评估与传播AI 解读

SUMMARY In most examples of inference and prediction, the expression of uncertainty about unknown quantities y on the basis of known quantities x is based on a model M that formalizes assumptions about how x and y are related. M will typically have two parts: structural assumptions S, such as the form of the link function and the choice of error distribution in a generalized linear model, and parameters θ whose meaning is specific to a given choice of S. It is common in…

量化初始值对非线性预测的影响AI 解读

SUMMARY Motivated by the m-step-ahead prediction problem in non-linear time series, a brief sketch of stochastic chaotic systems is provided. The accuracy of the prediction depends on the initial value, which is a typical feature of non-linear but not necessarily chaotic models. However, if the model is chaotic, small noise can be amplified very quickly through time evolution at some initial values, thereby decreasing dramatically the reliability of the prediction. Further,…

双指数先验下正态均值后验矩的一个注记AI 解读

SUMMARY General results on the behaviour of the posterior mean and variance of the mean of a normal distribution with known variance using a double-exponential prior are derived and complement the conjectures and particular examples given by Pericchi and Smith (1992) and Pericchi and Walley (1991).

复杂系统中的知识表示AI 解读

SUMMARY Modern sensor technologies, especially in biomedicine, produce increasingly detailed and informative image ensembles, many extremely complex. It will be argued that pattern theory can supply mathematical representations of subject-matter knowledge that can be used as a basis for algorithmic ‘understanding’ of such pictures. After a brief survey of the basic principles of pattern theory we shall illustrate them by an application to a concrete situation: high…

通过变换降低核密度估计的边界偏差AI 解读

SUMMARY We consider kernel estimation of a univariate density whose support is a compact interval. If the density is non-zero at either boundary, then the usual kernel estimator can be seriously biased. ‘Reflection’ at a boundary removes some bias, but unless the first derivative of the density is 0 at the boundary the estimator with reflection can still be much more severely biased at the boundary than in the interior. We propose to transform the data to a density that has…

极值指数的估计AI 解读

SUMMARY The extremal index is an important parameter measuring the degree of clustering of extremes in a stationary process. If we consider the point process of exceedance times over a high threshold, then this can be shown to converge asymptotically to a clustered Poisson process. The extremal index, a parameter in the interval [0, 1], is the reciprocal of the mean cluster size. Apart from being of interest in its own right, it is a crucial parameter for determining the…

三参数 Weibull 分布的估计与拟合检验AI 解读

SUMMARY Estimation techniques are given for the three-parameter Weibull distribution, with all parameters unknown. Tables are given for the empirical distribution function statistics W 2, U 2 and A 2, for testing for the distribution.