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缺失数据非参数分析的递归算法AI 解读

The mixture of Dirichlet processes posterior that arises in nonparametric Bayesian analysis has been analysed most effectively using Markov chain Monte Carlo. As a computationally simple alternative, we introduce a recursive approximation based on one-step posterior predictive distributions. Asymptotic calculations provide theoretical support for this approximation, and we investigate its actual behaviour in several numerical examples. From a non-Bayesian perspective, this…

缺失数据广义估计方程中的完全随机缺失检验AI 解读

We consider inference from generalised estimating equations when data are incomplete. A test for missing completely at random is proposed to help decide whether or not we should adjust estimating equations to correct the possible bias introduced by a missing-data mechanism that is not missing completely at random. Likelihood ratio tests have been introduced to test the missing completely at random hypothesis (Fuchs, 1982; Little, 1988). For the estimating equation setting,…

组序贯检验后的无偏估计AI 解读

It is shown that, in a group sequential test about the drift θ of a Brownian motion Χ(t) stopped at time Τ, the sufficient statistic (Τ, Χ(Τ)) is not complete for θ. There exist infinitely many unbiased estimators of θ and none has uniformly minimum variance. A truncation-adaptable criterion is proposed, and the uniformly-minimum-variance estimator among all truncation-adaptable unbiased estimators is found. This estimator is identical to estimators of Ferebee (1983) and…

频率估计的快速高效技术：解释与推广AI 解读

In Quinn & Fernandes (1991), an iterative technique was presented for the estimation of the frequency of a sinusoid in the presence of noise. The technique is more robust to poor initial estimates than is the periodogram maximiser. A generalisation to the case of multiple sinusoids is presented in this paper, and it is shown that the original estimator may be interpreted as the maximiser of a smoothed version of the periodogram.

刻画变点最大似然估计量的分布行为AI 解读

We consider the problem of estimating the unknown changepoint in a sequence of time-ordered observations. Upper and lower bounds are derived for the asymptotic distribution of the maximum likelihood estimator and methods of approximation are suggested. A computationally efficient algorithm is presented for deriving the bounds and approximations for the asymptotic probabilities of the maximum likelihood estimator when the parameters before and after the changepoint are…

利用变系数模型进行模型诊断AI 解读

The paper motivates the use of varying coefficient models for diagnostics in regression models with continuous and factorial covariates. The varying coefficient model, which is restricted only by assumptions concerning the smoothness of the effects, is considered as the alternative to a parametric generalised linear model. Estimation is based on local likelihood smoothing and asymptotic properties of the estimators are derived. For the investigation of the discrepancy…

非参数似然比置信区间AI 解读

We consider construction of two-sided nonparametric confidence intervals in a smooth function model setting. A nonparametric likelihood approach based on Stein's least favourable family is proposed as an alternative to empirical likelihood. The approach enjoys the same asymptotic properties as empirical likelihood, but is analytically and computationally less cumbersome. The simplicity of the method allows us to propose and analyse asymptotic and bootstrapping techniques as…

高维列联表中的交互作用：对数线性模型的自助法替代方法AI 解读

Based on a revised Lancaster-type representation of the additive interactions associated with a probability measure, a new approach for the analysis of high-dimensional contingency tables is proposed. The approach is essentially model-free because the additive interaction tensor is merely a convenient reparameterization of the given table. Single interaction terms are investigated using the bootstrap method whose first-order asymptotic validity is immediate. The global…

不连续回归与平滑回归的比较AI 解读

Z.Given measurements $(x_i,y_i) = 1,\dots,n$, we discuss methods to assess whether an underlying regression function is smooth (continuous or differentiable) or whether it has discontinuities. The variance of the measurements is assumed to be unknown, and is estimated simultane-ously. By regressing squared differences of the data formed with various span sizes on the span size itself, we obtain an asymptotic linear model with dependent errors. The parameters of this…

均匀分布对单调密度备择的检验AI 解读

The paper is concerned with testing uniformity versus a monotone den-sity. This problem arises in two important contexts, after transformations, testing whether a sample is a simple random sample or a biased sample, and testing whether the intensity function of a nonhomogeneous Poisson process is constant against monotone alternatives. A penalized likelihood ratio test ($P$-test) and a Dip likelihood test ($D$-test) are developed. The $D$-test is analogous to Hartigan and…

多变量游程检验AI 解读

For independent $d$-variate random variables $X_1,\dots,X_m$ with common density $f$ and $Y_1,\dots,Y_n$ with common density $g$, let $R_{m,n}$ be the number of edges in the minimal spanning tree with vertices $X_1,\dots,X_m$, $Y_1,\dots,Y_n$ that connect points from different samples. Friedman and Rafsky conjectured that a test of $H_0: f = g$ that rejects $H_0$ for small values of $R_{m,n}$ should have power against general alternatives. We prove that $R_{m,n}$ is…

逐步多重检验程序与方向性错误控制AI 解读

One of the most difficult problems occurring with stepwise multiple test procedures for a set of two-sided hypotheses is the control of direc-tional errors if rejection of a hypothesis is accomplished with a directional decision. In this paper we generalize a result for so-called step-down procedures derived by Shaffer to a large class of stepwise or closed multiple test procedures. In a unifying way we obtain results for a large class of order statistics procedures…

随机回归模型的残差经验过程及时间序列应用AI 解读

Motivated by Gaussian tests for a time series, we are led to investigate the asymptotic behavior of the residual empirical processes of stochastic regression models. These models cover the fixed design regression models as well as general AR$(q)$ models. Since the number of the regression coeffi-cients is allowed to grow as the sample size increases, the obtained results are also applicable to nonlinear regression and stationary AR$(\infty)$ models. In this paper, we first…

广义线性模型条件分布的 Gibbs 抽样收敛性与精度AI 解读

This paper presents convergence conditions for a Markov chain constructed using Gibbs sampling, when the equilibrium distribution is the conditional sampling distribution of sufficient statistics from a generalized linear model. For cases when this unidimensional sampling is done approximately rather than exactly, the difference between the target equilibrium distribution and the resulting equilibrium distribution is expressed in terms of the difference between the true and…

The quasi-likelihood function proposed by Wedderburn broadened the scope of generalized linear models by specifying the variance function in-stead of the entire distribution. However, complete specification of variance functions in the quasi-likelihood approach may not be realistic. We define a nonparametric quasi-likelihood by replacing the specified variance function in the conventional quasi-likelihood with a nonparametric variance function estimate. This nonparametric…

区块自助法的理论比较AI 解读

In this paper, we compare the asymptotic behavior of some common block bootstrap methods based on nonrandom as well as random block lengths. It is shown that, asymptotically, bootstrap estimators derived using any of the methods considered in the paper have the same amount of bias to the first order. However, the variances of these bootstrap estimators may be different even in the first order. Expansions for the bias, the variance and the mean-squared error of different…

时间序列的非参数模型检验AI 解读

This paper studies a class of tests useful for testing the goodness-of-fit of an autoregressive model. These tests are based on a class of empirical processes marked by certain residuals. The paper first gives their large sample behavior under null hypotheses. Then a martingale transformation of the underlying process is given that makes tests based on it asymptotically distribution free. Consistency of these tests is also discussed briefly.

泊松过程同质性的调整得分检验AI 解读

Tests of homogeneity are being increasingly used for the analysis of event time data, but relatively little attention has been paid to their distributional properties in settings with small to moderate sample sizes. Here we consider tests of homogeneity for recurrent event data in which the null model is a Poisson process and the alternative is a mixed Poisson process. We examine score and adjusted score statistics in the context of parametric and semiparametric regression…

最小维修模型的次序统计量性质、随机生成与拟合优度检验AI 解读

We present properties of statistics arising from the Block, Borges, and Savits age-dependent minimal repair model. These properties are analogous to the order statistic properties in homogeneous Poisson processes. These properties are exploited to obtain an algorithm for generating a realization from the minimal repair model, and for testing hypothesis concerning the initial distribution function or hazard function of the repair model.

含 Box–Cox 变换的 Logistic 模型中的处理效应AI 解读

We consider a logistic model for binary response data that allows the possibility of power transformation of x; that is, log[p/(1 - p)] = α + βx (λ) + γI, where x is a continuous variable, x (λ) is the Box–Cox transformation, and I is a binary variable indicating treatment or group. This model is applicable to observational studies or randomized trials when a treatment effect is investigated after controlling for a confounding variable x. Our focus is on inference concerning…

准线性小波估计AI 解读

The main paradigm of the modern wavelet theory of spatial adaptation formulated by Donoho and Johnstone is that there is a divergence between the linear minimax adaptation theory and the heuristic guiding algorithm development that leads to the necessity of using strongly nonlinear adaptive thresholded methods. On the other hand, it is well known that linear adaptive estimates are the best whenever an estimated function is smooth. Is it possible to suggest a quasi-linear…

非参数回归问题中的改进估计量AI 解读

Linear estimators of multivariate means are considered. Generalizations of some well-known theorems about admissibility of linear estimators are given. The results then are applied to show that commonly used kernel-type estimators in nonparametric regression problems can be constructively improved in a simple way. An asymptotic result is described that gives a quantitative measure of the maximum improvement to be gained in certain situations. A theoretical bound shows that…

比例优势回归模型中的半参数推断AI 解读

For fitting the proportional odds regression model with right-censored survival times, we introduce some weighted empirical odds functions. These functions are solutions of some self-consistency equations and have a nice martingale representation. From these functions, several classes of new regression estimators, such as the pseudo–maximum likelihood estimator, martingale residual-based estimators, and minimum distance estimators, are derived. These estimators have…

比较预期与实现结果：理论及收入变化应用AI 解读

Household surveys often elicit respondents' intentions or predictions of future outcomes. The survey questions may ask respondents to choose among a selection of (ordered) response categories. If panel data or repeated cross-sections are available, then predictions may be compared with realized outcomes. The categorical nature of the predictions data complicates this comparison, however. Generalizing previous findings on binary intentions data, we derive bounds on features…