日期精度：到日 13 篇 · 到月 3 篇 · 到年 3 篇
对Farewell等《构成回归》的致谢附议与讨论
Peter McCullagh; Seconder of the vote of thanks to Farewell et al. and contribution to the Discussion of Regression by composition', Journal of the Royal S
统计稀疏性
The main contribution of this paper is a mathematical definition of statistical sparsity, which is expressed as a limiting property of a sequence of probability distributions. The limit is characterized by an exceedance measure |$H$| and a rate parameter |$\rho > 0$|, both of which are unrelated to sample size. The definition encompasses all sparsity models that have been suggested in the signal-detection literature. Sparsity implies that |$\rho$| is small, and a sparse…
抽样偏差与 Logistic 模型
Summary In a regression model, the joint distribution for each finite sample of units is determined by a function px(y) depending only on the list of covariate values x=(x(u1),…,x(un)) on the sampled units. No random sampling of units is involved. In biological work, random sampling is frequently unavoidable, in which case the joint distribution p(y,x) depends on the sampling scheme. Regression models can be used for the study of dependence provided that the conditional…
对 Brooks、Giudici 与 Roberts 论文的讨论
This paper aims to develop general strategies for improving jumps between models in reversible jump Markov chain Monte Carlo (MCMC) algorithms, which is quite an important and timely goal. Indeed, in practical implementations of the method, we usually find that the choice of proposals is paramount: in many cases, the ‘natural choice’ leads to a zero acceptance probability and the construction of well-tuned moves is often quite costly. Given that the reversible jump MCMC…
什么是统计模型？
This paper addresses two closely related questions, "What is a statistical model?" and "What is a parameter?" The notions that a model must "make sense," and that a parameter must "have a well-defined meaning" are deeply ingrained in applied statistical work, reasonably well understood at an instinctive level, but absent from most formal theories of modelling and inference. In this paper, these concepts are defined in algebraic terms, using morphisms, functors and natural…
SUMMARY It is shown that the usual Laplace approximation is not a valid asymptotic approximation when the dimension of the integral is comparable with the limiting parameter n. The formal Laplace expansion for multidimensional integrals is given and used to construct asymptotic approximations for high dimensional integrals. One example is considered in which the dimension of the integral is O(n 1/2) and the relative error of the unmodified Laplace approximation is O(1).…
修正剖面似然与 Cox–Reid 调整剖面似然关系的一则札记
An adjustment to the profile likelihood proposed by Cox & Reid (1987) when the parameters are orthogonal is shown to agree with modified profile likelihood in a number of instances in which the parameters are not orthogonal. Several examples of the phenomenon are given. In the case of composite transformation models with invariant parameter as the parameter of interest, it is shown that the Cox-Reid adjustment agrees with modified profile likelihood in a large-deviation…
修正剖面似然与 Cox–Reid 调整剖面似然的关系
An adjustment to the profile likelihood proposed by Cox & Reid (1987) when the parameters are orthogonal is shown to agree with modified profile likelihood in a number of instances in which the parameters are not orthogonal. Several examples of the phenomenon are given. In the case of composite transformation models with invariant parameter as the parameter of interest, it is shown that the Cox-Reid adjustment agrees with modified profile likelihood in a large-deviation…
柯西模型中的条件推断
Many computations associated with the two-parameter Cauchy model are shown to be greatly simplified if the parameter space is represented by the complex plane rather than the real plane. With this convention we show that the family is closed under Mö bius transformation of the sample space: there is a similar induced transformation on the parameter space. The chief raison d'être of the paper, however, is that the two-parameter Cauchy model provides an example of a nonunique…
广义线性模型中的偏误校正
SUMMARY In this paper we derive general formulae for first-order biases of maximum likelihood estimates of the linear parameters, linear predictors, the dispersion parameter and fitted values in generalized linear models. These formulae may be implemented in the GLIM program to compute bias-corrected maximum likelihood estimates to order n −1, where n is the sample size, with minimal effort by means of a supplementary weighted regression. For linear logistic models it is…
格点分布的 Edgeworth 展开
This paper investigates the use of Edgeworth expansions for approximating the distribution function of the normalized sum of $n$ independent and identically distributed lattice-valued random variables. We prove that the continuity-corrected Edgeworth series, using Sheppard-adjusted cumulants, is accurate to the same order in $n$ as the usual Edgeworth approximation for continuous random variables. Finally, as a partial justification of the Sheppard adjustments, it is shown…
SUMMARY We propose a simple adjustment for profile likelihoods. The aim of the adjustment is to alleviate some of the problems inherent in the use of profile likelihoods, such as bias, inconsistency and overoptimistic variance estimates. The adjustment is applied to the profile log-likelihood score function at each parameter value so that its mean is zero and its variance is the negative expected derivative matrix of the adjusted score function. For cases in which explicit…
一类连续单变量分布的若干统计性质
A new two-parameter family of continuous univariate distributions on the interval (– 1, 1) is introduced, and some properties are given. It is shown that parameters θ and v are globally orthogonal in the Fisher information sense and that, to some extent, they have the properties of a location parameter and a precision parameter, respectively. A pivotal statistic is constructed whose distribution is independent of the location parameter. Finally, the connection with…
回归中的k统计量与离散程度效应
By the term $k$-statistic or polykay, we mean an unbiased estimate of a cumulant or product of cumulants [Fisher (1929) and Tukey (1950), 1956)]. In this paper, two sets of unbiased estimates are given for the case where the mean response, $E(Y)$, depends linearly on known covariates $x$. The $k$'s are symmetric functions of the least-squares residuals and have previously been discussed by Anscombe (1961; 1981, Appendix 2). The $l$'s are optimal in the sense of having…
离散数据拟合优度统计量的条件分布
I consider the distribution of Pearson's statistic and of the likelihood-ratio goodness-of-fit statistic for discrete data in the important case where the data are extensive but sparse. It is argued that the appropriate reference distribution is conditional on the sufficient statistic for the unknown regression parameters, β. The first three conditional asymptotic cumulants are derived by Edgeworth expansion, and these are used for the computation of tail probabilities. The…
比例优势模型中干扰参数的消除
SUMMARY The problem of eliminating nuisance parameters in the context of the proportional odds model is considered. The technique used involves a form of sequential conditioning but it is not equivalent to a conditional or partial likelihood. Applications to ordered responses in the context of a matched pairs design are considered but the method can also be used where the responses are continuous.
局部充分性
SUMMARY Non-Bayesian inference is considered for a scalar parameter θ based on a p-dimensional statisticXwhich need not constitute a sufficient reduction of the original data. It is shown that there exists a (p−1)-dimensional statistic A that is jointly second-order locally ancillary for θ near θ0 but that, for p > 2, A is not unique even up to nonsingular transformations. To avoid any ambiguity in the resulting inferences, we show that there exists a statistic S, to be…
拟似然函数
The connection between quasi-likelihood functions, exponential family models and nonlinear weighted least squares is examined. Consistency and asymptotic normality of the parameter estimates are discussed under second moment assumptions. The parameter estimates are shown to satisfy a property of asymptotic optimality similar in spirit to, but more general than, the corresponding optimal property of Gauss-Markov estimators.
Summary A general class of regression models for ordinal data is developed and discussed. These models utilize the ordinal nature of the data by describing various modes of stochastic ordering and this eliminates the need for assigning scores or otherwise assuming cardinality instead of ordinality. Two models in particular, the proportional odds and the proportional hazards models are likely to be most useful in practice because of the simplicity of their interpretation.…