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利用 Dirichlet 分布估计洛伦兹曲线AI 解读

The Lorenz curve relates the cumulative proportion of income to the cumulative proportion of population. When a particular functional form of the Lorenz curve is specified, it is typically estimated by linear or nonlinear least squares estimation techniques that have good properties when the error terms are independently and normally distributed. Observations on cumulative proportions are clearly neither independent nor normally distributed. This article proposes and applies…

短期利率的马尔可夫切换与随机波动率扩散模型AI 解读

This article empirically compares the Markov-switching and stochastic volatility diffusion models of the short rate. The evidence supports the Markov-switching diffusion model. Estimates of the elasticity of volatility parameter for single-regime models unanimously indicate an explosive volatility process, whereas the Markov-switching models estimates are reasonable. It is found that either Markov switching or stochastic volatility, but not both, is needed to adequately fit…

混合回归与空间自回归模型中最小二乘的一致性和效率AI 解读

Least squares estimation has casually been dismissed as an inconsistent estimation method for mixed regressive, spatial autoregressive models with or without spatial correlated disturbances. Although this statement is correct for a wide class of models, we show that, in economic spatial environments where each unit can be influenced aggregately by a significant portion of units in the population, least squares estimators can be consistent. Indeed, they can even be…

回顾性家庭研究的分析AI 解读

Case‐control samples allow straightforward calculation of estimates of the association between covariates and disease status by fitting a prospective logistic regression model. In genetic studies of disease, investigators often gather additional information on response and covariate variables from family members of cases and controls. The objective is to model the responses of all the family members in terms of the covariate data. Whittemore (1995) has discussed maximum…

协方差矩阵的谱模型AI 解读

A new model for the simultaneous eigenstructure of multiple covariance matrices is proposed. The model is much more flexible than existing models and subsumes most of them as special cases. A Fisher scoring algorithm for computing maximum likelihood estimates of the parameters under normality is given. Asymptotic distributions of the estimators are derived under normality as well as under arbitrary distributions having finite fourth‐order cumulants. Special attention is…

半参数与非参数后验分布的渐近正态性AI 解读

In this article it is shown that the marginal semiparametric and nonparametric posterior distributions for a parameter of interest behave like an ordinary parametric posterior distribution. This in practice provides support of the utility of marginal semiparametric and nonparametric posterior distributions. In particular, the marginal semiparametric and nonparametric posterior distributions are asymptotically normal and centered at the corresponding maximum likelihood…

伴随右删失的长度偏倚抽样AI 解读

When survival data arise from prevalent cases ascertained through a cross-sectional study, it is well known that the survivor function corresponding to these data is length biased and different from the survivor function derived from incident cases. Length-biased data have been treated both unconditionally and conditionally in the literature. In the latter case, where length bias is viewed as being induced by random left truncation of the survival times, the truncating…

响应延迟下临床试验自适应设计的渐近性质AI 解读

For adaptive clinical trials using a generalized Friedman’s urn design, we derive the limiting distribution of the urn composition under staggered entry and delayed response. The stochastic delay mechanism is assumed to depend on both the treatment assigned and the patient’s response. A very general setup is employed with $K$ treatments and $L$ responses. When $L = K =2$, one example of a generalized Friedman’s urn design is the randomized play-the-winner rule. An…

单纯形约束模型中遗传距离及其他量的估计偏差AI 解读

The genetic distance between two loci on a chromosome is defined as the mean number of crossovers between the loci. The parameters of the crossover distribution are constrained by the parameters of the distribution of chiasmata. Ott (1996) derived the maximum likelihood estimator (MLE) of the parameters of the crossover distribution and the MLE of the mean. We demonstrate that the MLE of the mean is pointwise less than or equal to the empirical mean number of crossovers. It…

分类数据的边际模型AI 解读

Statistical models defined by imposing restrictions on marginal distributions of contingency tables have received considerable attention recently. This paper introduces a general definition of marginal log-linear parameters and describes conditions for a marginal log-linear parameter to be a smooth parameterization of the distribution and to be variation independent. Statistical models defined by imposing affine restrictions on the marginal log-linear parameters are…

广义线性混合模型中的稳健估计AI 解读

Summary Generalized linear mixed models (GLMMs) are widely used to analyse non-normal response data with extra-variation, but non-robust estimators are still routinely used. We propose robust methods for maximum quasi-likelihood and residual maximum quasi-likelihood estimation to limit the influence of outlying observations in GLMMs. The estimation procedure parallels the development of robust estimation methods in linear mixed models, but with adjustments in the dependent…

伯恩斯坦多项式后验的一致性AI 解读

Summary A Bernstein prior is a probability measure on the space of all the distribution functions on [0, 1]. Under very general assumptions, it selects absolutely continuous distribution functions, whose densities are mixtures of known beta densities. The Bernstein prior is of interest in Bayesian nonparametric inference with continuous data. We study the consistency of the posterior from a Bernstein prior. We first show that, under mild assumptions, the posterior is weakly…

离散采样扩散过程的最大似然估计：闭式近似方法AI 解读

When a continuous-time diffusion is observed only at discrete dates, in most cases the transition distribution and hence the likelihood function of the observations is not explicitly computable. Using Hermite polynomials, I construct an explicit sequence of closed-form functions and show that it converges to the true (but unknown) likelihood function. I document that the approximation is very accurate and prove that maximizing the sequence results in an estimator that…

两步计量模型中的估计与推断AI 解读

A commonly used procedure in a wide class of empirical applications is to impute unobserved regressors, such as expectations, from an auxiliary econometric model. This two-step (T-S) procedure fails to account for the fact that imputed regressors are measured with sampling error, so hypothesis tests based on the estimated covariance matrix of the second-step estimator are biased, even in large samples. We present a simple yet general method of calculating asymptotically…

随机波动率模型的贝叶斯分析AI 解读

New techniques for the analysis of stochastic volatility models in which the logarithm of conditional variance follows an autoregressive model are developed. A cyclic Metropolis algorithm is used to construct a Markov-chain simulation tool. Simulations from this Markov chain coverage in distribution to draws from the posterior distribution enabling exact finite-sample inference. The exact solution to the filtering/smoothing problem of inferring about the unobserved variance…

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模型误设的最大似然估计与广义线性混合模型AI 解读

We investigate the impact of model violations on the estimate of a regression coefficient in a generalised linear mixed model. Specifically, we evaluate the asymptotic relative bias that results from incorrect assumptions regarding the random effects. We compare the impact of model violation for two parameterisations of the regression model. Substantial bias in the conditionally specified regression point estimators can result from using a simple random intercepts model when…