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混合回归模型中的假设检验AI 解读

Summary We establish asymptotic theory for both the maximum likelihood and the maximum modified likelihood estimators in mixture regression models. Moreover, under specific and reasonable conditions, we show that the optimal convergence rate of n−1/4 for estimating the mixing distribution is achievable for both the maximum likelihood and the maximum modified likelihood estimators. We also derive the asymptotic distributions of two log-likelihood ratio test statistics for…

有序性状分离分析的潜变量模型AI 解读

Many health conditions, including cancer and psychiatric disorders, are believed to have a complex genetic basis, and genes and environmental factors are likely to interact in the presence and severity of these conditions. Assessing familial aggregation and inheritability of disease is a classic topic of genetic epidemiology, commonly referred to as segregation analysis. Although today it is routine to conduct such analyses for quantitative and dichotomous traits, methods…

多元自适应样条模型中线性方向的识别AI 解读

Identifying linear directions in multivariate regression has been a statistical challenge and has attracted particular attention since projection pursuit was developed. To this end, we propose and investigate the use of linear discriminant analysis and projection Hessian directions in conjunction with multivariate adaptive regression splines. Simulation studies in a variety of settings demonstrate the usefulness of our approach in revealing both the functional forms and the…

随机场局部极大值的期望个数与管状邻域体积AI 解读

Using an expression for the expected number of local maxima of a random field, we derive an upper bound for the volume of a tube about a manifold in the unit sphere and show that under certain conditions our bound agrees with the evaluation of the tube volume in Weyl's formula. Applications to tests and confidence regions in nonlinear regression are discussed.

半线性回归中的置信区域AI 解读

For the simple semilinear regression model.y =βf(θ) +ɛ, we obtain conservative approximations to likelihood ratio confidence regions for 6 and joint regions for (θ,β) which in many cases are essentially exact. To approximate the required probability we adapt the upcrossings approach of Johnstone & Siegmund (1989). In simple examples we compare our regions with two others which have been widely discussed in the literature.

半线性回归中的置信区域AI 解读

For the simple semilinear regression model.y =βf(θ) +ɛ, we obtain conservative approximations to likelihood ratio confidence regions for 6 and joint regions for (θ,β) which in many cases are essentially exact. To approximate the required probability we adapt the upcrossings approach of Johnstone & Siegmund (1989). In simple examples we compare our regions with two others which have been widely discussed in the literature.