Flexible maximum likelihood methods for bivariate proportional hazards models

This article presents methodology for multivariate proportional hazards (PH) regression models. The methods employ flexible piecewise constant or spline specifications for baseline hazard functions in either marginal or conditional PH models, along with assumptions about the association among lifetimes. Because the models are parametric, ordinary maximum likelihood can be applied; it is able to deal easily with such data features as interval censoring or sequentially observed lifetimes, unlike existing semiparametric methods. A bivariate Clayton model (1978, Biometrika 65, 141-151) is used to illustrate the approach taken. Because a parametric assumption about association is made, efficiency and robustness comparisons are made between estimation based on the bivariate Clayton model and "working independence" methods that specify only marginal distributions for each lifetime variable.     

Monte Carlo Estimation for Nonlinear Non-Gaussian State Space Models

We develop a proposal or importance density for state spacemodels with a nonlinear non-Gaussian observation vector y p(y¦)and an unobserved linear Gaussian signal vector p(). The proposaldensity is obtained from the Laplace approximation of the smoothingdensity p(¦y). We present efficient algorithms to calculatethe mode of p(¦y) and to sample from the proposal density.The samples can be used for importance sampling and Markov chainMonte Carlo methods. The new results allow the application ofthese methods to state space models where the observation densityp(y¦) is not log-concave. Additional results are presentedthat lead to computationally efficient implementations. We illustratethe methods for the stochastic volatility model with leverage.     

Regression Modeling of a Physiological Parameter Affected by Both Intrinsic and Extrinsic Factors

We discuss regression modeling of a physiological parameter affected by both intrinsic and extrinsic factors. Such parameter commonly exists in our daily life (e.g., the sleeping quality of human beings or other animals). An additive regression model is suggested which consists of two parts. The first part is for explaining the effect of intrinsic factors and the second part is for describing the effect of extrinsic factors. The fitted model is proved to be statistically consistent. Hypothesis tests about the model coefficients are also discussed. Some simulation results are presented and the modeling procedure is applied to a rat sleep data set.     

Horizontal and elevational phylogeographic patterns of Himalayan and Southeast Asian forest passerines (Aves: Passeriformes)

Aim Zoogeographic patterns in the Himalayas and their neighbouring Southeast Asian mountain ranges include elevational parapatry and ecological segregation, particularly among passerine bird species. We estimate timings of lineage splits among close relatives from the north Palaearctic, the Sino‐Himalayan mountain forests and from adjacent Southeast Asia. We also compare phylogeographic affinities and timing of radiation among members of avian communities from different elevational belts. Location East Asia. Methods We reconstructed molecular phylogenies based on a mitochondrial marker (cytochrome b) and multilocus data sets for seven passerine groups: Aegithalidae, Certhiidae (Certhia), Fringillidae (Pyrrhula), Paridae (Periparus), Phylloscopidae, Regulidae and Timaliidae (Garrulax sensu lato). Molecular dating was carried out using a Bayesian approach applying a relaxed clock in beast . Time estimates were inferred from three independent calibrations based on either a fixed mean substitution rate or fixed node ages. The biogeographic history of each group was reconstructed using a parsimony‐based approach. Results Passerine radiation in Southeast Asia can be divided into roughly three major phases of separation events. We infer that an initial Miocene radiation within the Southeast Asian region included invasions of (sub)tropical faunal elements from the Indo‐Burmese region to the Himalayan foothills and further successive invasions to Central Asia and Taiwan towards the early Pliocene. During two further Pliocene/Pleistocene phases, the subalpine mountain belt of the Sino‐Himalayas was initially invaded by boreal species with clear phylogenetic affinities to the north Palaearctic taiga belt. Most terminal splits between boreal Himalayan/Chinese sister taxa were dated to the Pleistocene. Main conclusions Extant patterns of elevational parapatry and faunal transition in the Sino‐Himalayas originated from successive invasions from different climatic regions. The initiation of Southeast Asian passerine diversification and colonization of the Himalayan foothills in the mid‐Miocene coincides with the postulated onset of Asian monsoon climate and the resulting floral and faunal turnovers. Patterns of elevational parapatry were established by southward invasions of boreal avifaunal elements to the subalpine Sino‐Himalayan forest belt that were strongly connected to climate cooling towards the end of the Pliocene. Current patterns of allopatry and parapatry in boreal species (groups) were shaped through Pleistocene forest fragmentation in East Asia.     

Smoothed quantile regression analysis of competing risks

Censored quantile regression models, which offer great flexibility in assessing covariate effects on event times, have attracted considerable research interest. In this study, we consider flexible estimation and inference procedures for competing risks quantile regression, which not only provides meaningful interpretations by using cumulative incidence quantiles but also extends the conventional accelerated failure time model by relaxing some of the stringent model assumptions, such as global linearity and unconditional independence. Current method for censored quantile regressions often involves the minimization of the L₁‐type convex function or solving the nonsmoothed estimating equations. This approach could lead to multiple roots in practical settings, particularly with multiple covariates. Moreover, variance estimation involves an unknown error distribution and most methods rely on computationally intensive resampling techniques such as bootstrapping. We consider the induced smoothing procedure for censored quantile regressions to the competing risks setting. The proposed procedure permits the fast and accurate computation of quantile regression parameter estimates and standard variances by using conventional numerical methods such as the Newton–Raphson algorithm. Numerical studies show that the proposed estimators perform well and the resulting inference is reliable in practical settings. The method is finally applied to data from a soft tissue sarcoma study.     

The effect of end-point adjustments on smoothing splines used for tree-ring standardization

The cubic smoothing spline has been a popular method for detrending tree-ring data since the 1980s. The common implementation of this procedure (e.g., ARSTAN, dplR) uses a unique method for determining the smoothing parameter that is widely known as the %n criterion. However, this smoothing parameter selection method carries the assumption that end point effects are ignorable. In this paper, we complete the mathematical derivation and show how the original method differs from the complete version, both in the interpretation of the smoothing parameter and in the spline fit. Frequency response curves (FRC) demonstrate how the smoothing parameter is affected by the original assumption. For example, the FRC results indicate that a tree core of 250-year length has a 14% difference in the cut-off frequency when looking at the 67%n criterion. The FRC analysis shows that the existing approach produces a more flexible fit than anticipated, i.e., it is removing more variance than previously thought. For example, a 67%n spline under the existing approach corresponds to a 53%n spline fit. By using both simulated tree-core sequences and a dataset from a Midwest forest, we discuss which conditions result in greater differences between the spline fits and which conditions will have small differences. Tree-core sequences that have more curvature, such as a large-amplitude growth release, will lead to greater differences. Finally, we provide approximations to the end-point effect procedure. For example, using an 83%n criterion under the original approach produces a spline fit approximating the 67%n fit under the complete approach. These approximations could be easily implemented within existing programs like ARSTAN.