On partial local smoothing rules for curve estimation

We compare the performances of local and global rules for smoothingparameter choice, in terms of asymptotic mean squared errorsof the resulting estimators. In some instances there is surprisinglylittle to choose between local and global approaches; our analysisidentifies contexts where the differences are small or large.This work motivates development of smoothing rules that forma ‘half-way house’ between local and global smoothing.There, interpolation provides a basis for partial local smoothing.A key result shows that interpolation on even a coarse gridcan produce a very good approximation to full local smoothing.Our theoretical and numerical results lead us to suggest linearinterpolation of a bandwidth obtained by integral approximationson discrete intervals.     

Spectral Estimation by Variable Span Log Periodogram Smoothing: An Application to Annual Lynx Numbers

Spectral estimation is commonly based on smoothing the periodogram or its logarithm. In such a smoothing exercise, it is not entirely sensible to use the same bandwidth for all frequencies, since the smoothness of the underlying spectrum may vary. This note describes the use of a variable span smoother in estimating the log spectrum. An application to annual lynx data is presented.     

A genetic and spatial Bayesian analysis of mastitis resistance

A nationwide health card recording system for dairy cattle was introduced in Norway in 1975 (the Norwegian Cattle Health Services). The data base holds information on mastitis occurrences on an individual cow basis. A reduction in mastitis frequency across the population is desired, and for this purpose risk factors are investigated. In this paper a Bayesian proportional hazards model is used for modelling the time to first veterinary treatment of clinical mastitis, including both genetic and environmental covariates. Sire effects were modelled as shared random components, and veterinary district was included as an environmental effect with prior spatial smoothing. A non-informative smoothing prior was assumed for the baseline hazard, and Markov chain Monte Carlo methods (MCMC) were used for inference. We propose a new measure of quality for sires, in terms of their posterior probability of being among the, say 10% best sires. The probability is an easily interpretable measure that can be directly used to rank sires. Estimating these complex probabilities is straightforward in an MCMC setting. The results indicate considerable differences between sires with regards to their daughters disease resistance. A regional effect was also discovered with the lowest risk of disease in the south-eastern parts of Norway.     

Parametric and Parametrically Smoothed Distribution-Free Proportional Hazard Models with Discrete Data

This paper discusses discrete time proportional hazard models and suggests a new class of flexible hazard functions. Explicitly modeling the discreteness of data is important since standard continuous models are biased; allowing for flexibility in the hazard estimation is desirable since strong parametric restrictions are likely to be similarly misleading. Simulation compare continuous and discrete models when data are generated by grouping and demonstrate that simple approximations recover underlying hazards well and outperform nonparametric maximum likelihood estimates in term of mean squared error.     

Critical note on the application of the “two-third” spline

The “two-third spline” (2/3S) is a frequently applied method to detrend tree-ring series. It fits a spline with a 50% frequency cutoff at a frequency equal to two-thirds of each sample length in a dataset. It was introduced to ensure a minimum loss of low-frequency variance, which is resolvable during the detrending of ring-width series.In this paper I show potential problems that arise when rusing this method. The 2/3S runs counter the strengths of using a digital filter to detrend – i.e. one is giving up full control over the frequency-removing characteristics of the growth curve and each individual time series retains a different amount of low frequency. Thus, the 2/3S is less suitable for reconstructing climate or to compare environmental impacts on tree growth between groups – both of which comprise the majority of dendrochronological analyses – as it will likely introduce a temporal frequency bias. Within a long chronology it will result in decreasing power to resolve low frequencies towards present in a living-only trees setting, especially when the youngest segment lengths are 100 years and shorter, and more generally during the period where the chronology is constructed from samples with shorter segment lengths compared to the period with longer segment lengths. The frequency bias will also significantly impact regression slopes and correlation coefficients, possibly distorting analyses investigating multiple groups with different mean segment lengths. Highlighting these potential biases, I recommend the community to not use this method on an individual basis but rather to use a fixed spline stiffness for all samples based on the n% criterion (n = 67) of e.g. the mean segment length of the entire dataset.     

Non‐parametric habitat models with automatic interactions

Questions: Can a statistical model be designed to represent more directly the nature of organismal response to multiple interacting factors? Can multiplicative kernel smoothers be used for this purpose? What advantages does this approach have over more traditional habitat modelling methods? Methods: Non‐parametric multiplicative regression (NPMR) was developed from the premises that: the response variable has a minimum of zero and a physiologically‐determined maximum, species respond simultaneously to multiple ecological factors, the response to any one factor is conditioned by the values of other factors, and that if any of the factors is intolerable then the response is zero. Key features of NPMR are interactive effects of predictors, no need to specify an overall model form in advance, and built‐in controls on overfitting. The effectiveness of the method is demonstrated with simulated and real data sets. Results: Empirical and theoretical relationships of species response to multiple interacting predictors can be represented effectively by multiplicative kernel smoothers. NPMR allows us to abandon simplistic assumptions about overall model form, while embracing the ecological truism that habitat factors interact.     

一个适于最大似然法估计物种分化年代的进化速率平滑近似方法

众所周知 ,物种分化年代的估计对分子钟 (进化速率恒定 )假定很敏感。另一方面 ,在远缘物种 (例如哺乳纲不同目的动物 )的比较中 ,分子钟几乎总是不成立的。这样在估计分化时间时考虑不同进化区系的速率差异至为重要。最大似然法可以很自然地考虑这种速率差异 ,并且可以同时分析多个基因位点的资料以及同时利用多重化石校正数据。以前提出的似然法需要研究者将进化树的树枝按速率分组 ,本文提出一个近似方法以使这个过程自动化。本方法综合了以前的似然法、贝斯法及近似速率平滑法的一些特征。此外 ,还对算法加以改进 ,以适应综合数据分析时某些基因在某些物种中缺乏资料的情形。应用新提出的方法来分析马达加斯加的倭狐猴的分化年代 ,并与以前的似然法及贝斯法的分析进行了比较