Large sample estimation and prediction for explosive growth curve models

Asymptotic distributions of maximum likelihood estimators for the parameters in explosive growth curve models are derived. Limit distributions of prediction errors when the parameters are estimated are also obtained. The growth curve models are viewed as multivariate time-series models, and the usual time-series methods are used for prediction. Estimation constrained by a hypothesis of homogeneity of growth rates is also considered.     

中、美两国混凝土结构规范的一个差异

介绍了中，美两国现行规范中受压区混凝土应力应变曲线，并以此为基础，研究了两种不同曲线的异同点，展开了与此相关的讨论。     

Two-Event Model for Carcinogenesis: Biological, Mathematical, and Statistical Considerations

A two-mutation model for carcinogenesis is reviewed. General principles in fitting the model to epidemiologic and experimental data are discussed, and some examples are given. A general solution to the model with time-dependent parameters is developed, and its use is illustrated by application to data from an experiment in which rats exposed to radon developed lung tumors.     

Measuring non-linear dependence for two random variables distributed along a curve

We propose new dependence measures for two real random variables not necessarily linearly related. Covariance and linear correlation are expressed in terms of principal components and are generalized for variables distributed along a curve. Properties of these measures are discussed. The new measures are estimated using principal curves and are computed for simulated and real data sets. Finally, we present several statistical applications for the new dependence measures.     

Considerations for optimal nonparametric regression under a generalizederror structure

Nonparametric smoothing, such as kernel or spline estimation, has been examined extensively under the assumption of uncorrelated errors. This paper addresses the effects of potential correlation on consistency and other asymptotic properties in a repeated-measures model, using directly optimized linear smoothers of the replicate means. Unrestricted optimal weights, with respect to squared error loss, are used to confirm a lack of consistency for all linear estimators in an autocorrelated errors model. The results indicate kernel methods that work well for an uncorrelated errors model may not have the ability to perform satisfactorily when correlation is introduced, due to an asymmetry in the optimal weights, which disappears for an uncorrelated errors model. These would include data-driven bandwidth selection methods, adjustments of the bandwidth to accommodate correlation, higher-order kernels, and related bias reduction techniques. The analytic results suggest alternative approaches, not considered here in detail, which have shown merit.     

Adding functions to ensure regression converges

Regression fits a curve to data by minimizing a function of the residuals. The process of fitting a family of functions may fail to converge because the family of candidate functions has no minimum. After investigating what functions to add to a family to ensure a minimum exists, four families are examined. The family of polynomials needs no additional functions. Additional functions are found for the families of exponential growth curves, probit curves, and logistic curves. A sufficient condition tells when the minimum is not in the original family.     

Analysis of a factorial quantal response assay using inverse regression

An inverse regression approach to analyzing quantal response assays with one quanritative independent- variable and any number of qualitative independent variables is presented. A general factorial model ror LQC- inverted relationship and methods of testing hypotheses estimating qulitative Interest are developed. This naper provides a modified method of analysis which is easier to apply than previously existing methods.     

Local Power Analyses of Goodness-of-fit Tests for Copulas

Abstract.  The asymptotic behaviour of several goodness-of-fit statistics for copula families is obtained under contiguous alternatives. Many comparisons between a Cramér–von Mises functional of the empirical copula process and new moment-based goodness-of-fit statistics are made by considering their associated asymptotic local power curves. It is shown that the choice of the estimator for the unknown parameter can have a significant influence on the power of the Cramér–von Mises test and that some of the moment-based statistics can provide simple and efficient goodness-of-fit methods.     

CORRECTING FOR MEASUREMENT ERROR IN AN EXPOSURE-RESPONSE RELATIONSHIP BASED ON DICHOTOMISING A CONTINUOUS DEPENDENT VARIABLE

Random error in a continuous outcome variable does not affect its regression on a predictor. However, when a continuous outcome variable is dichotomised, random measurement error results in a flatter exposure-response relationship with a higher intercept. Although this consequence is similar to the effect of misclassification in a binary outcome variable, it cannot be corrected using techniques appropriate for binary data. Conditional distributions of the measurements of the continuous outcome variable can be corrected if the reliability coefficient of the measurements can be estimated. An unbiased estimate of the exposure-response relationship is then easily calculated. This procedure is demonstrated using data on the relationship between smoking and the development of airway obstruction.     

Some results concerning off-training-set and IID error for the Gibbs and the Bayes optimal generalizers

In this paper we analyse the average behaviour of the Bayes-optimal and Gibbs learning algorithms. We do this both for off-training-set error and conventional IID (independent identically distributed) error (for which test sets overlap with training sets). For the IID case we provide a major extension to one of the better known results. We also show that expected IID test set error is a non-increasing function of training set size for either algorithm. On the other hand, as we show, the expected off-training-set error for both learning algorithms can increase with training set size, for non-uniform sampling distributions. We characterize the relationship the sampling distribution must have with the prior for such an increase. We show in particular that for uniform sampling distributions and either algorithm, the expected off-training-set error is a non-increasing function of training set size. For uniform sampling distributions, we also characterize the priors for which the expected error of the Bayes-optimal algorithm stays constant. In addition we show that for the Bayes-optimal algorithm, expected off-training-set error can increase with training set size when the target function is fixed, but if and only if the expected error averaged over all targets decreases with training set size. Our results hold for arbitrary noise and arbitrary loss functions.