Random effects regression mixtures for analyzing infant habituation

Random effects regression mixture models are a way to classify longitudinal data (or trajectories) having possibly varying lengths. The mixture structure of the traditional random effects regression mixture model arises through the distribution of the random regression coefficients, which is assumed to be a mixture of multivariate normals. An extension of this standard model is presented that accounts for various levels of heterogeneity among the trajectories, depending on their assumed error structure. A standard likelihood ratio test is presented for testing this error structure assumption. Full details of an expectation-conditional maximization algorithm for maximum likelihood estimation are also presented. This model is used to analyze data from an infant habituation experiment, where it is desirable to assess whether infants comprise different populations in terms of their habituation time.     

递推关系式的建立和应用

通过建立递进关系 ,求解数学中有关数量的问题     

Bootstrapping estimators for the seemingly unrelated regressions model

In this paper we consider the possibility of using the bootstrap to estimate the finite sample variability of feasible generalized least squares and improved estimators applied to the seemingly unrelated regressions model. The improved estimators we employ include members of the Stein-rule family and a hierarchical Bayes estimator proposed by Blattberg and George (1991). Simulation experiments are carried out using several SUR examples as well as a very large example based on the price-promotion model, and data, from marketing research.     

Bivariate versus univariate ordinal categorical data with reference to an ophthalmologic study

The Wisconsin Epidemiologic Study of Diabetic Retinopathy is a population-based epidemiological study carried out in Southern Wisconsin during the 1980s. The resulting data were analysed by different statisticians and ophthalmologists during the last two decades. Most of the analyses were carried out on the baseline data, although there were two follow-up studies on the same population. A Bayesian analysis of the first follow-up data, taken four years after the baseline study, was carried out by Angers and Biswas [Angers, J.-F. and Biswas, A., 2004, A Bayesian analysis of the four-year follow-up data of theWisconsin epidemiologic study of diabetic retinopathy. Statistics in Medicine, 23, 601–615.], where the choice of the best model in terms of the covariate inclusion is done, and estimates of the associated covariate effects were obtained using the baseline data to set the prior for the parameters. In the present article we consider an univariate transformation of the bivariate ordinal data, and a parallel analysis with the much simpler univariate data is carried out. The results are then compared with the results of Angers and Biswas (2004). In conclusion, our analyses suggest that the univariate analysis fails to detect features of the data found by the bivariate analysis. Even an univariate transformation of our data with quite high correlation with both left and right eyes is inadequate.     

Comparative Study of Generalized Estimating Equations and Logistic Regressions on Different Sample Sizes and Correlation Levels

In this study, it was aimed to determine accuracy of generalized estimating equations versus logistic regressions on different correlation levels and sample sizes. For this aim, two methods were compared with different sample sizes 10, 25, 50 and 100 and correlation levels 0.0, 0.3, 0.5 and 0.8. Result of this study showed that using generalized estimating equations could be preferred versus logistic regression when the sample size is over than 25 and correlation level is higher than 0.3 on data taken from studies with repeated measurements, but logistic regression could be better when the autocorrelations do not exist.     

Asymptotic Bias in Parameter Estimation of AR-Processes Using Recursive Least Squares with Exponential Forgetting

The recursive least squares technique is often extended with exponential forgetting as a tool for parameter estimation in time-varying systems. The distribution of the resulting parameter estimates is, however, unknown when the forgetting factor is less than one. In this paper an approximative expression for bias of the recursively obtained parameter estimates in a time-invariant AR( n_a ) process with arbitrary noise is given, showing that the bias is non-zero and giving bounds on the approximation errors. Simulations confirm the approximation expressions.     

Recursive location and scale estimators

It is shown that a recursive estimator with the same asymptotic properties as the median has convergence properties in finite samples which depend heavily on the scale of the data. A simple modification which adjusts for the scale is suggested and its application illustrated on simulated data. The modified estimator has much improved properties which are similar to those of the sample (non-recursive) median.     

递归函数中的 Cache

由于 FFP 表达式具有引用透明性,对于给定的表达式每次计算都得到同样的结果,所以每一个值只需计算一次.然而,由于 FFP 语言支持递归程序,FC-机在处理递归结点时需要拷贝代码,运行时很难检查共享计算,因此可能导致重复计算,为此人们提出了用“记忆函数”(memo function)来解决这一问题.本文主要介绍如何在 FC-机中,利用 Cache 来实现“记忆函数”。最后给出了性能分析和在FFP 系统上的实际测试结果。     

Computation of the percentage points and the power for the two-sided Kolmogorov-Smirnov one sample test

Two recursive schemes are presented for the calculation of the probabilityP(g(x)≤S _n (x)≤h(x) for allx∈®), whereS _n is the empirical distribution function of a sample from a continuous distribution andh, g are continuous and isotone functions. The results are specialized for the calculation of the distribution and the corresponding percentage points of the test statistic of the two-sided Kolmogorov-Smirnov one sample test. The schemes allow the calculation of the power of the test too. Finally an extensive tabulation of percentage points for the Kolmogorov-Smirnov test is given.     

Bias Reduction through First-order Mean Correction, Bootstrapping and Recursive Mean Adjustment

Standard methods of estimation for autoregressive models are known to be biased in finite samples, which has implications for estimation, hypothesis testing, confidence interval construction and forecasting. Three methods of bias reduction are considered here: first-order bias correction, FOBC, where the total bias is approximated by the O(T^-1) bias; bootstrapping; and recursive mean adjustment, RMA. In addition, we show how first-order bias correction is related to linear bias correction. The practically important case where the AR model includes an unknown linear trend is considered in detail. The fidelity of nominal to actual coverage of confidence intervals is also assessed. A simulation study covers the AR(1) model and a number of extensions based on the empirical AR(p) models fitted by Nelson & Plosser (1982). Overall, which method dominates depends on the criterion adopted: bootstrapping tends to be the best at reducing bias, recursive mean adjustment is best at reducing mean squared error, whilst FOBC does particularly well in maintaining the fidelity of confidence intervals.