Finite Sample Performance of tests for Symmetry of the Errors in a Linear Model

The finite sample performance of a number of tests for symmetry of the distribution of the errors of a linear model is considered. The first family of tests is based on the discrepancy between two regression fits. The first fit is appropriate under symmetric errors while the second is appropriate for skewed as well as symmetric error distributions. The second family of procedures consists of tests for the univariate symmetry problem. Thus, in the linear model setting these tests are based on residuals. An extensive empirical study of the finite sample, null behavior of the tests is presented. The results of a power comparison among the tests is also discussed.     

Accounting for Uncertainty in Heteroscedasticity in Nonlinear Regression

Toxicologists and pharmacologists often describe toxicity of a chemical using parameters of a nonlinear regression model. Thus estimation of parameters of a nonlinear regression model is an important problem. The estimates of the parameters and their uncertainty estimates depend upon the underlying error variance structure in the model. Typically, a priori the researcher would not know if the error variances are homoscedastic (i.e., constant across dose) or if they are heteroscedastic (i.e., the variance is a function of dose). Motivated by this concern, in this paper we introduce an estimation procedure based on preliminary test which selects an appropriate estimation procedure accounting for the underlying error variance structure. Since outliers and influential observations are common in toxicological data, the proposed methodology uses M-estimators. The asymptotic properties of the preliminary test estimator are investigated; in particular its asymptotic covariance matrix is derived. The performance of the proposed estimator is compared with several standard estimators using simulation studies. The proposed methodology is also illustrated using a data set obtained from the National Toxicology Program.     

Proportional hazards model for competing risks data with missing cause of failure

We consider the semiparametric proportional hazards model for the cause-specific hazard function in analysis of competing risks data with missing cause of failure. The inverse probability weighted equation and augmented inverse probability weighted equation are proposed for estimating the regression parameters in the model, and their theoretical properties are established for inference. Simulation studies demonstrate that the augmented inverse probability weighted estimator is doubly robust and the proposed method is appropriate for practical use. The simulations also compare the proposed estimators with the multiple imputation estimator of Lu and Tsiatis (2001). The application of the proposed method is illustrated using data from a bone marrow transplant study.     

Tests for a difference in timing of physiological response between two brain regions measured by using functional magnetic resonance imaging

Summary.  Functional magnetic resonance imaging (FMRI) measures the physiological response of the human brain to experimentally controlled stimulation. In a periodically designed experiment it is of interest to test for a difference in the timing (phase shift) of the response between two anatomically distinct brain regions. We suggest two tests for an interregional difference in phase shift: one based on asymptotic theory and one based on bootstrapping. Whilst the two procedures differ in some of their assumptions, both tests rely on employing the large number of voxels (three-dimensional pixels) in non-activated brain regions to take account of spatial autocorrelation between voxelwise phase shift observations within the activated regions of interest. As an example we apply both tests, and their counterparts assuming spatial independence, to FMRI phase shift data that were acquired from a normal young woman during performance of a periodically designed covert verbal fluency task. We conclude that it is necessary to take account of spatial autocovariance between voxelwise FMRI time series parameter estimates such as the phase shift, and that the most promising way of achieving this is by modelling the spatial autocorrelation structure from a suitably defined base region of the image slice.     

本科实验教学模块建设与运行相关问题探讨

介绍了《材料性能实验教学模块》的概况及其总体规划思路,回顾了其建设与运行情况,以《材料性能实验教学模块》为实例,从实践和理论2个方面对本科实验教学模块建设、运行等相关问题进行了探讨,并总结了近年来的教学实践经验。     

Improving variance function estimation in semiparametric longitudinal data analysis

We propose an efficient and robust method for variance function estimation in semiparametric longitudinal data analysis. The method utilizes a local log‐linear approximation for the variance function and adopts a generalized estimating equation approach to account for within subject correlations. We show theoretically and empirically that our method outperforms estimators using working independence that ignores the correlations. The Canadian Journal of Statistics 39: 656–670; 2011. © 2011 Statistical Society of Canada     

Simultaneous confidence band for the difference of segmented linear models

Consider comparing between two treatments a response variable, whose expectation depends on the value of a continuous covariate in some nonlinear fashion. We fit separate segmented linear models to each treatment to approximate the nonlinear relationship. For this setting, we provide a simultaneous confidence band for the difference between treatments of the expected value functions. The treatments are said to differ significantly on intervals of the covariate where the simultaneous confidence band does not contain zero. We consider segmented linear models where the locations of the changepoints are both known and unknown. The band is obtained from asymptotic results.     

Super efficient frequency estimation

In this paper we propose a modified Newton-Raphson method to obtain super efficient estimators of the frequencies of a sinusoidal signal in presence of stationary noise. It is observed that if we start from an initial estimator with convergence rate O_p(n⁻¹) and use Newton-Raphson algorithm with proper step factor modification, then it produces super efficient frequency estimator in the sense that its asymptotic variance is lower than the asymptotic variance of the corresponding least squares estimator. The proposed frequency estimator is consistent and it has the same rate of convergence, namely O_p(n^−3/2), as the least squares estimator. Monte Carlo simulations are performed to observe the performance of the proposed estimator for different sample sizes and for different models. The results are quite satisfactory. One real data set has been analyzed for illustrative purpose.     

用声学测量预报等温淬火球墨铸铁强度

等温淬火球墨铸铁的机械性能与其声学性能相关。本文将两种碳当量球铁在８４５，８９９和９４５℃温度进行奥氏体处理，在２６０，３１６和３７１℃温度进行等温淬火得到证实。声学性能测量包括共振频率，声速和内耗。由共振频率转换成动态模量表示出这种关系可以用来预报球墨铸铁不同热处理条件下的机械性能。     

An efficient and fast algorithm for estimating the parameters of two-dimensional sinusoidal signals

In this paper we propose a computationally efficient algorithm to estimate the parameters of a 2-D sinusoidal model in the presence of stationary noise. The estimators obtained by the proposed algorithm are consistent and asymptotically equivalent to the least squares estimators. Monte Carlo simulations are performed for different sample sizes and it is observed that the performances of the proposed method are quite satisfactory and they are equivalent to the least squares estimators. The main advantage of the proposed method is that the estimators can be obtained using only finite number of iterations. In fact it is shown that starting from the average of periodogram estimators, the proposed algorithm converges in three steps only. One synthesized texture data and one original texture data have been analyzed using the proposed algorithm for illustrative purpose.