Specification testing in semi-parametric transformation models

In transformation regression models, the response is transformed before fitting a regression model to covariates and transformed response. We assume such a model where the errors are independent from the covariates and the regression function is modeled nonparametrically. We suggest a test for goodness-of-fit of a parametric transformation class based on a distance between a nonparametric transformation estimator and the parametric class. We present asymptotic theory under the null hypothesis of validity of the semi-parametric model and under local alternatives. A bootstrap algorithm is suggested in order to apply the test. We also consider relevant hypotheses to distinguish between large and small distances of the parametric transformation class to the ‘true’ transformation.

On semiparametric modelling, estimation and inference for survival data subject to dependent censoring

When modelling survival data, it is common to assume that the survival time T is conditionally independent of the censoring time C given a set of covariates. However, there are numerous situations in which this assumption is not realistic. The goal of this paper is therefore to develop a semiparametric normal transformation model, which assumes that after a proper nonparametric monotone transformation, the vector (T, C) follows a linear model, and the vector of errors in this bivariate linear model follows a standard bivariate normal distribution with possibly non-diagonal covariance matrix. We show that this semiparametric model is identifiable, and propose estimators of the nonparametric transformation, the regression coefficients and the correlation between the error terms. It is shown that the estimators of the model parameters and the transformation are consistent and asymptotically normal. We also assess the finite sample performance of the proposed method by comparing it with an estimation method under a fully parametric model. Finally, our method is illustrated using data from the AIDS Clinical Trial Group 175 study.

Investigating statistical bias correction with temporal subsample of the upper Ping River Basin, Thailand

This study aims to investigate different statistical bias correction techniques to improve the output of a regional climate model (RCM) of daily rainfall for the upper Ping River Basin in Northern Thailand. Three subsamples are used for each bias correction method, which are (1) using full calibrated 30-year-period data, (2) seasonal subsampling, and (3) monthly subsampling. The bias correction techniques are classified into three groups, which are (1) distribution-derived transformation, (2) parametric transformation, and (3) nonparametric transformation. Eleven bias correction techniques with three different subsamples are used to derive transfer function parameters to adjust model bias error. Generally, appropriate bias correction methods with optimal subsampling are locally dependent and need to be defined specifically for a study area. The study results show that monthly subsampling would be well established by capturing the monthly mean variation after correcting the model's daily rainfall. The results also give the best-fitted parameter set of the different subsamples. However, applying the full calibrated data and the seasonal subsamples cannot substantially improve internal variability. Thus, the effect of internal climate variability of the study region is greater than the choice of bias correction methods. Of the bias correction approaches, nonparametric transformation performed best in correcting daily rainfall bias error in this study area as evaluated by statistics and frequency distributions. Therefore, using a combination of methods between the nonparametric transformation and monthly subsampling offered the best accuracy and robustness. However, the nonparametric transformation was quite sensitive to the calibration time period.

NONPARAMETRIC TRANSFORMATION REGRESSION WITH NONSTATIONARY DATA

We examine a kernel regression estimator for time series that takes account of the error correlation structure as proposed by Xiao et al. (2003, Journal of the American Statistical Association 98, 980–992). We show that this method continues to improve estimation in the case where the regressor is a unit root or a near unit root process.