We consider the nonparametric estimation of a heteroscedastic regression model Y = m(X)+sigma(X)(& varepsilon;), where the error term & varepsilon; is independent of the covariate X, and the functions m and sigma are unknown. The response variable Y is allowed to be interfered by a left truncation random variable T. In this work, we propose kernel-estimators for both the location and scale functions m and sigma and investigate their strong uniform consistency rates as well as their asymptotic normality. The finite sample performance of the proposed estimator of the regression function m(& centerdot;) is extensively studied via simulation and indicate that in presence of heteroscedasticity, our new estimator outperforms the classical one (when ignoring heteroscedasticity) and is less sensitive to the presence of outliers. We also investigate the performance of the scale function estimator sigma(& centerdot;). Furthermore, an application to real data demonstrates the effectiveness of our method in terms of prediction accuracy.
Generalized Additive Models for Location, Scale and Shape (GAMLSS) are a flexible alternative to standard regression models, where only the mean of the response variable is modelled in terms of covariates. However, GAMLSS currently are seldom used in statistical applications. In this paper, we analyze data from wastewater measurements in Austria with respect to COVID-19. The goal is to model the viral load in the wastewater in terms of covariates. The results show that both the vaccination rate and the dominant virus variant are important covariates in the analysis of COVID-19 related viral load in the wastewater. Moreover, complex GAMLSS based on the four-parametric Box-Cox t distribution clearly outperformed simpler Generalized Additive Models (GAMs) based on the Gamma distribution. Moreover, GAMLSS show also better predictive performance than GAMs.
This paper investigates the Quasi-Maximum Likelihood Estimation (QMLE) method for time-varying GARCH models under the assumption that the innovations follow the standard Laplace distribution. We consider a locally stationary framework. The estimation process is based on a kernel-weighted likelihood approach. We establish the consistency and asymptotic normality of the proposed estimators under regularity assumptions. The efficacy of the method is demonstrated through simulation studies and an application to real-world financial data, highlighting the practical advantages of modeling heavy-tailed innovations with the Laplace distribution.
Accurate survival prediction in colorectal cancer (CRC) is essential for guiding prognosis and optimizing treatment strategies. This study applies a Bayesian Accelerated Failure Time (AFT) modeling framework using three parametric distributions namely Weibull, log-normal and log-logistic to estimate survival times based on clinical characteristics. The models were evaluated using the Widely Applicable Information Criterion (WAIC), Deviance Information Criterion (DIC) and Log Pseudo Marginal Likelihood (LPML). Among the three, the Bayesian log-normal AFT model achieved the best overall fit and ment, metastasis status and tumor histology were incorporated to assess their effects on survival time. The analysis confirmed a strong association between advanced nodal stage (N2) and prolonged survival, while estimates for tumor stages, tumor type and sex showed wider credible intervals, indicating greater uncertainty and highlighting the importance of individualized survival modeling. Posterior trace plots confirmed MCMC convergence and parameter stability, reinforcing the model's reliability. Moreover, The survival probability plots from the Bayesian lognormal AFT model illustrated how age, when combined with key clinical factors impacts the survivability of the patients. This work demonstrates the practical utility of Bayesian AFT models in handling non-proportional hazards and offers a flexible, interpretable framework for individualized survival estimation in CRC. The findings offer a foundation for future studies integrating more complex covariates and advancing personalized oncology.
In this paper, we propose a new non-parametric kernel estimator of the conditional hazard function where the explanatory variable takes values in an infinite-dimensional space and the response variable is subject to random left truncation and satisfies the alpha mixing property. Our main aim is to prove the strong uniform consistency rate for both functional and real arguments of the estimator. Furthermore, the performance of our estimator is evaluated via a simulation study and its practical relevance is illustrated by an application to real-world data.
