Right censoring weakens parametric survival model discrimination by reducing the information available in the observed-data likelihood, but this loss is not uniform across parameters or model families. This methodological review synthesizes established Fisher information results through a parameter-specific information-retention framework for right-censored lifetime data. For a given parameter, retained Fisher information can be expressed as a weighted average of the censoring survival function, where the weights describe how information is distributed over event time. This overlap representation shows that censoring affects model discrimination through the timing and mechanism of follow-up loss, rather than through censoring proportion alone. For nested parametric models, a local likelihood expansion connects observed-data likelihood separation to the efficient Fisher information in the parameter direction that distinguishes the wider model from its submodel. Weibull–exponential and Gompertz–exponential comparisons provide transparent worked examples involving, respectively, non-monotone and late-concentrated information profiles. Illustrative simulations under matched censoring proportions show that administrative censoring can reduce likelihood separation more severely than dispersed random censoring. Together, the reviewed theory, model-specific calculations, and simulations explain why similar censoring proportions can produce markedly different parametric model-selection behaviour.
The aim of this article is to apply methods of cluster analysis to functional data in order to determine if there are homogeneous groups among the provinces of Poland in terms of 20 features related to the labour market. In some existing studies all available features are used for cluster analysis, even though some of them may be insignificant for the task. Irrelevant features have a negative impact on the complexity and performance of clustering algorithms. In this study, before clusters of provinces were identified, features significantly differentiating provinces were selected. Our new feature selection criterion involves the use of coefficients of functional distance correlation and functional Hilbert-Schmidt correlation between the features characterizing provinces and their labels. The resulting clusters were nearly identical regardless of whether all 20 features were used or just the 9 significant ones, which indicates that irrelevant features do not contribute much to cluster identification. The methodology proposed in this article is flexible and can be successfully used in other research areas including, inter alia, poverty, socio-economic development or disability.
Estimating heterogeneous treatment effects has become increasingly important in statistical research. Accurately estimating these effects enables the application of the most effective treatments to heterogeneous units. This paper proposes a two-stage procedure to address this issue. First, we use Robinson’s transformation to decouple the nuisance parameters from the treatment effect of interest and apply machine learning algorithms to estimate these nuisance parameters. Next, after substituting the estimates of the nuisance parameters, we develop a model averaging method based on Robinson’s transformation (RMA). The criterion of RMA is quadratic in the weights, making computation straightforward through the use of quadratic programming. We demonstrate that our estimator is asymptotically optimal, achieving the lowest expected squared error. Additionally, we study the consistency of RMA weights, which converge to the optimal weights that minimize the mean squared error. Through Monte Carlo simulations and an illustrative example, we find that RMA outperforms existing model selection and averaging methods in most cases.
In this paper, we investigate the hypotheses testing of regression parameters in linear models with φ -mixing random errors. Based on the central limit theorem for weighted sums of φ -mixing sequences and Cram é r-Wold theorem, the limiting distribution of M-test statistics are obtained when there is a small deviation from a linear hypotheses. In addition, the weak consistent estimators of nuisance parameters which involved in the asymptotic distribution of M-test statistics are also established. Finally, we provide some numerical simulations to verify the finite sample performance of the theoretical results.
The generalized autoregressive conditional heteroscedasticity, GARCH, models are the most popular models for capturing time-varying symmetric volatility in financial and economic time series data. Most of the theoretical results on GARCH models assume a constant or linear conditional mean. The smooth transition autoregressive, STAR, models allow for nonlinear behavior in the time series. The STAR-GARCH model combines regime switching and volatility models, with the regime switching in the mean equation and volatility in the variance equation. The estimation of smooth transition autoregressive models with GARCH errors, STAR-GARCH, are not entirely straightforward. Therefore, likelihood functions are appratimed using numerical methods. It is worth mentioning that the convergence of the maximum likelihood estimator for STAR-GARCH models is sensitive to initial values. This paper investigates modified maximum likelihood estimators of the parameters of smooth transition autoregressive models with GARCH errors and asymptotic distribution of modified maximum likelihood estimators. As a result, we can select optimal models based on Vuong’s test. A simulation study leads strong support to the results presented in the paper. We studied Wilshire 5000 total market full cap index dataset and selected an optimal model for this data based on the theoretical results.
