Prediction of future failures in the log-logistic distribution based on hybrid censored data

We consider the prediction of future observations from the log-logistic distribution. The data is assumed hybrid right censored with possible left censoring. Different point predictors were derived. Specifically, we obtained the best unbiased, the conditional median, and the maximum likelihood predictors. Prediction intervals were derived using suitable pivotal quantities and intervals based on the highest density. We conducted a simulation study to compare the point and interval predictors. It is found that the point predictor BUP and the prediction interval HDI have the best overall performance. An illustrative example based on real data is given.

Cardiovascular Health Peaks and Meteorological Conditions: A Quantile Regression Approach

Cardiovascular morbidity and mortality are influenced by meteorological conditions, such as temperature or snowfall. Relationships between cardiovascular health and meteorological conditions are usually studied based on specific meteorological events or means. However, those studies bring little to no insight into health peaks and unusual events far from the mean, such as a day with an unusually high number of hospitalizations. Health peaks represent a heavy burden for the public health system; they are, however, usually studied specifically when they occur (e.g., the European 2003 heatwave). Specific analyses are needed, using appropriate statistical tools. Quantile regression can provide such analysis by focusing not only on the conditional median, but on different conditional quantiles of the dependent variable. In particular, high quantiles of a health issue can be treated as health peaks. In this study, quantile regression is used to model the relationships between conditional quantiles of cardiovascular variables and meteorological variables in Montreal (Canada), focusing on health peaks. Results show that meteorological impacts are not constant throughout the conditional quantiles. They are stronger in health peaks compared to quantiles around the median. Results also show that temperature is the main significant variable. This study highlights the fact that classical statistical methods are not appropriate when health peaks are of interest. Quantile regression allows for more precise estimations for health peaks, which could lead to refined public health warnings.

Education, Occupation, and the Cognitive Performance Distribution of South Korean Older Adults

Earlier research suggests that educational attainment up to early adulthood are crucial for the development of cognitive reserve, while intellectually stimulating activities later in the life course are of limited impact. We sought to explore the effects of educational attainment and occupational factors (occupation type and currently having work) across the distribution of cognitive performance for adults aged 45-65 years in South Korea. We analysed scores from the Korean Mini Mental State Exam (MMSE) provided in the 2006 wave of the Korean Longitudinal Study of Aging. We used quantile regressions to both investigate relationships across the distribution and to reduce bias for measures of the central tendency as the MMSE is known for its ceiling effects. The quantile function at the lowest conditional decile of MMSE scores suggested that education level was the dominant significant factor for adult performance on the MMSE (lowest MMSE decile, primary education: β = 6.11 points, p < 0.001; secondary education β = 9.56 points, p < 0.001). All occupational factors were non-significant. Further factors with a significant association with the MMSE were hearing loss, the log-transformed household income, and age squared. With the conditional median function, occupational factors became significant in the middle of the distribution but remained much less important than education levels. In summary, educational levels were more important to explain variation in cognitive functioning than occupational factors, echoing studies with Western samples. We discuss the findings with regard to the historically gender unequal educational and occupational opportunities in Korea.

IDENTIFICATION AND ESTIMATION IN A CORRELATED RANDOM COEFFICIENTS TRANSFORMATION MODEL

This study examines identification and estimation in a correlated random coefficients (CRC) model with an unknown transformation of the dependent variable, namely $\lambda \left (Y^{*}\right)=B_{0}+X^{\prime }B$ , where the latent outcome $Y^{*}$ may be subject to a certain kind of censoring mechanism, $\lambda (\cdot)$ is an unknown, one-to-one monotone function, and the random coefficients $\left (B_{0},B\right)$ are allowed to be correlated with one or several components of X. Under a conditional median independence plus a conditional median zero restriction, the mean of B is shown to be identified up to scale. Moreover, we show the derivative of the median structural function (MSF) is point identified. This derivative of MSF resembles the marginal treatment effect introduced by Heckman and Vytlacil (2005, Econometrica 73, 669–738). It generalizes the usual average treatment effect in a linear CRC model and coincides with $E(B)$ when $\lambda $ is equal to the identity function; it is invariant to both location and scale normalization on the coefficients. We develop estimators for the identified parameters and derive asymptotic properties for the derivative of MSF. An empirical example using the U.K. Family Expenditure Survey is provided.

New Insights Into Learning With Correntropy-Based Regression

Stemming from information-theoretic learning, the correntropy criterion and its applications to machine learning tasks have been extensively studied and explored. Its application to regression problems leads to the robustness-enhanced regression paradigm: correntropy-based regression. Having drawn a great variety of successful real-world applications, its theoretical properties have also been investigated recently in a series of studies from a statistical learning viewpoint. The resulting big picture is that correntropy-based regression regresses toward the conditional mode function or the conditional mean function robustly under certain conditions. Continuing this trend and going further, in this study, we report some new insights into this problem. First, we show that under the additive noise regression model, such a regression paradigm can be deduced from minimum distance estimation, implying that the resulting estimator is essentially a minimum distance estimator and thus possesses robustness properties. Second, we show that the regression paradigm in fact provides a unified approach to regression problems in that it approaches the conditional mean, the conditional mode, and the conditional median functions under certain conditions. Third, we present some new results when it is used to learn the conditional mean function by developing its error bounds and exponential convergence rates under conditional ([Formula: see text])-moment assumptions. The saturation effect on the established convergence rates, which was observed under ([Formula: see text])-moment assumptions, still occurs, indicating the inherent bias of the regression estimator. These novel insights deepen our understanding of correntropy-based regression, help cement the theoretic correntropy framework, and enable us to investigate learning schemes induced by general bounded nonconvex loss functions.

On Efficient Monitoring of Weibull Lifetimes Using Censored Median Hybrid DEWMA Chart

A control chart named as the hybrid double exponentially weighted moving average (HDEWMA) to monitor the mean of Weibull distribution in the presence of type-I censored data is proposed in this study. In particular, the focus of this study is to use the conditional median (CM) for the imputation of censored observations. The control chart performance is assessed by the average run length (ARL). A comparison between CM-DEWMA control chart and CM-based HDEWMA control chart is also presented in this article. Assuming different shift sizes and censoring rates, it is observed that the proposed control chart outperforms the CM-DEWMA chart. The effect of estimation, particularly the scale parameter estimation, on ARL is also a part of this study. Finally, a practical example is provided to understand the application and to investigate the performance of the proposal in practical scenarios.

A General Family of Autoregressive Conditional Duration Models Applied to High-Frequency Financial Data

In this paper, we propose a general family of Birnbaum–Saunders autoregressive conditional duration (BS-ACD) models based on generalized Birnbaum–Saunders (GBS) distributions, denoted by GBS-ACD. We further generalize these GBS-ACD models by using a Box-Cox transformation with a shape parameter λ to the conditional median dynamics and an asymmetric response to shocks; this is denoted by GBS-AACD. We then carry out a Monte Carlo simulation study to evaluate the performance of the GBS-ACD models. Finally, an illustration of the proposed models is made by using New York stock exchange (NYSE) transaction data.