This paper aims to evaluate the statistical association between exposure to air pollution and forced expiratory volume in the first second (FEV1) in both asthmatic and non-asthmatic children and teenagers, in which the response variable FEV1 was repeatedly measured on a monthly basis, characterizing a longitudinal experiment. Due to the nature of the data, an robust linear mixed model (RLMM), combined with a robust principal component analysis (RPCA), is proposed to handle the multicollinearity among the covariates and the impact of extreme observations (high levels of air contaminants) on the estimates. The Huber and Tukey loss functions are considered to obtain robust estimators of the parameters in the linear mixed model (LMM). A finite sample size investigation is conducted under the scenario where the covariates follow linear time series models with and without additive outliers (AO). The impact of the time-correlation and the outliers on the estimates of the fixed effect parameters in the LMM is investigated. In the real data analysis, the robust model strategy evidenced that RPCA exhibits three principal component (PC), mainly related to relative humidity (Hmd), particulate matter with a diameter smaller than 10 μm (PM10) and particulate matter with a diameter smaller than 2.5 μm (PM2.5).

In the mechanical cutting industry, trial production is used for predicting and evaluating the quality of product processes before batch production, and it can be expressed through the qualification rate. However, it cannot objectively and comprehensively evaluate the quality of product processes. This study optimizes the analysis of outliers and stability in mathematical statistics to better apply it in the mechanical cutting industry; then, it combines them with process capability analysis. Simultaneously, considering the non-normal distribution of process parameters, a batch production-prediction model is proposed. The reliability of batch production-prediction model is verified by the diameter, roundness and roughness of structural common samples. Meanwhile, for other mechanical parts in the mechanical cutting industry, the model proposed in this paper can be used to quickly and accurately predict and evaluate batch production.

In a recent study employing time production, a number of participants presented aberrant data, which normally would have marked them as being outliers. Given the ongoing discussion in the literature regarding the illusory nature of the flow of time, in this paper we consider whether their data may indicate discontinuity in time perception. We analyze the log-log plots for these outliers, investigating to what degree linearity is preserved for all the data points, as opposed to achieving a better fit using bisegmental regression. The current results, though preliminary, can contribute to the debate regarding the non-linearity of subjective time. It would seem that with longer target durations, the ongoing experience of time can be either one of a subjective slowing down of time (longer time units, increase in slope), or of a subjective speeding up of time (shorter time units, decrease in slope).

The linear regression is critical for data modelling, especially for scientists. Nevertheless, with the plenty of high-dimensional data, there are data with more explanatory variables than the number of observations. In such circumstances, traditional approaches fail. This paper proposes a modified sparse regression model that solves the problem of heterogeneity using seaweed big data as a use case. The modified heterogeneity models for ridge, LASSO and Elastic net were used to model the data. Robust estimations M Bi-Square, M Hampel, M Huber, MM and S were used. Based on the results, the hybrid model of sparse regression for before, after, and modified heterogeneity robust regression with the 45 high ranking variables and a 2-sigma limit can be used efficiently and effectively to reduce the outliers. The obtained results confirm that the hybrid model of the modified sparse LASSO with the M Bi-Square estimator for the 45 high ranking parameters performed better compared with other existing methods.

When investigating unobservable, complex traits, data collection and aggregation processes can introduce distinctive features to the data such as boundedness, measurement error, clustering, outliers, and heteroscedasticity. Failure to collectively address these features can result in statistical challenges that prevent the investigation of hypotheses regarding these traits. This study aimed to demonstrate the efficacy of the Bayesian beta-proportion generalized linear latent and mixed model (beta-proportion GLLAMM) (Rabe-Hesketh et al., Psychometrika, 69(2), 167-90, 2004a, Journal of Econometrics, 128(2), 301-23, 2004c, 2004b; Skrondal and Rabe-Hesketh 2004) in handling data features when exploring research hypotheses concerning speech intelligibility. To achieve this objective, the study reexamined data from transcriptions of spontaneous speech samples initially collected by Boonen et al. (Journal of Child Language, 50(1), 78-103, 2023). The data were aggregated into entropy scores. The research compared the prediction accuracy of the beta-proportion GLLAMM with the normal linear mixed model (LMM) (Holmes et al., 2019) and investigated its capacity to estimate a latent intelligibility from entropy scores. The study also illustrated how hypotheses concerning the impact of speaker-related factors on intelligibility can be explored with the proposed model. The beta-proportion GLLAMM was not free of challenges; its implementation required formulating assumptions about the data-generating process and knowledge of probabilistic programming languages, both central to Bayesian methods. Nevertheless, results indicated the superiority of the model in predicting empirical phenomena over the normal LMM, and its ability to quantify a latent potential intelligibility. Additionally, the proposed model facilitated the exploration of hypotheses concerning speaker-related factors and intelligibility. Ultimately, this research has implications for researchers and data analysts interested in quantitatively measuring intricate, unobservable constructs while accurately predicting the empirical phenomena.

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Meta-analysis is an essential tool to comprehensively synthesize and quantitatively evaluate results of multiple clinical studies in evidence-based medicine. In many meta-analyses, the characteristics of some studies might markedly differ from those of the others, and these outlying studies can generate biases and potentially yield misleading results. In this article, we provide effective robust statistical inference methods using generalized likelihoods based on the density power divergence. The robust inference methods are designed to adjust the influences of outliers through the use of modified estimating equations based on a robust criterion, even when multiple and serious influential outliers are present. We provide the robust estimators, statistical tests, and confidence intervals via the generalized likelihoods for the fixed-effect and random-effects models of meta-analysis. We also assess the contribution rates of individual studies to the robust overall estimators that indicate how the influences of outlying studies are adjusted. Through simulations and applications to two recently published systematic reviews, we demonstrate that the overall conclusions and interpretations of meta-analyses can be markedly changed if the robust inference methods are applied and that only the conventional inference methods might produce misleading evidence. These methods would be recommended to be used at least as a sensitivity analysis method in the practice of meta-analysis. We have also developed an R package, robustmeta, that implements the robust inference methods.

In real-life situations, we have to analyze the data that contains the atypical observations, and the presence of outliers has adverse effects on the performance of ordinary least square estimates. In this situation, redescedning M-estimators, proposed by Huber (1964), are used to tackle the effects of outliers to increase the efficiency of least square estimates. In this study, we introduce a redescending M-estimator designed to generate robust estimates by mitigating the influence of outlier observations, even when the tuning constant is set to low values. This innovative estimator exhibits enhanced linearity at its core and maintains continuity throughout its range. Our proposed estimator stands out for its novelty, simplicity, differentiability, and practical applicability across real-world scenarios. The results of the proposed redescedning M-estimators are compared with existing robust estimators using an extensive simulation study. Two examples based on real-life data are also added to validate the performance of the suggested function. The formulated redescedning M-estimator produced efficient results as compared to all the considered redescedning M-estimators.

A methodological problem in most reaction time (RT) studies is that some measured RTs may be outliers-that is, they may be very fast or very slow for reasons unconnected to the task-related processing of interest. Numerous ad hoc methods have been suggested to discriminate between such outliers and the valid RTs of interest, but it is extremely difficult to determine how well these methods work in practice because virtually nothing is known about the actual characteristics of outliers in real RT datasets. This article proposes a new method of pooling cumulative distribution function values for examining empirical RT distributions to assess both the proportions of outliers and their latencies relative to those of the valid RTs. As the method is developed, its strengths and weaknesses are examined using simulations based on previously suggested ad hoc models for RT outliers with particular assumed proportions and distributions of valid RTs and outliers. The method is then applied to several large RT datasets from lexical decision tasks, and the results provide the first empirically based description of outlier RTs. For these datasets, fewer than 1% of the RTs seem to be outliers, and the median outlier latency appears to be approximately 4-6 standard deviations of RT above the mean of the valid RT distribution.

Angiotensin-converting enzyme (ACE) metabolizes a number of important peptides participating in blood pressure regulation and vascular remodeling. Elevated ACE expression in tissues (which is generally reflected by blood ACE levels) is associated with an increased risk of cardiovascular diseases. Elevated blood ACE is also a marker for granulomatous diseases. Decreased blood ACE activity is becoming a new risk factor for Alzheimer\'s disease. We applied our novel approach-ACE phenotyping-to characterize pairs of tissues (lung, heart, lymph nodes) and serum ACE in 50 patients. ACE phenotyping includes (1) measurement of ACE activity with two substrates (ZPHL and HHL); (2) calculation of the ratio of hydrolysis of these substrates (ZPHL/HHL ratio); (3) determination of ACE immunoreactive protein levels using mAbs to ACE; and (4) ACE conformation with a set of mAbs to ACE. The ACE phenotyping approach in screening format with special attention to outliers, combined with analysis of sequencing data, allowed us to identify patient with a unique ACE phenotype related to decreased ability of inhibition of ACE activity by albumin, likely due to competition with high CCL18 in this patient for binding to ACE. We also confirmed recently discovered gender differences in sialylation of some glycosylation sites of ACE. ACE phenotyping is a promising new approach for the identification of ACE phenotype outliers with potential clinical significance, making it useful for screening in a personalized medicine approach.