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"Nonparametric Statistical Analysis"
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Human mental search: a new population-based metaheuristic optimization algorithm
Population-based metaheuristic algorithms have become popular in recent years with them getting used in different fields such as business, medicine, and agriculture. The present paper proposes a simple but efficient population-based metaheuristic algorithm called Human Mental Search (HMS). HMS algorithm mimics the exploration strategies of the bid space in online auctions. The three leading steps of HMS algorithm are: (1) the mental search that explores the region around each solution based on Levy flight, (2) grouping that determines a promising region, and (3) moving the solutions toward the best strategy. To evaluate the efficiency of HMS algorithm, some test functions with different characteristics are studied. The results are compared with nine state-of-the-art metaheuristic algorithms. Moreover, some nonparametric statistical methods, including Wilcoxon signed rank test and Friedman test, are provided. The experimental results demonstrate that the HMS algorithm can present competitive results compared to other algorithms.
Journal Article
Component Selection and Smoothing in Multivariate Nonparametric Regression
We propose a new method for model selection and model fitting in multivariate nonparametric regression models, in the framework of smoothing spline ANOVA. The \"COSSO\" is a method of regularization with the penalty functional being the sum of component norms, instead of the squared norm employed in the traditional smoothing spline method. The COSSO provides a unified framework for several recent proposals for model selection in linear models and smoothing spline ANOVA models. Theoretical properties, such as the existence and the rate of convergence of the COSSO estimator, are studied. In the special case of a tensor product design with periodic functions, a detailed analysis reveals that the COSSO does model selection by applying a novel soft thresholding type operation to the function components. We give an equivalent formulation of the COSSO estimator which leads naturally to an iterative algorithm. We compare the COSSO with MARS, a popular method that builds functional ANOVA models, in simulations and real examples. The COSSO method can be extended to classification problems and we compare its performance with those of a number of machine learning algorithms on real datasets. The COSSO gives very competitive performance in these studies.
Journal Article
Prediction in Functional Linear Regression
There has been substantial recent work on methods for estimating the slope function in linear regression for functional data analysis. However, as in the case of more conventional finite-dimensional regression, much of the practical interest in the slope centers on its application for the purpose of prediction, rather than on its significance in its own right. We show that the problems of slope-function estimation, and of prediction from an estimator of the slope function, have very different characteristics. While the former is intrinsically nonparametric, the latter can be either nonparametric or semi-parametric. In particular, the optimal mean-square convergence rate of predictors is n⁻¹, where n denotes sample size, if the predictand is a sufficiently smooth function. In other cases, convergence occurs at a polynomial rate that is strictly slower than n⁻¹. At the boundary between these two regimes, the mean-square convergence rate is less than n⁻¹ by only a logarithmic factor. More generally, the rate of convergence of the predicted value of the mean response in the regression model, given a particular value of the explanatory variable, is determined by a subtle interaction among the smoothness of the predictand, of the slope function in the model, and of the autocovariance function for the distribution of explanatory variables.
Journal Article
Normality analysis of numeric rating scale scores in patients with chronic axial spine pain before and after medial branch blocks: a multicenter study
Objective
The statistical analysis typically used to compare pain before and after interventions assumes that scores are normally distributed. The present study evaluates whether numeric rating scale (NRS) scores, specifically NRS-11 scores, are indeed normally distributed in a clinically relevant cohort of adults with chronic axial spine pain before and after analgesic intervention.
Methods
Retrospective review from 4 academic medical centers of prospectively collected data from a uniform pain diary administered to consecutive patients after they had undergone medial branch blocks. The pain diary assessed NRS-11 scores immediately before injection and at 12 different time points after injection up to 48 hours. D’Agostino–Pearson tests were used to test normality at all time points.
Results
One hundred fifty pain diaries were reviewed, and despite normally distributed pre-injection NRS-11 scores (K2 = 0.655, P = .72), all post-injection NRS-11 data were not normally distributed (K2 = 9.70– 17.62, P = .0001–.008).
Conclusions
Although the results of parametric analyses of NRS-11 scores are commonly reported in pain research, some properties of the NRS-11 do not satisfy the assumptions required for these analyses. The data demonstrate non-normal distributions in post-intervention NRS-11 scores, thereby violating a key requisite for parametric analysis. We urge pain researchers to consider appropriate statistical analysis and reporting for non-normally distributed NRS-11 scores to ensure accurate interpretation and communication of these data. Practicing pain physicians should similarly recognize that parametric post-intervention pain score statistics might not accurately describe the data and should expect articles to utilize measures of normality to justify the selected statistical methods.
Journal Article
From ε-Entropy to KL-Entropy: Analysis of Minimum Information Complexity Density Estimation
We consider an extension of ε-entropy to a KL-divergence based complexity measure for randomized density estimation methods. Based on this extension, we develop a general information-theoretical inequality that measures the statistical complexity of some deterministic and randomized density estimators. Consequences of the new inequality will be presented. In particular, we show that this technique can lead to improvements of some classical results concerning the convergence of minimum description length and Bayesian posterior distributions. Moreover, we are able to derive clean finite-sample convergence bounds that are not obtainable using previous approaches.
Journal Article
Teachers' and professors' perception of telework in Romania
The first mentions of working from home date from 1979, the appearance of the Internet leading to an increase in the number of companies that have applied this system. Remote work, work from home, telecommuting, as well as teleworking are concepts that describe an alternative activity of performing traditional work. With the onset of the Coronavirus pandemic, the shift in a higher or lower proportion of companies' online activities, depending on the economic sector in which they operate, has become inevitable and sudden, with telework becoming the new normality among employees and employers. The objective of this study is to find out to what extent teachers in Romania agree to carry out teaching activities in the telework system and whether the educational environment (pre-university or univeristar), the degree of effort put in and the degree of fatigue felt in the telework system influence the extent to which teachers agree to carry out teaching activities in this type of system.The data was collected through a questionnaire-based exploratory research on a sample of 208 higher education professors and pre-university teachers. Non-parametric statistical methods of data analysis were used to measure the perception of study participants in the telework system and statistical methods suitable for qualitative data analysis were used for the assumptions: ordinal regression, Mann-Whitney U Test and Kruskal-Wallis Test. Research results show that teachers make an additional effort to carry out telework system activitiescompared to the teaching activity period in schools/campus'to the majority of respondents (87.5%), leading to a much higher feeling of fatigue (73.5%), and as the main impediment to online teaching, the evaluation of the progress of pupils/students. The study can support the management of Romanian education, at micro and macro level, in the correct substantiation of decisions on the sizing and evaluation of teaching activities and related processes that teachers carry out in telework conditions.
Journal Article
Adequacy analysis of drinking water treatment technologies in regard to the parameter turbidity, considering the quality of natural waters treated by large-scale WTPs in Brazil
This paper seeks to present a performance evaluation of large-scale water treatment plants and verify the adjustment of the treatment to the parameter turbidity of natural waters. Nonparametric and multivariate statistical tools were used to analyze raw water and treated water turbidity of a large on-line monitoring databank for the period from 2013 to 2015, from six large-scale treatment plants utilizing different technologies. Cluster analysis was able to differentiate adequately groups of treatment plants with similar raw and treated water quality. Considering the effluent turbidity as a marker parameter, the results indicated that selection of the technology to be applied must be well studied to always seek the best solution, and that other factors than only the raw water characteristics should be evaluated. It was also demonstrated that utilization of the same treatment technology does not always result in the same effluent quality, since there are many factors related to operation, maintenance, raw water variability, climatic interferences, and others.
Journal Article
Multidimensional Trimming Based on Projection Depth
As estimators of location parameters, univariate trimmed means are well known for their robustness and efficiency. They can serve as robust alternatives to the sample mean while possessing high efficiencies at normal as well as heavy-tailed models. This paper introduces multidimensional trimmed means based on projection depth induced regions. Robustness of these depth trimmed means is investigated in terms of the influence function and finite sample breakdown point. The influence function captures the local robustness whereas the breakdown point measures the global robustness of estimators. It is found that the projection depth trimmed means are highly robust locally as well as globally. Asymptotics of the depth trimmed means are investigated via those of the directional radius of the depth induced regions. The strong consistency, asymptotic representation and limiting distribution of the depth trimmed means are obtained. Relative to the mean and other leading competitors, the depth trimmed means are highly efficient at normal or symmetric models and overwhelmingly more efficient when these models are contaminated. Simulation studies confirm the validity of the asymptotic efficiency results at finite samples.
Journal Article
A Simple Smooth Backfitting Method for Additive Models
In this paper a new smooth backfitting estimate is proposed for additive regression models. The estimate has the simple structure of Nadaraya-Watson smooth backfitting but at the same time achieves the oracle property of local linear smooth backfitting. Each component is estimated with the same asymptotic accuracy as if the other components were known.
Journal Article