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This study evaluates the symmetry of data distributions after normalization, focusing on various statistical tests, including a few explored test named Rp. We apply normalization techniques, such as variance stabilizing transformations, to ribonucleic acid sequencing data with varying sample sizes to assess their effectiveness in achieving symmetric data distributions. Our findings reveal that while normalization generally induces symmetry, some samples retain asymmetric distributions, challenging the conventional assumption of post-normalization symmetry. The Rp test, in particular, shows superior performance when there are variations in sample size and data distribution, making it a preferred tool for assessing symmetry when applied to genomic data. This finding underscores the importance of validating symmetry assumptions during data normalization, especially in genomic data, as overlooked asymmetries can lead to potential inaccuracies in downstream analyses. We analyze postmortem lateral temporal lobe samples to explore normal aging and Alzheimer’s disease, highlighting the critical role of symmetry testing in the accurate interpretation of genomic data.

High-dimensional gene expression data cause challenges for traditional statistical tools, particularly when dealing with non-linear relationships and outliers. The present study addresses these challenges by employing a generalized correlation coefficient (GCC) that incorporates a flexibility parameter, allowing it to adapt to varying levels of symmetry and asymmetry in the data distribution. This adaptability is crucial for analyzing gene association networks, where the GCC demonstrates advantages over traditional measures such as Kendall, Pearson, and Spearman coefficients. We introduce two novel adaptations of this metric, enhancing its precision and broadening its applicability in the context of complex gene interactions. By applying the GCC to relevance networks, we show how different levels of the flexibility parameter reveal distinct patterns in gene interactions, capturing both linear and non-linear relationships. The maximum likelihood and Spearman-based estimators of the GCC offer a refined approach for disentangling the complexity of biological networks, with potential implications for precision medicine. Our methodology provides a powerful tool for constructing and interpreting relevance networks in biomedicine, supporting advancements in the understanding of biological interactions and healthcare research.

Residuals are essential in regression analysis for evaluating model adequacy, validating assumptions, and detecting outliers or influential data. While traditional residuals perform well in linear regression, they face limitations in exponential family models, such as those based on the binomial and Poisson distributions, due to heteroscedasticity and dependence among observations. This article introduces a novel standardized combined residual for linear and nonlinear regression models within the exponential family. By integrating information from both the mean and dispersion sub-models, the new residual provides a unified diagnostic tool that enhances computational efficiency and eliminates the need for projection matrices. Simulation studies and real-world applications demonstrate its advantages in efficiency and interpretability over traditional residuals.

Abstract In this work, we focus on obtaining insights of the performances of some well-known machine learning image classification techniques (k-NN, Support Vector Machine, randomized decision tree and one based on stochastic distances) for PolSAR (Polarimetric Synthetic Aperture Radar) imagery. We test the classifiers methods on a set of actual PolSAR data and provide some conclusions. The aim of this work is to show that suitable adapted standard machine learning methods offer excellent performances vs. computational complexity trade-off for PolSAR image classification. In this work, we evaluate well-known machine learning techniques for PolSAR (Polarimetric Synthetic Aperture Radar) image classification, including K-Nearest Neighbors (KNN), Support Vector Machine (SVM), randomized decision tree, and a method based on the Kullback-Leibler stochastic distance. Our experiments with real PolSAR data show that standard machine learning methods, when adapted appropriately, offer a favourable trade-off between performance and computational complexity. The KNN and SVM perform poorly on these data, likely due to their failure to account for the inherent speckle presence and properties of the studied reliefs. Overall, our findings highlight the potential of the Kullback-Leibler stochastic distance method for PolSAR image classification.

In January 2020, the world was taken by surprise as a novel disease, COVID-19, emerged, attributed to the new SARS-CoV-2 virus. Initial cases were reported in China, and the virus rapidly disseminated globally, leading the World Health Organization (WHO) to declare it a pandemic on 11 March 2020. Given the novelty of this pathogen, limited information was available regarding its infection rate and symptoms. Consequently, the necessity of employing mathematical models to enable researchers to describe the progression of the epidemic and make accurate forecasts became evident. This study focuses on the analysis of several dynamic growth models, including the logistics, Gompertz, and Richards growth models, which are commonly employed to depict the spread of infectious diseases. These models are integrated to harness their predictive capabilities, utilizing an ensemble modeling approach. The resulting ensemble algorithm was trained using COVID-19 data from the Brazilian state of Paraíba. The proposed ensemble model approach effectively reduced forecasting errors, showcasing itself as a promising methodology for estimating COVID-19 growth curves, improving data forecasting accuracy, and providing rapid responses in the early stages of the pandemic.

Learning methods in survival analysis have the ability to handle censored observations. The Cox model is a predictive prevalent statistical technique for survival analysis, but its use rests on the strong assumption of hazard proportionality, which can be challenging to verify, particularly when working with non-linearity and high-dimensional data. Therefore, it may be necessary to consider a more flexible and generalizable approach, such as support vector machines. This paper aims to propose a new method, namely wavelet support vector censored regression, and compare the Cox model with traditional support vector regression and traditional support vector regression for censored data models, survival models based on support vector machines. In addition, to evaluate the effectiveness of different kernel functions in the support vector censored regression approach to survival data, we conducted a series of simulations with varying number of observations and ratios of censored data. Based on the simulation results, we found that the wavelet support vector censored regression outperformed the other methods in terms of the C-index. The evaluation was performed on simulations, survival benchmarking datasets and in a biomedical real application.

Crop area estimates based on counting pixels over classified satellite images are a promising application of remote sensing to agriculture. However, such area estimates are biased, and their variance is a function of the error rates of the classification rule. To redress the bias, estimators (direct and inverse) relying on the so-called confusion matrix have been proposed, but analytic estimators for variances can be tricky to derive. This article proposes a bootstrap method for assessing statistical properties of such estimators based on information from a sample confusion matrix. The proposed method can be applied to any other type of estimator that is built upon confusion matrix information. The resampling procedure is illustrated in a small study to assess the biases and variances of estimates using purely pixel counting and estimates provided by both direct and inverse estimators. The method has the advantage of being simple to implement even when the sample confusion matrix is generated under unequal probability sample design. The results show the limitations of estimates based solely on pixel counting as well as respective advantages and drawbacks of the direct and inverse estimators with respect to their feasibility, unbiasedness, and variance.

This research aims to enhance the classification and prediction of ischemic heart diseases using machine learning techniques, with a focus on resource efficiency and clinical applicability. Specifically, we introduce novel non-invasive indicators known as Campello de Souza features, which require only a tensiometer and a clock for data collection. These features were evaluated using a comprehensive dataset of heart disease cases from a machine learning data repository. Our findings highlight the ability of machine learning algorithms to not only streamline diagnostic procedures but also reduce diagnostic errors and the dependency on extensive clinical testing. Three key features—mean arterial pressure, pulsatile blood pressure index, and resistance-compliance indicator—were found to significantly improve the accuracy of machine learning algorithms in binary heart disease classification. Logistic regression achieved the highest average accuracy among the examined classifiers when utilizing these features. While such novel indicators contribute substantially to the classification process, they should be integrated into a broader diagnostic framework that includes comprehensive patient evaluations and medical expertise. Therefore, the present study offers valuable insights for leveraging data science techniques in the diagnosis and management of cardiovascular diseases.

A fractile is a location on a probability density function with the associated surface being a proportion of such a density function. The present study introduces a novel methodological approach to modeling data within the continuous unit interval using fractile or quantile regression. This approach has a unique advantage as it allows for a direct interpretation of the response variable in relation to the explanatory variables. The new approach provides robustness against outliers and permits heteroscedasticity to be modeled, making it a tool for analyzing datasets with diverse characteristics. Importantly, our approach does not require assumptions about the distribution of the response variable, offering increased flexibility and applicability across a variety of scenarios. Furthermore, the approach addresses and mitigates criticisms and limitations inherent to existing methodologies, thereby giving an improved framework for data modeling in the unit interval. We validate the effectiveness of the introduced approach with two empirical applications, which highlight its practical utility and superior performance in real-world data settings.

This comprehensive overview focuses on the issues presented by the pandemic due to COVID-19, understanding its spread and the wide-ranging effects of government-imposed restrictions. The overview examines the utility of autoregressive integrated moving average (ARIMA) models, which are often overlooked in pandemic forecasting due to perceived limitations in handling complex and dynamic scenarios. Our work applies ARIMA models to a case study using data from Recife, the capital of Pernambuco, Brazil, collected between March and September 2020. The research provides insights into the implications and adaptability of predictive methods in the context of a global pandemic. The findings highlight the ARIMA models’ strength in generating accurate short-term forecasts, crucial for an immediate response to slow down the disease’s rapid spread. Accurate and timely predictions serve as the basis for evidence-based public health strategies and interventions, greatly assisting in pandemic management. Our model selection involves an automated process optimizing parameters by using autocorrelation and partial autocorrelation plots, as well as various precise measures. The performance of the chosen ARIMA model is confirmed when comparing its forecasts with real data reported after the forecast period. The study successfully forecasts both confirmed and recovered COVID-19 cases across the preventive plan phases in Recife. However, limitations in the model’s performance are observed as forecasts extend into the future. By the end of the study period, the model’s error substantially increased, and it failed to detect the stabilization and deceleration of cases. The research highlights challenges associated with COVID-19 data in Brazil, such as under-reporting and data recording delays. Despite these limitations, the study emphasizes the potential of ARIMA models for short-term pandemic forecasting while emphasizing the need for further research to enhance long-term predictions.

The maximum diversity problem (MDP) aims to select a subset with a predetermined number of elements from a given set, maximizing the diversity among them. This NP-hard problem requires efficient algorithms that can generate high-quality solutions within reasonable computational time. In this study, we propose a novel approach that combines the biased random-key genetic algorithm (BRKGA) with local search to tackle the MDP. Our computational study utilizes a comprehensive set of MDPLib instances, and demonstrates the superior average performance of our proposed algorithm compared to existing literature results. The MDP has a wide range of practical applications, including biology, ecology, and management. We provide future research directions for improving the algorithm’s performance and exploring its applicability in real-world scenarios.

The data envelopment analysis is related to a non-parametric mathematical tool used to assess the relative efficiency of productive units. In different studies on productive efficiency, it is common to employ semi-parametric procedures in two stages to determine whether any exogenous factors of interest affect the performance of productive units. However, some of these procedures, particularly those based on conventional statistical inference, generate inconsistent estimates when dealing with incoherent data-generating processes. This inconsistency arises due to the efficiency scores being limited to the unit interval, and the estimated scores often exhibit serial correlation and have limited observations. To address such inconsistency, several strategies have been suggested, with the most well-known being an algorithm based on a parametric bootstrap procedure using the truncated normal distribution and its regression model. In this work, we present a modification of this algorithm that utilizes the beta distribution and its regression structure. The beta model allows for better accommodation of asymmetry in the data distribution. Our proposed algorithm introduces inferential characteristics that are superior to the original algorithm, resulting in a more statistically coherent data-generating process and improving the consistency property. We have conducted computational experiments that demonstrate the improved results achieved by our proposal.

Predictive models based on empirical similarity are instrumental in biology and data science, where the premise is to measure the likeness of one observation with others in the same dataset. Biological datasets often encompass data that can be categorized. When using empirical similarity-based predictive models, two strategies for handling categorical covariates exist. The first strategy retains categorical covariates in their original form, applying distance measures and allocating weights to each covariate. In contrast, the second strategy creates binary variables, representing each variable level independently, and computes similarity measures solely through the Euclidean distance. This study performs a sensitivity analysis of these two strategies using computational simulations, and applies the results to a biological context. We use a linear regression model as a reference point, and consider two methods for estimating the model parameters, alongside exponential and fractional inverse similarity functions. The sensitivity is evaluated by determining the coefficient of variation of the parameter estimators across the three models as a measure of relative variability. Our results suggest that the first strategy excels over the second one in effectively dealing with categorical variables, and offers greater parsimony due to the use of fewer parameters.

The development of a country involves directly investing in the education of its citizens. Learning analytics/educational data mining (LA/EDM) allows access to big observational structured/unstructured data captured from educational settings and relies mostly on machine learning algorithms to extract useful information. Support vector regression (SVR) is a supervised statistical learning approach that allows modelling and predicts the performance tendency of students to direct strategic plans for the development of high-quality education. In Brazil, performance can be evaluated at the national level using the average grades of a student on their National High School Exams (ENEMs) based on their socioeconomic information and school records. In this paper, we focus on increasing the computational efficiency of SVR applied to ENEM for online requisitions. The results are based on an analysis of a massive data set composed of more than five million observations, and they also indicate computational learning time savings of more than 90%, as well as providing a prediction of performance that is compatible with traditional modeling.

Abstract We apply a versatile growth model, whose growth rate is given by a generalised beta distribution, to describe the complex behaviour of the fatality curves of the COVID-19 disease for several countries in Europe and North America. We show that the COVID-19 epidemic curves not only may present a subexponential early growth but can also exhibit a similar subexponential (power-law) behaviour in the saturation regime. We argue that the power-law exponent of the latter regime, which measures how quickly the curve approaches the plateau, is directly related to control measures, in the sense that the less strict the control, the smaller the exponent and hence the slower the diseases progresses to its end. The power-law saturation uncovered here is an important result, because it signals to policymakers and health authorities that it is important to keep control measures for as long as possible, so as to avoid a slow, power-law ending of the disease. The slower the approach to the plateau, the longer the virus lingers on in the population, and the greater not only the final death toll but also the risk of a resurgence of infections.

In this article, we propose a comparative study between two models that can be used by researchers for the analysis of survival data: (i) the Weibull regression model and (ii) the random survival forest (RSF) model. The models are compared considering the error rate, the performance of the model through the Harrell C-index, and the identification of the relevant variables for survival prediction. A statistical analysis of a data set from the Heart Institute of the University of São Paulo, Brazil, has been carried out. In the study, the length of stay of patients undergoing cardiac surgery, within the operating room, was used as the response variable. The obtained results show that the RSF model has less error rate for the training and testing data sets, at 23.55% and 20.31%, respectively, than the Weibull model, which has an error rate of 23.82%. Regarding the Harrell C-index, we obtain the values 0.76, 0.79, and 0.76, for the RSF and Weibull models, respectively. After the selection procedure, the Weibull model contains variables associated with the type of protocol and type of patient being statistically significant at 5%. The RSF model chooses age, type of patient, and type of protocol as relevant variables for prediction. We employ the randomForestSRC package of the R software to perform our data analysis and computational experiments. The proposal that we present has many applications in biology and medicine, which are discussed in the conclusions of this work.

Source coding maps elements from an information source to a sequence of alphabetic symbols. Then, the source symbols can be recovered exactly from the binary units. In this paper, we derive an approach that includes information variation in the source coding. The approach is more realistic than its standard version. We employ the Shannon entropy for coding the sequences of a source. Our approach is also helpful for short sequences when the central limit theorem does not apply. We rely on a quantifier of the information variation as a source. This quantifier corresponds to the second central moment of a random variable that measures the information content of a source symbol; that is, considering the standard deviation. An interpretation of typical sequences is also provided through this approach. We show how to use a binary memoryless source as an example. In addition, Monte Carlo simulation studies are conducted to evaluate the performance of our approach. We apply this approach to two real datasets related to purity and wheat prices in Brazil.

Abstract The interpretation of odds ratios (OR) as prevalence ratios (PR) in cross-sectional studies have been criticized since this equivalence is not true unless under specific circumstances. The logistic regression model is a very well known statistical tool for analysis of binary outcomes and frequently used to obtain adjusted OR. Here, we introduce the prLogistic for the R statistical computing environment which can be obtained from The Comprehensive R Archive Network, https://cran.r-project.org/package=prLogistic. The package prLogistic was built to assist the estimation of PR via logistic regression models adjusted by delta method and bootstrap for analysis of independent and correlated binary data. Two applications are presented to illustrate its use for analysis of independent observations and data from clustered studies.

Many machine learning procedures, including clustering analysis are often affected by missing values. This work aims to propose and evaluate a Kernel Fuzzy C-means clustering algorithm considering the kernelization of the metric with local adaptive distances (VKFCM-K-LP) under three types of strategies to deal with missing data. The first strategy, called Whole Data Strategy (WDS), performs clustering only on the complete part of the dataset, i.e. it discards all instances with missing data. The second approach uses the Partial Distance Strategy (PDS), in which partial distances are computed among all available resources and then re-scaled by the reciprocal of the proportion of observed values. The third technique, called Optimal Completion Strategy (OCS), computes missing values iteratively as auxiliary variables in the optimization of a suitable objective function. The clustering results were evaluated according to different metrics. The best performance of the clustering algorithm was achieved under the PDS and OCS strategies. Under the OCS approach, new datasets were derive and the missing values were estimated dynamically in the optimization process. The results of clustering under the OCS strategy also presented a superior performance when compared to the resulting clusters obtained by applying the VKFCM-K-LP algorithm on a version where missing values are previously imputed by the mean or the median of the observed values.

In this paper, we propose a new privatization mechanism based on a naive theory of a perturbation on a probability using wavelets, such as a noise perturbs the signal of a digital image sensor. Wavelets are employed to extract information from a wide range of types of data, including audio signals and images often related to sensors, as unstructured data. Specifically, the cumulative wavelet integral function is defined to build the perturbation on a probability with the help of this function. We show that an arbitrary distribution function additively perturbed is still a distribution function, which can be seen as a privatized distribution, with the privatization mechanism being a wavelet function. Thus, we offer a mathematical method for choosing a suitable probability distribution for data by starting from some guessed initial distribution. Examples of the proposed method are discussed. Computational experiments were carried out using a database-sensor and two related algorithms. Several knowledge areas can benefit from the new approach proposed in this investigation. The areas of artificial intelligence, machine learning, and deep learning constantly need techniques for data fitting, whose areas are closely related to sensors. Therefore, we believe that the proposed privatization mechanism is an important contribution to increasing the spectrum of existing techniques.

The main objective of the present article is twofold: first, to model the fatality curves of the COVID-19 disease, as represented by the cumulative number of deaths as a function of time; and second, to use the corresponding mathematical model to study the effectiveness of possible intervention strategies. We applied the Richards growth model (RGM) to the COVID-19 fatality curves from several countries, where we used the data from the Johns Hopkins University database up to May 8, 2020. Countries selected for analysis with the RGM were China, France, Germany, Iran, Italy, South Korea, and Spain. The RGM was shown to describe very well the fatality curves of China, which is in a late stage of the COVID-19 outbreak, as well as of the other above countries, which supposedly are in the middle or towards the end of the outbreak at the time of this writing. We also analysed the case of Brazil, which is in an initial sub-exponential growth regime, and so we used the generalised growth model which is more appropriate for such cases. An analytic formula for the efficiency of intervention strategies within the context of the RGM is derived. Our findings show that there is only a narrow window of opportunity, after the onset of the epidemic, during which effective countermeasures can be taken. We applied our intervention model to the COVID-19 fatality curve of Italy of the outbreak to illustrate the effect of several possible interventions.

Beta regressions describe the relationship between a response that assumes values in the zero-one range and covariates. These regressions are used for modeling rates, ratios, and proportions. We study computational aspects related to parameter estimation of a class of beta regressions for the mean with fixed precision by maximizing the log-likelihood function with heuristics and other optimization methods. Through Monte Carlo simulations, we analyze the behavior of ten algorithms, where four of them present satisfactory results. These are the differential evolutionary, simulated annealing, stochastic ranking evolutionary, and controlled random search algorithms, with the latter one having the best performance. Using the four algorithms and the optim function of R, we study sets of parameters that are hard to be estimated. We detect that this function fails in most cases, but when it is successful, it is more accurate and faster than the others. The annealing algorithm obtains satisfactory estimates in viable time with few failures so that we recommend its use when the optim function fails.

The classic coefficient of variation (CV) is the ratio of the standard deviation to the mean and can be used to compare normally distributed data with respect to their variability, this measure has been widely used in many fields. In the Social Sciences, the CV is used to evaluate demographic heterogeneity and social aggregates such as race, sex, education and others. Data of this nature are usually not normally distributed, and the distributional characteristics can vary widely. In this sense, more accurate and robust estimator variations of the classic CV are needed to give a more realistic picture of the behavior of collected data. In this work, we empirically evaluate five measures of relative variability, including the classic CV, of finite sample sizes via Monte Carlo simulations. Our purpose is to give an insight into the behavior of these estimators, as their performance has not previously been systematically investigated. To represent different behaviors of the data, we considered some statistical distributions—which are frequently used to model data across various research fields. To enable comparisons, we consider parameters of these distributions that lead to a similar range of values for the CV. Our results indicate that CV estimators based on robust statistics of scale and location are more accurate and give the highest measure of efficiency. Finally, we study the stability of a robust CV estimator in psychological and genetic data and compare the results with the traditional CV.

Research on the metaphorical mapping of valenced concepts onto space indicates that positive, neutral, and negative concepts are mapped onto upward, midward, and downward locations, respectively. More recently, this type of research has been tested for the very first time in 3D physical space. The findings corroborate the mapping of valenced concepts onto the vertical space as described above but further show that positive and negative concepts are placed close to and away from the body; neutral concepts are placed midway. The current study aimed at investigating whether valenced perceptual stimuli are positioned onto 3D space akin to the way valenced concepts are positioned. By using a unique device known as the cognition cube, participants placed visual, auditory, tactile and olfactory stimuli on 3D space. The results mimicked the placing of valenced concepts onto 3D space; i.e., positive percepts were placed in upward and close-to-the-body locations and negative percepts were placed in downward and away-from-the-body locations; neutral percepts were placed midway. These pattern of results was more pronounced in the case of visual stimuli, followed by auditory, tactile, and olfactory stimuli.Significance StatementJust recently, a unique device called “the cognition cube” (CC) enabled to find that positive words are mapped onto upward and close-to-the-body locations and negative words are mapped onto downward and away-from-the-body locations; neutral words are placed midway. This way of placing words in relation to the body is consistent with an approach-avoidance effect such that “good” and “bad” things are kept close to and away from one’s body. We demonstrate for the very first time that this same pattern emerges when visual, auditory, tactile, and olfactory perceptual stimuli are placed on 3D physical space. We believe these results are significant in that the CC can be used as a new tool to diagnose emotion-related disorders.

We argue that making accept/reject decisions on scientific hypotheses, including a recent call for changing the canonical alpha level from p = 0.05 to p = 0.005, is deleterious for the finding of new discoveries and the progress of science. Given that blanket and variable alpha levels both are problematic, it is sensible to dispense with significance testing altogether. There are alternatives that address study design and sample size much more directly than significance testing does; but none of the statistical tools should be taken as the new magic method giving clear-cut mechanical answers. Inference should not be based on single studies at all, but on cumulative evidence from multiple independent studies. When evaluating the strength of the evidence, we should consider, for example, auxiliary assumptions, the strength of the experimental design, and implications for applications. To boil all this down to a binary decision based on a p-value threshold of 0.05, 0.01, 0.005, or anything else, is not acceptable.

A topic of current research in discussion about the Brazilian economy is the exemption from payroll taxes, which aims to stimulate competitiveness of the firms, boosting economic growth. This topic was introduced in Brazil by new laws that proposed replacing the payroll tax with a new tax on revenues. The payroll tax rate of 20% was replaced by a tax rate of 1% or 2% on revenue. This change has been applied primarily in labor-intensive economic sectors. In this paper, a neoclassical model was used to evaluate some sectoral impacts of these tax changes. The results show positive effects of this reform, among them, the increase in aggregate consumption and capital stock. Employment also grows in the labor-intensive sector. However, under a government revenue neutral scenario, these effects are almost completely lost, which shows some evidence about the low efficiency of these reforms.

After discussing the main characteristics of the histogram and of a number of variations in the boxplot, this work presents a visualization tool specifically tailored to deal with skewed data. The idea is to use various types of boxplots (the classical one, which is tuned for skewness of the data, the shifting boxplot, and the box-percentile plot), the violin plot, and the histogram with a nonparametric estimate of the density overlay. The plots are presented in such a way that they facilitate the extraction of additional information from each one. We show that a good deal of information can be extracted from the inspection of the output using example data from synthetic aperture radar images. We provide an implementation in R based on functions already available.

The M estimator is a recently proposed image-quality index used to evaluate the despeckling operation in SAR (Synthetic Aperture Radar) data. It is used also to rank despeckling filters and to improve their design. As a difference with traditional image-quality estimators, it operates not on the filtered result but on a derived one, i.e., the ratio image. However, a deep statistical analysis of its properties remains open and, with it, the ability to use it as a test statistic. In this work, we focus on obtaining insights into its distribution as well as on exploring other remarkable statistical properties of this unassisted estimator. This study is performed through EDA (Exploratory Data Analysis) and the well-known ANOVA (ANalysis Of VAriance). We test our results on a set of simulated SAR data and provide guides to enrich the M estimator to extend its capabilities.

Resource selection functions (RSFs) are used for quantify how animals are selective in the use of the habitat period or food. A Resource Selection Probability Function (RSPF) can be estimated if N, the total number of units in the population, and n1 the total number of used units in the study period are both known and small. An approximation of the RSPF can then be estimated using any standard program for logistic regression but the variances of the estimates of the parameters are too small. Three methods of bootstrap sampling, parametric, nonparametric and a modified parametric method are proposed for the estimation of variances, with a discussion about the limitations of logistic regression for estimating RSPF. The method for estimating the RSPF described here has potential applications in medicine, ecology and other areas.

We present a new approach for handwritten signature classification and verification based on descriptors stemming from time causal information theory. The proposal uses the Shannon entropy, the statistical complexity, and the Fisher information evaluated over the Bandt and Pompe symbolization of the horizontal and vertical coordinates of signatures. These six features are easy and fast to compute, and they are the input to an One-Class Support Vector Machine classifier. The results are better than state-of-the-art online techniques that employ higher-dimensional feature spaces which often require specialized software and hardware. We assess the consistency of our proposal with respect to the size of the training sample, and we also use it to classify the signatures into meaningful groups.