A goodness-of-fit test is a frequently used modern statistics tool. However, it is still unclear what the most reliable approach is to check assumptions about data set normality. A particular data set (especially with a small number of observations) only partly describes the process, which leaves many options for the interpretation of its true distribution. As a consequence, many goodness-of-fit statistical tests have been developed, the power of which depends on particular circumstances (i.e., sample size, outlets, etc.). With the aim of developing a more universal goodness-of-fit test, we propose an approach based on an N-metric with our chosen kernel function. To compare the power of 40 normality tests, the goodness-of-fit hypothesis was tested for 15 data distributions with 6 different sample sizes. Based on exhaustive comparative research results, we recommend the use of our test for samples of size $n\ge 118$.

Objective: To assess the significance of prostate-specific antigen (PSA) persistence at the first measurement after radical prostatectomy (RP) on long-term outcomes in different prostate cancer risk groups. Methods: Persistent PSA was defined as ≥0.1 ng/mL at 4–8 weeks after RP. Patients were stratified into low-, intermediate- and high-risk groups, according to the preoperative PSA, pathological stage, grade group and lymph nodes status. The ten-year cumulative incidence of biochemical recurrence (BCR), metastases, cancer-specific mortality (CSM) and overall mortality (OM) were calculated in patients with undetectable and persistent PSA in different PCa-risk groups. Multivariate regression analyses depicted the significance of PSA persistence on each study endpoint. Results: Of all 1225 men, in 246 (20.1%), PSA persistence was detected. These men had an increased risk of BCR (hazard ratio (HR) 4.2, p < 0.0001), metastases (HR: 2.7, p = 0.002), CRM (HR: 5.5, p = 0.002) and OM (HR: 1.8, p = 0.01) compared to the men with undetectable PSA. The same significance of PSA persistence on each study endpoint was found in the high-risk group (HR: 2.5 to 6.2, p = 0.02 to p < 0.0001). In the intermediate-risk group, PSA persistence was found as a predictor of BCR (HR: 3.9, p < 0.0001), while, in the low-risk group, PSA persistence was not detected as a significant predictor of outcomes after RP. Conclusions: Persistent PSA could be used as an independent predictor of worse long-term outcomes in high-risk PCa patients, while, in intermediate-risk patients, this parameter significantly predicts only biochemical recurrence and has no impact on the outcomes in low-risk PCa patients.

Tax authorities face the challenge of effectively identifying companies that avoid paying taxes, which is not unique to European Union countries. Limited resources often constrain tax administrators, who traditionally rely on time-consuming and labour-intensive tax audit tools. As a result of this established practice, governments are losing a lot of tax revenue. The main objective of this study is to increase the efficiency of the detection of tax evasion by applying data mining methods in the East European country Lithuania, which has a rapidly developing economy, by applying data mining methods concerning affluence-related impacts. The study develops various models for segmentation, risk assessment, behavioral templates, and tax crime detection. Results show that the data mining technique can effectively detect tax evasion and extract hidden knowledge that can be used to reduce revenue losses resulting from tax evasion. This study’s methods, software, and findings can assist decision-makers, experts, and scientists in developing countries in predicting tax fraud detection.

The testing of multivariate normality remains a significant scientific problem. Although it is being extensively researched, it is still unclear how to choose the best test based on the sample size, variance, covariance matrix and others. In order to contribute to this field, a new goodness of fit test for multivariate normality is introduced. This test is based on the mean absolute deviation of the empirical distribution density from the theoretical distribution density. A new test was compared with the most popular tests in terms of empirical power. The power of the tests was estimated for the selected alternative distributions and examined by the Monte Carlo modeling method for the chosen sample sizes and dimensions. Based on the modeling results, it can be concluded that a new test is one of the most powerful tests for checking multivariate normality, especially for smaller samples. In addition, the assumption of normality of two real data sets was checked.

Data clustering is one area of data mining that falls into the data mining class of unsupervised learning. Cluster analysis divides data into different classes by discovering the internal structure of data set objects and their relationship. This paper presented a new density clustering method based on the modified inversion formula density estimation. This new method should allow one to improve the performance and robustness of the k-means, Gaussian mixture model, and other methods. The primary process of the proposed clustering algorithm consists of three main steps. Firstly, we initialized parameters and generated a T matrix. Secondly, we estimated the densities of each point and cluster. Third, we updated mean, sigma, and phi matrices. The new method based on the inversion formula works quite well with different datasets compared with K-means, Gaussian Mixture Model, and Bayesian Gaussian Mixture model. On the other hand, new methods have limitations because this one method in the current state cannot work with higher-dimensional data (d > 15). This will be solved in the future versions of the model, detailed further in future work. Additionally, based on the results, we can see that the MIDEv2 method works the best with generated data with outliers in all datasets (0.5%, 1%, 2%, 4% outliers). The interesting point is that a new method based on the inversion formula can cluster the data even if data do not have outliers; one of the most popular, for example, is the Iris dataset.

The outbreak of war and the earlier and ongoing COVID-19 pandemic determined the need for real-time monitoring of economic activity. The economic activity of a country can be defined in different ways. Most often, the country’s economic activity is characterized by various indicators such as the gross domestic product, the level of employment or unemployment of the population, the price level in the country, inflation, and other frequently used economic indicators. The most popular were the gross domestic product (GDP) and industrial production. However, such traditional tools have started to decline in modern times (as the timely knowledge of information becomes a critical factor in decision making in a rapidly changing environment) as they are published with significant delays. This work aims to use the information in the Lithuanian mass media and machine learning methods to assess whether these data can be used to assess economic activity. The aim of using these data is to determine the correlation between the usual indicators of economic activity assessment and media sentiments and to forecast traditional indicators. When evaluating consumer confidence, it is observed that the forecasting of this economic activity indicator is better based on the general index of negative sentiment (comparisons with univariate time series). In this case, the average absolute percentage error is 1.3% lower. However, if all sentiments are included in the forecasting instead of the best one, the forecasting is worse and in this case the MAPE is 5.9% higher. It is noticeable that forecasting the monthly and annual inflation rate is thus best when the overall negative sentiment is used. The MAPE of the monthly inflation rate is as much as8.5% lower, while the MAPE of the annual inflation rate is 1.5% lower.