StatsPub Date : 2024-01-10DOI: 10.3390/stats7010003
Nathaniel E. Helwig
{"title":"Precise Tensor Product Smoothing via Spectral Splines","authors":"Nathaniel E. Helwig","doi":"10.3390/stats7010003","DOIUrl":"https://doi.org/10.3390/stats7010003","url":null,"abstract":"Tensor product smoothers are frequently used to include interaction effects in multiple nonparametric regression models. Current implementations of tensor product smoothers either require using approximate penalties, such as those typically used in generalized additive models, or costly parameterizations, such as those used in smoothing spline analysis of variance models. In this paper, I propose a computationally efficient and theoretically precise approach for tensor product smoothing. Specifically, I propose a spectral representation of a univariate smoothing spline basis, and I develop an efficient approach for building tensor product smooths from marginal spectral spline representations. The developed theory suggests that current tensor product smoothing methods could be improved by incorporating the proposed tensor product spectral smoothers. Simulation results demonstrate that the proposed approach can outperform popular tensor product smoothing implementations, which supports the theoretical results developed in the paper.","PeriodicalId":93142,"journal":{"name":"Stats","volume":"59 20","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139440934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
StatsPub Date : 2024-01-08DOI: 10.3390/stats7010002
Mulubrhan G. Haile, Lingling Zhang, David J. Olive
{"title":"Predicting Random Walks and a Data-Splitting Prediction Region","authors":"Mulubrhan G. Haile, Lingling Zhang, David J. Olive","doi":"10.3390/stats7010002","DOIUrl":"https://doi.org/10.3390/stats7010002","url":null,"abstract":"Perhaps the first nonparametric, asymptotically optimal prediction intervals are provided for univariate random walks, with applications to renewal processes. Perhaps the first nonparametric prediction regions are introduced for vector-valued random walks. This paper further derives nonparametric data-splitting prediction regions, which are underpinned by very simple theory. Some of the prediction regions can be used when the data distribution does not have first moments, and some can be used for high-dimensional data, where the number of predictors is larger than the sample size. The prediction regions can make use of many estimators of multivariate location and dispersion.","PeriodicalId":93142,"journal":{"name":"Stats","volume":"53 36","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139447266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
StatsPub Date : 2023-12-30DOI: 10.3390/stats7010001
Shieh-Liang Chen, Kuo-Liang Chen
{"title":"The Mediating Impact of Innovation Types in the Relationship between Innovation Use Theory and Market Performance","authors":"Shieh-Liang Chen, Kuo-Liang Chen","doi":"10.3390/stats7010001","DOIUrl":"https://doi.org/10.3390/stats7010001","url":null,"abstract":"The ultimate goal of innovation is to improve performance. But if people’s needs and uses are ignored, innovation will only be a formality. In the past, research on innovation mostly focused on technology, processes, business models, services, and organizations. The measurement of innovation focuses on capabilities, processes, results, and methods, but there has always been a lack of pre-innovation measurements and tools. This study is the first to use the innovation use theory proposed by Christensen et al. combined with innovation types, and it uses the measurement focus on the early stage of innovation as a post-innovation performance prediction. This study collected 590 valid samples and used SPSS and the four-step BK method to conduct regression analysis and mediation tests. The empirical results obtained the following: (1) a confirmed model and scale of the innovation use theory; (2) that three constructs of innovation use theory have an impact on market performance; and (3) that innovation types acting as mediators will improve market performance. This study establishes an academic model of the innovation use theory to provide a clear scale tool for subsequent research. In practice, it can first measure the direction of innovation and performance prediction, providing managers with a reference when developing new products and applying market strategies.","PeriodicalId":93142,"journal":{"name":"Stats","volume":" 19","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139138519","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
StatsPub Date : 2023-12-12DOI: 10.3390/stats6040082
Julien Chevallier, Bilel Sanhaji
{"title":"Jump-Robust Realized-GARCH-MIDAS-X Estimators for Bitcoin and Ethereum Volatility Indices","authors":"Julien Chevallier, Bilel Sanhaji","doi":"10.3390/stats6040082","DOIUrl":"https://doi.org/10.3390/stats6040082","url":null,"abstract":"In this paper, we conducted an empirical investigation of the realized volatility of cryptocurrencies using an econometric approach. This work’s two main characteristics are: (i) the realized volatility to be forecast filters jumps, and (ii) the benefit of using various historical/implied volatility indices from brokers as exogenous variables was explicitly considered. We feature a jump-robust extension of the REGARCH-MIDAS-X model incorporating realized beta GARCH processes and MIDAS filters with monthly, daily, and hourly components. First, we estimated six jump-robust estimators of realized volatility for Bitcoin and Ethereum that were retained as the dependent variable. Second, we inserted ten Bitcoin and Ethereum volatility indices gathered from various exchanges as an exogenous variable, each at a time. Third, we explored their forecasting ability based on the MSE and QLIKE statistics. Our sample spanned the period from May 2018 to January 2023. The main result featured the best predictors among the volatility indices for Bitcoin and Ethereum derived from 30-day implied volatility. The significance of the findings could mostly be attributable to the ability of our new model to incorporate financial and technological variables directly into the specification of the Bitcoin and Ethereum volatility dynamics.","PeriodicalId":93142,"journal":{"name":"Stats","volume":"3 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139007733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
StatsPub Date : 2023-12-05DOI: 10.3390/stats6040081
Aris Spanos
{"title":"Revisiting the Large n (Sample Size) Problem: How to Avert Spurious Significance Results","authors":"Aris Spanos","doi":"10.3390/stats6040081","DOIUrl":"https://doi.org/10.3390/stats6040081","url":null,"abstract":"Although large data sets are generally viewed as advantageous for their ability to provide more precise and reliable evidence, it is often overlooked that these benefits are contingent upon certain conditions being met. The primary condition is the approximate validity (statistical adequacy) of the probabilistic assumptions comprising the statistical model Mθ(x) applied to the data. In the case of a statistically adequate Mθ(x) and a given significance level α, as n increases, the power of a test increases, and the p-value decreases due to the inherent trade-off between type I and type II error probabilities in frequentist testing. This trade-off raises concerns about the reliability of declaring ‘statistical significance’ based on conventional significance levels when n is exceptionally large. To address this issue, the author proposes that a principled approach, in the form of post-data severity (SEV) evaluation, be employed. The SEV evaluation represents a post-data error probability that converts unduly data-specific ‘accept/reject H0 results’ into evidence either supporting or contradicting inferential claims regarding the parameters of interest. This approach offers a more nuanced and robust perspective in navigating the challenges posed by the large n problem.","PeriodicalId":93142,"journal":{"name":"Stats","volume":"68 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138598495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Process Monitoring Using Truncated Gamma Distribution","authors":"Sajid Ali, Shayaan Rajput, Ismail Shah, Hassan Houmani","doi":"10.3390/stats6040080","DOIUrl":"https://doi.org/10.3390/stats6040080","url":null,"abstract":"The time-between-events idea is commonly used for monitoring high-quality processes. This study aims to monitor the increase and/or decrease in the process mean rapidly using a one-sided exponentially weighted moving average (EWMA) chart for the detection of upward or downward mean shifts using a truncated gamma distribution. The use of the truncation method helps to enhance and improve the sensitivity of the proposed chart. The performance of the proposed chart with known and estimated parameters is analyzed by using the run length properties, including the average run length (ARL) and standard deviation run length (SDRL), through extensive Monte Carlo simulation. The numerical results show that the proposed scheme is more sensitive than the existing ones. Finally, the chart is implemented in real-world situations to highlight the significance of the proposed chart.","PeriodicalId":93142,"journal":{"name":"Stats","volume":" 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138613377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
StatsPub Date : 2023-11-29DOI: 10.3390/stats6040079
A. Adebanji, Franz Aschl, Ednah Chepkemoi Chumo, Emmanuel Odame Owiredu, Johannes Müller, Tukae Mbegalo
{"title":"Social Response and Measles Dynamics","authors":"A. Adebanji, Franz Aschl, Ednah Chepkemoi Chumo, Emmanuel Odame Owiredu, Johannes Müller, Tukae Mbegalo","doi":"10.3390/stats6040079","DOIUrl":"https://doi.org/10.3390/stats6040079","url":null,"abstract":"Measles remains one of the leading causes of death among young children globally, even though a safe and cost-effective vaccine is available. Vaccine hesitancy and social response to vaccination continue to undermine efforts to eradicate measles. In this study, we consider data about measles vaccination and measles prevalence in Germany for the years 2008–2012 in 345 districts. In the first part of the paper, we show that the probability of a local outbreak does not significantly depend on the vaccination coverage, but—if an outbreak does take place—the scale of the outbreak depends significantly on the vaccination coverage. Additionally, we show that the willingness to be vaccinated is significantly increased by local outbreaks, with a delay of about one year. In the second part of the paper, we consider a deterministic delay model to investigate the consequences of the statistical findings on the dynamics of the infection. Here, we find that the delay might induce oscillations if the vaccination coverage is rather low and the social response to an outbreak is sufficiently strong. The relevance of our findings is discussed at the end of the paper.","PeriodicalId":93142,"journal":{"name":"Stats","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139212369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
StatsPub Date : 2023-11-21DOI: 10.3390/stats6040078
R. Guerra, Fernando A. Peña-Ramírez, G. Cordeiro
{"title":"The Logistic Burr XII Distribution: Properties and Applications to Income Data","authors":"R. Guerra, Fernando A. Peña-Ramírez, G. Cordeiro","doi":"10.3390/stats6040078","DOIUrl":"https://doi.org/10.3390/stats6040078","url":null,"abstract":"We define and study the four-parameter logistic Burr XII distribution. It is obtained by inserting the three-parameter Burr XII distribution as the baseline in the logistic-X family and may be a useful alternative method to model income distribution and could be applied to other areas. We illustrate that the new distribution can have decreasing and upside-down-bathtub hazard functions and that its density function is an infinite linear combination of Burr XII densities. Some mathematical properties of the proposed model are determined, such as the quantile function, ordinary and incomplete moments, and generating function. We also obtain the maximum likelihood estimators of the model parameters and perform a Monte Carlo simulation study. Further, we present a parametric regression model based on the introduced distribution as an alternative to the location-scale regression model. The potentiality of the new distribution is illustrated by means of two applications to income data sets.","PeriodicalId":93142,"journal":{"name":"Stats","volume":"92 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139252783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
StatsPub Date : 2023-11-11DOI: 10.3390/stats6040077
Javier Linkolk López-Gonzales, Ana María Gómez Lamus, Romina Torres, Paulo Canas Rodrigues, Rodrigo Salas
{"title":"Self-Organizing Topological Multilayer Perceptron: A Hybrid Method to Improve the Forecasting of Extreme Pollution Values","authors":"Javier Linkolk López-Gonzales, Ana María Gómez Lamus, Romina Torres, Paulo Canas Rodrigues, Rodrigo Salas","doi":"10.3390/stats6040077","DOIUrl":"https://doi.org/10.3390/stats6040077","url":null,"abstract":"Forecasting air pollutant levels is essential in regulatory plans focused on controlling and mitigating air pollutants, such as particulate matter. Focusing the forecast on air pollution peaks is challenging and complex since the pollutant time series behavior is not regular and is affected by several environmental and urban factors. In this study, we propose a new hybrid method based on artificial neural networks to forecast daily extreme events of PM2.5 pollution concentration. The hybrid method combines self-organizing maps to identify temporal patterns of excessive daily pollution found at different monitoring stations, with a set of multilayer perceptron to forecast extreme values of PM2.5 for each cluster. The proposed model was applied to analyze five-year pollution data obtained from nine weather stations in the metropolitan area of Santiago, Chile. Simulation results show that the hybrid method improves performance metrics when forecasting daily extreme values of PM2.5.","PeriodicalId":93142,"journal":{"name":"Stats","volume":"39 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135086869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
StatsPub Date : 2023-11-04DOI: 10.3390/stats6040076
Célestin C. Kokonendji, Sobom M. Somé, Youssef Esstafa, Marcelo Bourguignon
{"title":"On Underdispersed Count Kernels for Smoothing Probability Mass Functions","authors":"Célestin C. Kokonendji, Sobom M. Somé, Youssef Esstafa, Marcelo Bourguignon","doi":"10.3390/stats6040076","DOIUrl":"https://doi.org/10.3390/stats6040076","url":null,"abstract":"Only a few count smoothers are available for the widespread use of discrete associated kernel estimators, and their constructions lack systematic approaches. This paper proposes the mean dispersion technique for building count kernels. It is only applicable to count distributions that exhibit the underdispersion property, which ensures the convergence of the corresponding estimators. In addition to the well-known binomial and recent CoM-Poisson kernels, we introduce two new ones such the double Poisson and gamma-count kernels. Despite the challenging problem of obtaining explicit expressions, these kernels effectively smooth densities. Their good performances are pointed out from both numerical and comparative analyses, particularly for small and moderate sample sizes. The optimal tuning parameter is here investigated by integrated squared errors. Also, the added advantage of faster computation times is really very interesting. Thus, the overall accuracy of two newly suggested kernels appears to be between the two old ones. Finally, an application including a tail probability estimation on a real count data and some concluding remarks are given.","PeriodicalId":93142,"journal":{"name":"Stats","volume":"39 26","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135773638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}