Article
Statistics & Probability
Anna Klimova, Tamas Rudas
Summary: Relational models generalize log-linear models to arbitrary discrete sample spaces by specifying effects associated with subsets of cells. The properties of maximum likelihood estimates (MLEs) in a relational model with an overall effect resemble those of traditional log-linear models, while without an overall effect, the properties of MLEs are considerably different. The Poisson and multinomial MLEs are not equivalent when an overall effect is absent in the Poisson case.
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
(2022)
Article
Statistics & Probability
Rina Foygel Barber, Lucas Janson
Summary: Goodness-of-fit testing is widely used in statistics and has various applications in model selection, confidence interval construction, conditional independence testing, and multiple testing. Current GoF tests for composite null hypotheses are often restricted in the choice of test statistic, except for co-sufficient sampling (CSS) testing which requires a compact sufficient statistic for the null model. In this paper, we propose approximate CSS (aCSS) testing that generalizes CSS testing to almost any parametric model with an asymptotically efficient estimator, overcoming the limitations of CSS testing.
ANNALS OF STATISTICS
(2022)
Article
Statistics & Probability
Adel Javanmard, Mohammad Mehrabi
Summary: This paper discusses the fundamental problem of assessing the goodness-of-fit for a general binary classifier and proposes a novel test method called GRASP. The method is applicable in finite sample settings and is not restricted by the distribution of features. Additionally, an improved method called model-X GRASP is proposed for situations where the joint distribution of the features vector is known, which can achieve better power.
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
(2023)
Article
Statistics & Probability
Ghislain Verdier
Summary: Gamma processes are commonly used for modelling accumulative deterioration, but it is not always easy to confirm the correctness of the choice of a gamma process model given a series of observations. This paper proposes a practical procedure combining three statistical tests to reject the gamma process model when the observations contradict the basic properties of a homogeneous gamma process, and extends the procedure to non-homogeneous gamma process and aperiodic inspection times. The efficiency of the approach is investigated through numerical simulations and real data.
COMPUTATIONAL STATISTICS
(2023)
Article
Mathematics
Juan Pan, Yunhua Zhou
Summary: In this paper, we investigate the style number, independence number, and entropy of a frame bundle dynamical system. The base system is a countable discrete amenable group action on a compact metric space. We establish the existence of cover measures, an ergodic theorem concerning mean linear independence and the style number, and a variational principle for style numbers and independence numbers. Furthermore, we examine the relationship between the entropy of base systems and that of their bundle systems.
ACTA MATHEMATICA SCIENTIA
(2023)
Article
Computer Science, Information Systems
Alexander Shapiro, Yao Xie, Rui Zhang
Summary: The research develops a general theory for the goodness-of-fit test to non-linear models, where the residual of the model fit follows a chi(2) distribution related to the model order and problem dimension. A sequential method for selecting model orders is presented, demonstrating broad applications in machine learning and signal processing.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2021)
Article
Statistics & Probability
Tingyu Lai, Zhongzhan Zhang, Yafei Wang
Summary: A conventional regression model for functional data requires the relationship between the predictor function and the response variable to be expressed. Two assumptions regarding independence between predictor function and error, as well as a functional linear model for the relationship, are usually added to the model. A test procedure based on generalized distance covariance is developed to check these assumptions simultaneously, showing consistent performance against alternatives.
JOURNAL OF THE KOREAN STATISTICAL SOCIETY
(2021)
Article
Computer Science, Interdisciplinary Applications
Chihiro Watanabe, Taiji Suzuki
Summary: This study developed a new goodness-of-fit test for latent block models to test whether an observed data matrix fits a given set of row and column cluster numbers, or it consists of more clusters in at least one direction of the row and the column.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2021)
Article
Computer Science, Hardware & Architecture
Jan Strappa, Facundo Bromberg
Summary: Log-linear models are probability distributions that capture the relationships between variables, and they have been widely used in various fields. This work proposes a measure for the direct and efficient comparison of independence structures in log-linear models, which only requires the independence structure of the models. This measure is useful for obtaining knowledge from the structure or comparing the performance of structure learning algorithms.
Article
Statistics & Probability
Nikola Surjanovic, Thomas M. Loughin
Summary: This paper discusses the application of the Hosmer-Lemeshow (HL) test in logistic regression models and explores the performance of the HL and generalized HL (GHL) tests through simulations and analysis of real-life data. The results show that the power of the HL test decreases with increasing model complexity, while the GHL test offers some protection in the presence of binary replicates or clusters.
JOURNAL OF APPLIED STATISTICS
(2023)
Article
Statistics & Probability
Ludwig Baringhaus, Daniel Gaigall
Summary: This study focuses on testing the hypothesis that the distribution of bivariate data (S, N) belongs to the parametric class of distributions in the compound Poisson exponential model. The compound Poisson exponential model is often used in stochastic hydrology and actuarial science, involving variables like raindays and total rainfall amount or loss frequency and total loss expenditure. A specific transform associated with the distribution of (S, N) satisfies a certain differential equation, and this study proposes a test statistic based on the empirical counterparts of the transform. Critical values are obtained using a parametric bootstrap procedure, and the asymptotic behavior of the tests is discussed. The performance of the tests is demonstrated through simulation studies on rainfall data and an actuarial dataset, and a potential multivariate extension is also discussed.
JOURNAL OF MULTIVARIATE ANALYSIS
(2023)
Article
Engineering, Chemical
Haifang Mao, Chaoyang Wang, Jibo Liu, Kejia Liu, Wei Zheng, Ting Tang, Miaomiao Jin
Summary: Six mathematical models were used to fit and regress the particle size distribution (PSD) of MAEM. The goodness-of-fit was evaluated using R-2, AIC, and RMSE. The top three models were applied and compared for MAEM PSD under two different stirring speeds. FBRM was used to monitor particle number trends on a lab scale. A feasible reaction mechanism was presented, indicating the influence of stirring speed on the rate-controlling step of reactant dissolution.
CHEMICAL ENGINEERING & TECHNOLOGY
(2023)
Article
Computer Science, Information Systems
T. Delacroix, P. Lenca, S. Lallich
Summary: This paper introduces the concept of Mutual Constrained Independence (MCI) and proposes a method for computing MCI models based on algebraic geometry. It aims to address the challenge of redundancy in frequency-based data mining and itemset mining. The research also establishes the link between MCI models and a class of MaxEnt models used in pattern mining.
INFORMATION SCIENCES
(2022)
Review
Chemistry, Analytical
Francisco Raposo, Damia Barcelo
Summary: This critical review paper discusses the main analytical calibration models and their practical use guidelines. It proposes a three-step simple calibration diagnosis method based on a combination of graphical plots, statistical significance tests, and numerical parameters. Experimental conditions and calibration procedure design are crucial for the appropriate selection of models.
TRAC-TRENDS IN ANALYTICAL CHEMISTRY
(2021)
Article
Mathematics
A. Pekgor
Summary: Recently, new goodness-of-fit tests based on Kullback-Leibler divergence and likelihood ratio have been introduced for the Cauchy distribution, claiming to be more powerful than traditional tests. This study proposes a novel test for the Cauchy distribution and derives its asymptotic null distribution. Critical values are determined through Monte Carlo simulation for various sample sizes, and power analysis reveals the superiority of the proposed test under certain conditions.
JOURNAL OF MATHEMATICS
(2023)
