Asta-Advances in Statistical Analysis最新文献

Dimension reduction, by means of Principal Component Analysis (PCA), is often employed to obtain a reduced set of components preserving the largest possible part of the total variance of the observed variables. Several methodologies have been proposed either to improve the interpretation of PCA results (e.g., by means of orthogonal, oblique rotations, shrinkage methods), or to model oblique components or factors with a hierarchical structure, such as in Bi-factor and High-Order Factor analyses. In this paper, we propose a new methodology, called Hierarchical Disjoint Principal Component Analysis (HierDPCA), that aims at building a hierarchy of disjoint principal components of maximum variance associated with disjoint groups of observed variables, from Q up to a unique, general one. HierDPCA also allows choosing the type of the relationship among disjoint principal components of two sequential levels, from the lowest upwards, by testing the component correlation per level and changing from a reflective to a formative approach when this correlation turns out to be not statistically significant. The methodology is formulated in a semi-parametric least-squares framework and a coordinate descent algorithm is proposed to estimate the model parameters. A simulation study and two real applications are illustrated to highlight the empirical properties of the proposed methodology.

We introduce a selection model-based imputation approach to be used within the Fully Conditional Specification (FCS) framework for the Multiple Imputation (MI) of incomplete ordinal variables that are supposed to be Missing Not at Random (MNAR). Thereby, we generalise previous work on this topic which involved binary single-level and multilevel data to ordinal variables. We apply an ordered probit model with sample selection as base of our imputation algorithm. The applied model involves two equations that are modelled jointly where the first one describes the missing-data mechanism and the second one specifies the variable to be imputed. In addition, we develop a version for hierarchical data by incorporating random intercept terms in both equations. To fit this multilevel imputation model we use quadrature techniques. Two simulation studies validate the overall good performance of our single-level and multilevel imputation methods. In addition, we show its applicability to empirical data by applying it to a common research topic in educational science using data of the National Educational Panel Study (NEPS) and conducting a short sensitivity analysis. Our approach is designed to be used within the R software package mice which makes it easy to access and apply.

The evaluation of the possible effects of a treatment on an outcome plays a central role in both theoretical and applied statistical and econometrical literature. This paper focuses on nonparametric tests for possible difference in the distribution of potential outcomes due to receiving or not receiving a treatment. The approach is based on weighting observed data on the basis on the estimated propensity score. Kolmogorov–Smirnov type and Wilcoxon–Mann–Whitney type tests are constructed, and their limiting distributions are studied. Rejection regions are obtained by inverting confidence intervals. This involves the study of appropriate estimators of the limiting variance of test statistics. Approximations of quantiles via subsampling are also considered. The merits of the different tests are studied by Monte Carlo simulation. An application to the construction of tests for stochastic dominance is provided.

Within the stochastic approach, this paper establishes a closed-form solution to the price index problem for an arbitrary number of periods or countries. The index’s reference basket merges the intersections of all couples of baskets in all periods/countries and provides an effective commodity coverage. Under spherical regression errors, the index satisfies the Geary–Khamis equation system and, as such, offers a general and compact representation of the latter as well as the inferential framework as a dowry. Furthermore, by relaxing sphericalness in favor of a more realistic assumption of commodity-dependent variances, a broader result is achieved. The solution to the price index problem thus obtained encompasses the Geary–Khamis formulation and sows the seeds to further advances.

Triggered by advances in data gathering technologies, the use of statistical analyzes, predictions and modeling techniques in sports has gained a rapidly growing interest over the last decades. Today, professional sports teams have access to precise player positioning data and sports scientists design experiments involving non-standard data structures like movement-trajectories. This special issue on statistics in sports is dedicated to further foster the development of statistics and its applications in sports. The contributed articles address a wide range of statistical problems such as statistical methods for prediction of game outcomes, for prevention of sports injuries, for analyzing sports science data from movement laboratories, for measurement and evaluation of player performance, etc. Finally, also SARS-CoV-2 pandemic-related impacts on the sport’s framework are investigated.

In this contribution, we investigate the importance of Oliver’s Four Factors, proposed in the literature to identify a basketball team’s strengths and weaknesses in terms of shooting, turnovers, rebounding and free throws, as success drivers of a basketball game. In order to investigate the role of each factor in the success of a team in a match, we applied the MOdel-Based recursive partitioning (MOB) algorithm to real data concerning 19,138 matches of 16 National Basketball Association (NBA) regular seasons (from 2004–2005 to 2019–2020). MOB, instead of fitting one global Generalized Linear Model (GLM) to all observations, partitions the observations according to selected partitioning variables and estimates several ad hoc local GLMs for subgroups of observations. The manuscript’s aim is twofold: (1) in order to deal with (quasi) separation problems leading to convergence problems in the numerical solution of Maximum Likelihood (ML) estimation in MOB, we propose a methodological extension of GLM-based recursive partitioning from standard ML estimation to bias-reduced (BR) estimation; and (2) we apply the BR-based GLM trees to basketball analytics. The results show models very easy to interpret that can provide useful support to coaching staff’s decisions.

We comment the paper by Jahn et al. (On the role of data, statistics and decisions in a pandemic, 2022).

Many popular sports involve matches between two teams or players where each team have the possibility of scoring points throughout the match. While the overall match winner and result is interesting, it conveys little information about the underlying scoring trends throughout the match. Modeling approaches that accommodate a finer granularity of the score difference throughout the match is needed to evaluate in-game strategies, discuss scoring streaks, teams strengths, and other aspects of the game. We propose a latent Gaussian process to model the score difference between two teams and introduce the Trend Direction Index as an easily interpretable probabilistic measure of the current trend in the match as well as a measure of post-game trend evaluation. In addition we propose the Excitement Trend Index—the expected number of monotonicity changes in the running score difference—as a measure of overall game excitement. Our proposed methodology is applied to all 1143 matches from the 2019–2020 National Basketball Association season. We show how the trends can be interpreted in individual games and how the excitement score can be used to cluster teams according to how exciting they are to watch.