Computational Statistics最新文献

Nonconvex penalties are utilized for regularization in high-dimensional statistical learning algorithms primarily because they yield unbiased or nearly unbiased estimators for the parameters in the model. Nonconvex penalties existing in the literature such as SCAD, MCP, Laplace and arctan have a singularity at origin which makes them useful also for variable selection. However, in several high-dimensional frameworks such as deep learning, variable selection is less of a concern. In this paper, we present a nonconvex penalty which is smooth at origin. The paper includes asymptotic results for ordinary least squares estimators regularized with the new penalty function, showing asymptotic bias that vanishes exponentially fast. We also conducted simulations to better understand the finite sample properties and conducted an empirical study employing deep neural network architecture on three datasets and convolutional neural network on four datasets. The empirical study based on artificial neural networks showed better performance for the new regularization approach in five out of the seven datasets.

The power of data and correct statistical analysis has never been more prevalent. Academics and practitioners require nowadays an accurate application of quantitative methods. Yet many branches are subject to a crisis of integrity, which is shown in an improper use of statistical models, p-hacking, HARKing, or failure to replicate results. We propose the use of a Peer-to-Peer (P2P) ecosystem based on a blockchain network, Quantinar, to support quantitative analytics knowledge paired with code in the form of Quantlets or software snippets. The integration of blockchain technology allows Quantinar to ensure fully transparent and reproducible scientific research.

We make Bayesian additive regression networks (BARN) available as a Python package, barmpy, with documentation at https://dvbuntu.github.io/barmpy/ for general machine learning practitioners. Our object-oriented design is compatible with SciKit-Learn, allowing usage of their tools like cross-validation. To ease learning to use barmpy, we produce a companion tutorial that expands on reference information in the documentation. Any interested user can pip install barmpy from the official PyPi repository. barmpy also serves as a baseline Python library for generic Bayesian additive regression models.

Meta-analysis is an important statistical technique for synthesizing the results of multiple studies regarding the same or closely related research question. So-called meta-regression extends meta-analysis models by accounting for study-level covariates. Mixed-effects meta-regression models provide a powerful tool for evidence synthesis, by appropriately accounting for between-study heterogeneity. In fact, modelling the study effect in terms of random effects and moderators not only allows to examine the impact of the moderators, but often leads to more accurate estimates of the involved parameters. Nevertheless, due to the often small number of studies on a specific research topic, interactions are often neglected in meta-regression. In this work we consider the research questions (i) how moderator interactions influence inference in mixed-effects meta-regression models and (ii) whether some inference methods are more reliable than others. Here we review robust methods for confidence intervals in meta-regression models including interaction effects. These methods are based on the application of robust sandwich estimators of Hartung-Knapp-Sidik-Jonkman (HKSJ) or heteroscedasticity-consistent (HC)-type for estimating the variance-covariance matrix of the vector of model coefficients. Furthermore, we compare different versions of these robust estimators in an extensive simulation study. We thereby investigate coverage and width of seven different confidence intervals under varying conditions. Our simulation study shows that the coverage rates as well as the interval widths of the parameter estimates are only slightly affected by adjustment of the parameters. It also turned out that using the Satterthwaite approximation for the degrees of freedom seems to be advantageous for accurate coverage rates. In addition, different to previous analyses for simpler models, the (textbf{HKSJ})-estimator shows a worse performance in this more complex setting compared to some of the (textbf{HC})-estimators.

This work focuses on learning causal network structures from ordinal categorical data. By combining constraint-based with score-and-search methodologies in structural learning, we propose a hybrid method called Markov Blanket Based Ordinal Causal Discovery (MBOCD) algorithm, which can capture the ordinal relationship of values in ordinal categorical variables. Theoretically, it is proved that for ordinal causal networks, two adjacent DAGs belonging to the same Markov equivalence class are identifiable, which results in the generation of a causal graph. Simulation experiments demonstrate that the proposed algorithm outperforms existing methods in terms of computational efficiency and accuracy. The code of this work is open at: https://github.com/leoydu/MBOCDcode.git.

This paper introduces the Metropolis–Hastings variational inference Robbins–Monro (MHVIRM) algorithm, a modification of the Metropolis–Hastings Robbins–Monro (MHRM) method, designed for estimating parameters in complex multidimensional graded response models (MGRM). By integrating a black-box variational inference (BBVI) approach, MHVIRM enhances computational efficiency and estimation accuracy, particularly for models with high-dimensional data and complex test structures. The algorithms effectiveness is demonstrated through simulations, showing improved precision over traditional MHRM, especially in scenarios with complex structures and small sample sizes. Moreover, MHVIRM is robust to initial values. The applicability is further illustrated with a real dataset analysis.

Panel binary data arise in an event history study when study subjects are observed only at discrete time points instead of continuously and the only available information on the occurrence of the recurrent event of interest is whether the event has occurred over two consecutive observation times or each observation window. Although some methods have been proposed for regression analysis of such data, all of them assume independent observation times or processes, which may not be true sometimes. To address this, we propose a joint modeling procedure that allows for informative observation processes. For the implementation of the proposed method, a computationally efficient EM algorithm is developed and the resulting estimators are consistent and asymptotically normal. The simulation study conducted to assess its performance indicates that it works well in practical situations, and the proposed approach is applied to the motivating data set from the Health and Retirement Study.

Power transformations of count data, including cell frequencies of a contingency table, have been well understood for nearly 100 years, with much of the attention focused on the square root transformation. Over the past 15 years, this topic has been the focus of some new insights into areas of correspondence analysis where two forms of power transformation have been discussed. One type considers the impact of raising the joint proportions of the cell frequencies of a table to a known power while the other examines the power transformation of the relative distribution of the cell frequencies. While the foundations of the graphical features of correspondence analysis rest with the numerical algorithms like reciprocal averaging, and other analogous techniques, discussions of the role of power transformations in reciprocal averaging have not been described. Therefore, this paper examines this link where a power transformation is applied to the cell frequencies of a two-way contingency table. In doing so, we show that reciprocal averaging can be performed under such a transformation to obtain row and column scores that provide the maximum association between the variables and the greatest discrimination between the categories. Finally, we discuss the connection between performing reciprocal averaging and singular value decomposition under this type of power transformation. The R function, powerRA.exe is included in the Appendix and performs reciprocal averaging of a power transformation of the cell frequencies of a two-way contingency table.

This paper discusses dynamic ARMA-type regression models for positive time series, which can handle bounded non-Gaussian time series without requiring data transformations. Our proposed model includes a conditional mean modeled by a dynamic structure containing autoregressive and moving average terms, time-varying covariates, unknown parameters, and link functions. Additionally, we present the PTSR package and discuss partial maximum likelihood estimation, asymptotic theory, hypothesis testing inference, diagnostic analysis, and forecasting for a variety of regression-based dynamic models for positive time series. A Monte Carlo simulation and a real data application are provided.

The study of aggregated data influenced by time, space, and extra changes in geographic region borders was the main emphasis of the current paper. This may occur if the regions used to count the reported incidences of a health outcome over time change periodically. In order to handle the spatial-temporal scenario, we enhance the spatial root-Gaussian Cox Process (RGCP), which makes use of the square-root link function rather than the more typical log-link function. The algorithm’s ability to estimate a risk surface has been proven by a simulation study, and it has also been validated by real datasets.