Computational Statistics最新文献

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.

Bayesian Kriging (BK) provides a way to estimate regression models where the parameters are smoothed across space. Such estimates could help guide site-specific fertilizer recommendations. One advantage of BK is that it can readily fill in the missing values that are common in yield monitor data. The problem is that previous methods are too computationally intensive to be commercially feasible when estimating a nonlinear production function. This paper sought to increase computational speed by imposing restrictions on the spatial covariance matrix. Previous research used an exponential function for the spatial covariance matrix. The two alternatives considered are the conditional autoregressive and simultaneous autoregressive models. In addition, a new analytical solution is provided for finding the optimal value of nitrogen with a stochastic linear plateau model. A comparison among models in the accuracy and computational burden shows that the restrictions significantly reduced the computational burden, although they did sacrifice some accuracy in the dataset considered.

This paper studies a Bayesian local influence method to detect influential observations in a partially linear model with first-order autoregressive skew-normal errors. This method appears suitable for small or moderate-sized data sets ((n=200{sim }400)) and overcomes some theoretical limitations, bridging the diagnostic gap for small or moderate-sized data in classical methods. The MCMC algorithm is employed for parameter estimation, and Bayesian local influence analysis is made using three perturbation schemes (priors, variances, and data) and three measurement scales (Bayes factor, (phi )-divergence, and posterior mean). Simulation studies are conducted to validate the reliability of the diagnostics. Finally, a practical application uses data on the 1976 Los Angeles ozone concentration to further demonstrate the effectiveness of the diagnostics.

Quantile regression is an extension of linear regression which estimates a conditional quantile of interest. In this paper, we propose an empirical likelihood-based non-parametric procedure to detect structural changes in the quantile regression models. Further, we have modified the proposed smoothed empirical likelihood-based method using adjusted smoothed empirical likelihood and transformed smoothed empirical likelihood techniques. We have shown that under the null hypothesis, the limiting distribution of the smoothed empirical likelihood ratio test statistic is identical to that of the classical parametric likelihood. Simulations are conducted to investigate the finite sample properties of the proposed methods. Finally, to demonstrate the effectiveness of the proposed method, it is applied to urinary Glycosaminoglycans (GAGs) data to detect structural changes.

Additive coefficient models generalize linear regression models by assuming that the relationship between the response and some covariates is linear, while their regression coefficients are additive functions. Because of its advantages in dealing with the “curse of dimensionality”, additive coefficient models gain a lot of attention. The commonly used estimation methods for additive coefficient models are not robust against high leverage points. To circumvent this difficulty, we develop a robust variable selection procedure based on the exponential squared loss function and group penalty for the additive coefficient models, which can tackle outliers in the response and covariates simultaneously. Under some regularity conditions, we show that the oracle estimator is a local solution of the proposed method. Furthermore, we apply the local linear approximation and minorization-maximization algorithm for the implementation of the proposed estimator. Meanwhile, we propose a data-driven procedure to select the tuning parameters. Simulation studies and an application to a plasma beta-carotene level data set illustrate that the proposed method can offer more reliable results than other existing methods in contamination schemes.

This paper proposes a polynomial structure identification (PSI) method for variable selection and model structure identification of additive models with longitudinal data. First, the backfitting algorithm and zero-order local polynomial smoothing method are used to select important variables in the additive model, and the importance of variables is determined through the inverse of the bandwidth parameter in the nonparametric partial kernel function. Second, the backfitting algorithm and Q-order local polynomial smoothing method are utilized to identify the specific structure of each selected predictor. To incorporate correlations within longitudinal data, a two-stage estimation method is proposed for estimating the regression parameters of the identified important variables: (i) Parameter estimators of the important variables are firstly obtained under an independence working model assumption; (ii) Generalized estimating equations with a working correlation matrix based on B-splines are constructed to obtain the final estimators of the parameters, which improve the efficiency of parameter estimation. Finally, simulation studies are carried out to evaluate the performance of the proposed method, followed by the presentation of two real-world examples for illustration.

In time-to-event analyses, a competing risk is an event whose occurrence precludes the occurrence of the event of interest. Settings with competing risks occur frequently in clinical research. Missing data, which is a common problem in research, occurs when the value of a variable is recorded for some, but not all, records in the dataset. Multiple Imputation (MI) is a popular method to address the presence of missing data. MI uses an imputation model to generate M (M > 1) values for each variable that is missing, resulting in the creation of M complete datasets. A popular algorithm for imputing missing data is multivariate imputation using chained equations (MICE). We used a complex simulation design with covariates and missing data patterns reflective of patients hospitalized with acute myocardial infarction (AMI) to compare three strategies for imputing missing predictor variables when the analysis model is a cause-specific hazard when there were three different event types. We compared two MICE-based strategies that differed according to which cause-specific cumulative hazard functions were included in the imputation models (the three cause-specific cumulative hazard functions vs. only the cause-specific cumulative hazard function for the primary outcome) with the use of the substantive model compatible fully conditional specification (SMCFCS) algorithm. While no strategy had consistently superior performance compared to the other strategies, SMCFCS may be the preferred strategy. We illustrated the application of the strategies using a case study of patients hospitalized with AMI.