Testing stability in a spatial unilateral autoregressive model

ABSTRACT

Least squares estimator of the stability parameter ? ? |α| + |β| for a spatial unilateral autoregressive process X_{k, ?} = αX_{k ? 1, ?} + βX_{k, ? ? 1} + ?_{k, ?} is investigated and asymptotic normality with a scaling factor n^5/4 is shown in the unstable case ? = 1. The result is in contrast to the unit root case of the AR(p) model X_k = α₁X_{k ? 1} + ??? + α_pX_{k ? p} + ?_k, where the limiting distribution of the least squares estimator of the unit root parameter ? ? α₁ + ??? + α_p is not normal.     

Estimating and Validating Nonlinear Regression Metamodels in Simulation

Frequently, the main objective of statistically designed simulation experiments is to estimate and validate regression metamodels, where the regressors are functions of the design variables and the dependent variable is the system response. In this article, a weighted least squares procedure for estimating the unknown parameters of a nonlinear regression metamodel is formulated and evaluated. Since the validity of a fitted regression model must be tested, a method for validating nonlinear regression simulation metamodels is presented. This method is a generalization of the cross-validation test proposed by Kleijnen (1983 Kleijnen , J. P. C. ( 1983 ). Cross-validation using the t statistic . European Journal of Operational Research 13 : 133 – 141 .[Crossref] , [Google Scholar]) in the context of linear regression metamodels. One drawback of the cross-validation strategy is the need to perform a large number of nonlinear regressions, if the number of experimental points is large. In this article, cross-validation is implemented using only one nonlinear regression. The proposed statistical analysis allows us to obtain Scheffé-type simultaneous confidence intervals for linear combinations of the metamodel's unknown parameters. Using the well-known M/M/1 example, a metamodel is built and validated with the aid of the proposed procedure.     

The Effect of Verification Bias in the Naïve Estimators of Accuracy of a Binary Diagnostic Test

The assessment of a binary diagnostic test requires a knowledge of the disease status of all the patients in the sample through the application of a gold standard. In practice, the gold standard is not always applied to all of the patients, which leads to the problem of partial verification of the disease. When the accuracy of the diagnostic test is assessed using only those patients whose disease status has been verified using the gold standard, the estimators obtained in this way, known as Naïve estimators, may be biased. In this study, we obtain the explicit expressions of the bias of the Naïve estimators of sensitivity and specificity of a binary diagnostic test. We also carry out simulation experiments in order to study the effect of the verification probabilities on the Naïve estimators of sensitivity and specificity.     

Analysis of Type I Error Rates of Univariate and Multivariate Procedures in Repeated Measures Designs

We compared the robustness of univariate and multivariate statistical procedures to control Type I error rates when the normality and homocedasticity assumptions were not fulfilled. The procedures we evaluated are the mixed model adjusted by means of the SAS Proc Mixed module, and Bootstrap-F approach, Brown–Forsythe multivariate approach, Welch–James multivariate approach, and Welch–James multivariate approach with robust estimators. The results suggest that the Kenward Roger, Brown–Forsythe, Welch–James, and Improved Generalized Aprroximate procedures satisfactorily kept Type I error rates within the nominal levels for both the main and interaction effects under most of the conditions assessed.     

A Simulation Study Comparing Modeling Approaches in an Illness-Death Multi-State Model

In many medical studies, there are covariates that change their values over time and their analysis is most often modeled using the Cox regression model. However, many of these time-dependent covariates can be expressed as an intermediate event, which can be modeled using a multi-state model. Using the relationship of time-dependent (discrete) covariates and multi-state models, we compare (via simulation studies) the Cox model with time-dependent covariates with the most frequently used multi-state regression models. This article also details the procedures for generating survival data arising from all approaches, including the Cox model with time-dependent covariates.     

How are Time-Dependent Childbearing Intentions Realized? Realization,Postponement, Abandonment,Bringing Forward

Our study aims to identify factors that facilitate or inhibit the realization of fertility intentions. The analysis uses data collected in the first two waves of a Hungarian longitudinal survey. Fertility intentions recorded at the first wave pertain to the subsequent 3-year period, just similar to the behavior variable measuring the realization of intentions, i.e., a birth within the 3-year period in question. For this analysis, we used the respondents’ demographic, socio-structural, and orientational traits recorded at the first interview. Our findings show that age, parity, and partnership play a determining role in the realization of fertility intentions, but employment status, religious affiliation, and overall life satisfaction all exhibit significant effects. A marked gender difference was detected not only with regard to employment status but in the area of values and orientations as well.     

A Model of Minimal Probabilistic Belief Revision

In the literature there are at least two models for probabilistic belief revision: Bayesian updating and imaging [Lewis, D. K. (1973), Counterfactuals, Blackwell, Oxford; Gärdenfors, P. (1988), Knowledge in flux: modeling the dynamics of epistemic states, MIT Press, Cambridge, MA]. In this paper we focus on imaging rules that can be described by the following procedure: (1) Identify every state with some real valued vector of characteristics, and accordingly identify every probabilistic belief with an expected vector of characteristics; (2) For every initial belief and every piece of information, choose the revised belief which is compatible with this information and for which the expected vector of characteristics has minimal Euclidean distance to the expected vector of characteristics of the initial belief. This class of rules thus satisfies an intuitive notion of minimal belief revision. The main result in this paper is to provide an axiomatic characterization of this class of imaging rules.     

Readouts for echo-state networks built using locally regularized orthogonal forward regression

Echo state network (ESN) is viewed as a temporal expansion which naturally give rise to regressors of various relevance to a teacher output. We illustrate that often only a certain amount of the generated echo-regressors effectively explain the teacher output and we propose to determine the importance of the echo-regressors by a joint calculation of the individual variance contributions and Bayesian relevance using the locally regularized orthogonal forward regression (LROFR). This information can be advantageously used in a variety of ways for an analysis of an ESN structure. We present a locally regularized linear readout built using LROFR. The readout may have a smaller dimensionality than the ESN model itself, and improves robustness and accuracy of an ESN. Its main advantage is ability to determine what type of an additional readout is suitable for a task at hand. Comparison with PCA is provided too. We also propose a radial basis function (RBF) readout built using LROFR, since flexibility of the linear readout has limitations and might be insufficient for complex tasks. Its excellent generalization abilities make it a viable alternative to feed-forward neural networks or relevance-vector-machines. For cases where more temporal capacity is required we propose well studied delay&sum readout.     

Bayesian Additive Regression Trees using Bayesian model averaging

Bayesian Additive Regression Trees (BART) is a statistical sum of trees model. It can be considered a Bayesian version of machine learning tree ensemble methods where the individual trees are the base learners. However, for datasets where the number of variables p is large the algorithm can become inefficient and computationally expensive. Another method which is popular for high-dimensional data is random forests, a machine learning algorithm which grows trees using a greedy search for the best split points. However, its default implementation does not produce probabilistic estimates or predictions. We propose an alternative fitting algorithm for BART called BART-BMA, which uses Bayesian model averaging and a greedy search algorithm to obtain a posterior distribution more efficiently than BART for datasets with large p. BART-BMA incorporates elements of both BART and random forests to offer a model-based algorithm which can deal with high-dimensional data. We have found that BART-BMA can be run in a reasonable time on a standard laptop for the “small n large p” scenario which is common in many areas of bioinformatics. We showcase this method using simulated data and data from two real proteomic experiments, one to distinguish between patients with cardiovascular disease and controls and another to classify aggressive from non-aggressive prostate cancer. We compare our results to their main competitors. Open source code written in R and Rcpp to run BART-BMA can be found at: https://github.com/BelindaHernandez/BART-BMA.git.     

Effect of autocorrelation when estimating the trend of a time series via penalized least squares with controlled smoothness

This paper studies the effect of autocorrelation on the smoothness of the trend of a univariate time series estimated by means of penalized least squares. An index of smoothness is deduced for the case of a time series represented by a signal-plus-noise model, where the noise follows an autoregressive process of order one. This index is useful for measuring the distortion of the amount of smoothness by incorporating the effect of autocorrelation. Different autocorrelation values are used to appreciate the numerical effect on smoothness for estimated trends of time series with different sample sizes. For comparative purposes, several graphs of two simulated time series are presented, where the estimated trend is compared with and without autocorrelation in the noise. Some findings are as follows, on the one hand, when the autocorrelation is negative (no matter how large) or positive but small, the estimated trend gets very close to the true trend. Even in this case, the estimation is improved by fixing the index of smoothness according to the sample size. On the other hand, when the autocorrelation is positive and large the simulated and estimated trends lie far away from the true trend. This situation is mitigated by fixing an appropriate index of smoothness for the estimated trend in accordance to the sample size at hand. Finally, an empirical example serves to illustrate the use of the smoothness index when estimating the trend of Mexico’s quarterly GDP.