An objective look at obtaining the plotting positions for QQ-plots

ABSTRACT

Choosing the plotting positions for the QQ-plot has been a subject of much debate in the statistical and engineering literature. This paper looks at this problem objectively by considering three frameworks: distribution-theoretic; decision-theoretic; game-theoretic. In each framework, we derive the plotting positions and show that there are more than one legitimate solution depending on the practitioner’s objective. This work clarifies the choice of the plotting positions by allowing one to easily find the mathematical equivalent of their view and choose the corresponding solution. This work also discusses approximations to the plotting positions when no closed form is available.     

Nonparametric approach to intervention time series modeling

Time series are often affected by interventions such as strikes, earthquakes, or policy changes. In the current paper, we build a practical nonparametric intervention model using the central mean subspace in time series. We estimate the central mean subspace for time series taking into account known interventions by using the Nadaraya–Watson kernel estimator. We use the modified Bayesian information criterion to estimate the unknown lag and dimension. Finally, we demonstrate that this nonparametric approach for intervened time series performs well in simulations and in a real data analysis such as the Monthly average of the oxidant.     

A new reproducing kernel-based nonlinear dimension reduction method for survival data

Based on the theories of sliced inverse regression (SIR) and reproducing kernel Hilbert space (RKHS), a new approach RDSIR (RKHS-based Double SIR) to nonlinear dimension reduction for survival data is proposed. An isometric isomorphism is constructed based on the RKHS property, then the nonlinear function in the RKHS can be represented by the inner product of two elements that reside in the isomorphic feature space. Due to the censorship of survival data, double slicing is used to estimate the weight function to adjust for the censoring bias. The nonlinear sufficient dimension reduction (SDR) subspace is estimated by a generalized eigen-decomposition problem. The asymptotic property of the estimator is established based on the perturbation theory. Finally, the performance of RDSIR is illustrated on simulated and real data. The numerical results show that RDSIR is comparable with the linear SDR method. Most importantly, RDSIR can also effectively extract nonlinearity from survival data.     

Pseudo-perfect and adaptive variants of the Metropolis–Hastings algorithm with an independent candidate density

We describe and examine an imperfect variant of a perfect sampling algorithm based on the Metropolis–Hastings algorithm that appears to perform better than a more traditional approach in terms of speed and accuracy. We then describe and examine an ‘adaptive’ Metropolis–Hastings algorithm which generates and updates a self-target candidate density in such a way that there is no ‘wrong choice’ for an initial candidate density. Simulation examples are provided.     

Testing for a Unit Root in ARIMA Processes

A unit root has important long-run implications for many time series in economics and finance. This paper develops a unit-root test of an ARIMA(p-1, 1, q) with drift null process against a trend-stationary ARMA(p, q) alternative process, where the order of the time series is assumed known through previous statistical testing or relevant theory. This test uses a point-optimal test statistic, but it estimates the null and alternative variance-covariance matrices that are used in the test statistic. Consequently, this test approximates a point-optimal test. Simulations show that its small-sample size is close to the nominal test level for a variety of unit-root processes, that it has a robust power curve against a variety of stationary alternatives, that its combined small-sample size and power properties are highly competitive with previous unit-root tests, and that it is robust to conditional heteroskedasticity. An application to post-Second World War real per capita gross domestic product is provided.     

Dimension reduction transfer function model

The dimension reduction in regression is an efficient method of overcoming the curse of dimensionality in non-parametric regression. Motivated by recent developments for dimension reduction in time series, an empirical extension of central mean subspace in time series to a single-input transfer function model is performed in this paper. Here, we use central mean subspace as a tool of dimension reduction for bivariate time series in the case when the dimension and lag are known and estimate the central mean subspace through the Nadaraya–Watson kernel smoother. Furthermore, we develop a data-dependent approach based on a modified Schwarz Bayesian criterion to estimate the unknown dimension and lag. Finally, we show that the approach in bivariate time series works well using an expository demonstration, two simulations, and a real data analysis such as El Niño and fish Population.     

C434. Local bounds on power of T2 in scale families

In this paper, we have developed a likelihood ratio factorization technique for variable selection for multiple observations model. The asymptotic distribution of the selection criterion is also given. This technique has been applied to a marketing data set for illustration of the technique developed.     

Save: a method for dimension reduction and graphics in regression

Sliced average variance estimation (SAVE) is a method for constructing sufficient summary plots in regressions with many predictors. The summary plots are designed to capture all the information about the response that is available from the predictors, and do not require a model for their construction. They can be particularly helpful for guiding the choice of a first model. Methodological aspects of SAVE are studied in this article.