Jane L. Harvill

Functional coefficient autoregressive models for vector time series

We extend the functional coefficient autoregressive (FCAR) model to the multivariate nonlinear time series framework. We show how to estimate parameters of the model using kernel regression techniques, discuss properties of the estimators, and provide a bootstrap test for determining the presence of nonlinearity in a vector time series. The power of the test is examined through extensive simulations. For illustration, we apply the methods to a series of annual temperatures and tree ring widths. Computational issues are also briefly discussed.

Photonic Monitoring in Real Time of Vascular Endothelial Growth Factor Receptor 2 Gene Expression under Relaxin‐Induced Conditions in a Novel Murine Wound Model

Abstract: Relaxin is known to promote vascular endothelial growth factor (VEGF) expression in reproductive tissue, and successful wound healing depends on good vascularization of wound sites, a process that relaxin may facilitate. Thus, the objective of this study was to evaluate the efficacy of relaxin on the development of vascular tissue at wound sites in a novel VEGF receptor 2‐luc (VEGFR2‐luc) transgenic mouse wound model by monitoring the rate of VEGFR2‐luc‐mediated gene expression using bioluminescence and real‐time imaging. To this end, 12 FVB/N VEGFR2‐luc transgenic male mice were assigned to treatments (six per group): saline alone or relaxin (1 g/6 h/14 days) administered intraperitoneally (i.p.). On day 0, a set of full‐thickness wounds (6‐mm punch) were generated under anesthesia on the dorsal aspect of each mouse. Photonic emissions were recorded (5‐min collection of photons) from wound sites 10 min after the administration of luciferin (150 mg/kg i.p.) on day 0 and on days 1, 2, 4, 7, 9, 11, and 14 postwounding to quantify luciferase activity using an IVIS 100 biophotonic imaging system. Animals were sacrificed (three per group) on day 7 or 14, and wound tissue specimens were recovered for molecular and histologic analyses. Although photonic emission from wound sites increased (P <.001) over time with peak values obtained by day 7, no significant (P >.05) effect of relaxin treatment on VEGFR2‐luc gene expression was noted at wound sites. Whereas measuring relaxins effect on angiogenesis indirectly via the VEGFR2 model was not successful, photonic imaging provides an exciting new tool using alternative models (i.e., VEGF‐luc mouse) to study relaxin‐induced gene expression in normal (i.e., wound healing) or tumorigenic tissues in real time.

Analysis of Integrated and Co-Integrated Time Series With R

• Meta-data: Biological annotation and visualization (four chapters): incorporating gene ontology and annotation; querying Entrez and PubMed; creating hyperlinked reports; visualizing biological data • Statistical analysis for genomic experiments (eight chapters): distance concepts; differential expression; cluster analysis; machine learning concepts and ensemble methods; multiple comparisons; workflow support for Affymetrix analysis • Graphs and networks (four chapters): graph concepts; graph software; case study on graphs and biological data • Case studies (three chapters): linear models for microarray data (the popular limma package); classification, from raw Affymetrix data to annotated reports.

Bispectral-based methods for clustering time series

Distinguishing among linear and nonlinear time series or between nonlinear time series generated by different underlying processes is challenging, as second-order properties are generally insufficient for the task. Different nonlinear processes have different nonconstant bispectral signatures, whereas the bispectral density function of a Gaussian or linear time series is constant. Based on this, we propose a procedure to distinguish among various nonlinear time series and between nonlinear and linear time series through application of a hierarchical clustering algorithm based on distance measures computed from the square modulus of the estimated normalized bispectra. We find that clustering using a distance measure computed by averaging the ratio of normalized bispectral periodogram ordinates over the intersection of the principle domain of each pair of time series provides good performance, subject to trimming of extreme bispectral values prior to taking the ratios. Additionally, we show through simulation studies that the distance procedure performs better than a significance test that we derive. Moreover, it is robust with respect to the choice of smoothing parameter in estimating the bispectrum. As an example, we apply the method to a set of time series of intensities of gamma-ray bursts, some of which exhibit nonlinear behavior; this enables us to identify gamma-ray bursts that may be emanating from the same type of astral event.

Bispectral-Based Goodness-of-Fit Tests of Gaussianity and Linearity of Stationary Time Series

Spectral domain tests for time series linearity typically suffer from a lack of power compared to time domain tests. We present two tests for Gaussianity and linearity of a stationary time series. The tests are two-stage procedures applying goodness-of-fit techniques to the estimated normalized bispectrum. We illustrate the performances of the tests are competitive with time domain tests. The new tests typically outperform Hinichs (1982) bispectral based test, especially when the length of the time series is not large.

Computational challenges in vector functional coefficient autoregressive models

An important research area in statistical computing is found in the literature for vector functional coefficient autoregressive models, a special case of vector nonlinear time series. Methods used are computationally intensive. As a result, analyses and simulations can run into weeks, or even months. Statisticians have been known to base empirical results on a relatively small number of simulation replications, sacrificing precision, accuracy and reliability of results in the interest of time and productivity. The simulations are amenable for parallelization; however, parallel computing technology has not yet been widely used in this specific research area. This paper proposes an approach to the parallelization of statistical simulation codes to address the challenge of long running times, without resorting to extensive code revisions. This approach takes advantage of recent advances in dynamic loop scheduling on workstation clusters to achieve high performance, even with the presence of unpredictable load imbalance factors. Preliminary results of applying this approach in the simulation of normal white noise and threshold autoregressive model obtains efficiencies in the range 95–98% on 8–64 processors.

Testing time series linearity via goodness-of-fit methods

Abstract We consider the problem of testing time series linearity. Existing time domain and spectral domain tests are discussed. A new approach relying on spectral domain properties of a time series under the null hypothesis of linearity is suggested. Under linearity, the normalized bispectral density function Z is a constant. Under the null hypothesis of linearity, properly constructed estimators of 2|Z|2 have a non-central chi-squared distribution with two degrees of freedom and constant non-centrality parameter 2|Z|2. If the null hypothesis is false, the non-centrality parameter is non-constant. This suggests goodness-of-fit tests might be effective in diagnosing non-linearity. Several approaches are introduced.

Using symbolic math to evaluate saddlepoint approximations for the difference of order statistics

We show how symbolic math can be used to calculate saddlepoint approximations for the difference of order statistics from any continuous parent distribution. The difference of order statistics is commonly used as a test statistic in nonparametric tests for constancy of a process. The usefulness of the program is shown by examining the steps required to obtain saddlepoint approximations for a single distribution. A sample session of the a program is presented for the interquartile range of a sample of size 100 from an exponential distribution with mean 2. The results are graphically compared to the true density.

Investigating asymptotic properties of vector nonlinear time series models

Analyses and simulations of vector nonlinear time series typically run into weeks or even months because the methods used are computationally intensive. Statisticians have been known to base empirical results on a relatively small number of simulation replications, sacrificing precision and reliability of results in the interest of time and productivity. The simulations are amenable for parallelization. However, parallel computing technology has not yet been widely used in this specific research area. This paper proposes an approach to the parallelization of statistical simulation codes to address the challenge of long running times. Requiring minimal code revision, this approach takes advantage of recent advances in dynamic loop scheduling to achieve high performance on general-purpose clusters, even with the presence of unpredictable load imbalance factors. Preliminary results of applying this approach in the simulation of normal white noise and threshold autoregressive model obtains efficiencies in the range 95%-98% on 8-64 processors. Furthermore, previously unobserved properties of the statistical procedures for the models are uncovered by the simulation.

StatConcepts: A Visual Tour of Statistical Ideas

StatConcepts: A Visual Tour of Statistical Ideas is a collection of programs written in the language of StataQuest. There are twenty-eight labs providing students a powerful tool for graphical, interactive exploration of statistical concepts. StatConcepts is not intended as a text, but instead as a supplement. The focus of StatConcepts is the correct interpretation and understanding of statistical concepts, terminology, and results, and is not on computation. Although the labs are intended primarily for introductory statistics courses, they can be valuable in courses at all levels.