My current research is devoted to developing statistical methods and theory towards understanding the interaction between a changing climate and cryospheric processes. A cryospheric process is one that involves permafrost, seasonally frozen soil, snow, ice, or any physical entity that freezes and thaws. As of yet, most data driven trend estimates on cryoshperic processes come from simple linear trend estimation, ignoring statistical correlation of time series, changepoint effects, and the zero modified support set issue-snow depths cannot be negative.
One of my current research projects introduces proper statistical modeling expertise to the snow depth trends community. This is not an easy task, as some of the most cited work essentially applied simple linear regression on yearly snow depth averages to compute trends. The problem is statistically much more problematic than current methods are equipped to handle. Note than one can replace snow depths with Snow Water Equivalents (SWE’s) if one has such data without having to change the statistical methodologies developed.
A LINEAR REGRESSION MODEL WITH PERSISTENT LEVEL SHIFTS: AN ALTERNATIVE TO INFILL ASYMPTOTICS
Abstract: A changepoint in a time series is a time of change in the marginal distribution, autocovariance, or any other distributional structure of the series. Examples include mean level shifts and volatility (variance) changes. Climate data, for example, is replete with mean shift changepoints, occurring whenever a recording instrument is changed or the observing station is moved. Here, we consider the problem of incorporating known changepoint times into a regression model framework. Specifically, we establish consistency and asymptotic normality of ordinary least squares regression estimators that account for an arbitrary number of mean shifts in the record. In a sense, this provides an alternative to the customary infill asymptotics for regression models that assume an asymptotic infinity of data observations between all changepoint times.
APPLICATION OF MULTIVARIATE STORAGE MODEL TO QUANTIFY TRENDS IN SEASONALLY FROZEN SOIL
Abstract: This article presents a study of the ground thermal regime recorded at 11 stations in the North Dakota Agricultural Network. Particular focus is placed on detecting trends in the annual ground freeze process portion of the ground thermal regime’s daily temperature signature. A multivariate storage model fromqueuing theory is _t to quantity of estimated daily depths of frozen soil. Statistical inference on a trend parameter is obtained by minimizing a weighted sum of squares of a sequence of daily one-stepahead predictions. Standard errors for the trend estimates are presented. It is shown that the daily quantity of frozen ground experienced at these 11 sites exhibited a negative trend over the observation period
TUNING EXTREME NEXRAD AND CMORPH PRECIPITATION ESTIMATES
Abstract: High-resolution satellite precipitation estimates, such as the Climate Prediction Center morphing technique (CMORPH), provide alternative sources of precipitation data for hydrological applications, especially in regions where adequate ground-based instruments are unavailable. These estimates are, however, subject to large errors, especially at times of heavy precipitation. This paper presents a method to distributionally convert a set of CMORPH estimates into ground-based Next Generation Weather Radar (NEXRAD) estimates. As our concern lies with floods and extreme precipitation events, a peaks-over-threshold extreme value approach is adopted that fits a generalized Pareto distribution to the large precipitation estimates. A quantile matching transformation is then used to convert CMORPH values into NEXRAD values. The methods are applied in the analysis of 6 years of precipitation observations from 625 pixels centered around eastern Oklahoma.
TESTING FOR SEASONAL MEANS IN TIME SERIES DATA
Abstract: The statistician often needs to test whether or not a time series has a seasonal first moment. The problem often arises in environmental series, where most time-ordered data display some type of periodic structure. This paper reviews the problem, proposing new statistics in both the time and frequency domains. Our new time domain statistic has an analysis of variance form that is based on the one-step-ahead prediction errors of the series. This statistic inherits the classic traits of the F -distribution arising in one-way analysis of variance tests, is easy to use, and is asymptotically equivalent to the likelihood ratio test. The statistics asymptotic distribution is quantified when time series parameters are estimated. In the frequency domain, a statistic modifying Fisher’s classical test for a sinusoidal mean superimposed on independent and identically distributed Gaussian noise is devised. The performance and comparison of these statistics are studied via simulation. Implementation of the methods merely requires sample means, autocovariances, and periodograms of the series. Application to a data set of monthly temperatures from Tuscaloosa, Alabama, is given.
TIME SERIES REGRESSION WITH PERSISTENT LEVEL SHIFTS
Abstract: A changepoint in a time series is a time in which any change in the distributional form (marginal or joint) of the series occurs. This includes changes in mean or covariance structure of the time series. Mean level shift changepoints have been shown to dramatically influence linear trend estimates obtained from a simple linear regression model. This study provides an asymptotic analysis of a time series regression model experiencing an increasing number of mean level shifts at known times. It is shown that one may consistently estimate any finite number of unknown parameters in a time series polynomial regression, so long as two or more consecutive observations without a changepoint occurs infinity often in the limit.
A STORAGE MODEL APPROACH TO THE ASSESSMENT OF SNOW DEPTH TRENDS
Abstract: This paper introduces a stochastic storage model capable of assessing trends in daily snow depth series. The model allows for seasonal features, which permits the analysis of daily data. Breakpoint times, which occur when the observing station changes location or instrumentation, are shown to greatly influence estimated trend margins and are accounted for in this analysis. The model is fitted by numerically minimizing a sum of squares of daily prediction errors. Standard errors for the model parameters, useful in making trend inferences, are presented. The methods are illustrated in the analysis of a century of daily snow depth observations from Napoleon, North Dakota. The results here show that snow depths are significantly declining at Napoleon, with spring ablation occurring earlier, and that breakpoint features are very influential in deriving realistic trend estimates.
Statistics students at Mississippi State University have many different needs. The most difficult task in meeting these needs is learning to communicate with the students effectively. For example, our statistics group within the Depart- ment of Mathematics and Statistics teaches mainly graduate students, most of whom are majoring in disciplines outside of Mathematics and Statistics. The job here is to teach the art and practice of statistics. These students need a practical understanding of statistical methodology likely to be of use in their research studies. This is the most difficult task we have to do, and it requires nothing less than experience. This is an area that I continue to gain experience.
In order to teach statistics to Statistics majors, we need to construct a balanced education. They need to be able to perform basic data analysis (just as students of other majors), but they need a heavier emphasis on theoretical considerations as well. It is important to strive to find problems involving real data (which is not always possible), and to develop the technical machinery yielding the relevant statistical techniques.
- Data Analysis
- Multivariate Statistical Methods
- Applied Probability
- Introduction to Probability
- Statistical Methods
- Statistical Packages
- Time Series
- Linear Models I
- Advanced Stochastic Processes
- Computational Statistics
Jia (Amy) Wang: “Modeling Patient Arrival Times as a Doubly Stochastic Process,” April 2012
Yan Wang: “Application of Multivariate Storage Model to Quantify Trends in Seasonally Frozen Soil,” April 2014
Li He: “Testing Seasonal Means in Time Series Data,” April 2015
Leigh Ellen Barefield: “Detecting Multiple Changepoints via Genetic Al- gorithm,” December 2015
Carol Sui: “Quantile Regression and its Application,” April 2016
Jei Zhu: “Forecasting Stationary Time Series,” July 2016
Yang Xu (jointly advised with Dr. Prakash Patil): “On non-parametric confidence intervals for density and hazard rate functions & trends in daily snow depths in the United States and Canada,” Expected graduation: December 2016.
Department of Mathematics & Statistics
Mississippi State University