Stat 505 - Environmental Statistics - References for part 3
Analysis of data with trends
General Books / Book Chapters
Gilbert, R.O. 1987. Statistical Methods for Environmental Pollution Monitoring. Van Nostrand
Reinhold.
My favorite introductory book, but a bit out of date now. Clearly written. Focuses on useful
techniques and avoids being an encyclopedia. Chapters 16 and 17 describe trend analysis
and trend analysis with seasonal data.
Helsel, D.R. 2012. Statistics for Censored Environmental Data Using Minitab and R. Wiley.
Applied, emphasizing how to carry out various methods, and comparison between methods.
More details on computations than Helsel and Hirsch. Chapter 12 describes methods for
Regression with < dl values.
Helsel, D.R. and Hirsch, R.M. 1992. Statistical Methods in Water Resources. Elsevier.
Now out of print. Applied, written for hydrologists. Chapter 12 covers trend analysis. Good
basic intro. On line at: http://pubs.usgs.gov/twri/twri4a3/
Millard, S.M. and Neerchal, N. 2001. Environmental Statistics with S-plus. CRC/Chapman
and Hall
Text with Splus code for diverse methods in environmental statistics. About same technical
level as Helsel. Chapters 9 and 11 deals with linear models (regression) and time series
analysis.
Overview of methods
Hirsch, R.M., Alexander, R.B. and Smith, R.A. 1991. Selection of methods for detection and
estimation of trends in water quality. Water Resources Research 27:803-813.
McLeod, A.I. Hipel, K.W. and Bodo, B.A. 1991. Trend analysis methodlogy for water quality
time series. Econometrics 2:169-200
Effects of/adjustment for autocorrelation
The theory is discussed in various places, especially Econometrics texts. I relied on section 6.3
(pp 250-257) in
Theil, H. 1971. Principles of Econometrics. Wiley.
Lettenmaier, D.P. 1976. Detection of trends in water quality data from records with dependent
observations. Water Resources Research 12:1037-1046.
An effective sample size approach to adjusting for autocorrelation. We didn’t talk about the
details here.
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Regression with < dl values
Akritas, M. G., Russell, T.F., and Patil, G.P. 1994. Statistical analysis of censored environmental data. pp 221-242 In Patil, G.P. and Rao, C.R. (eds) Handbook of Statistics 12,
Environmental Statistics. North-Holland, New York.
Emphasizes statistical theory underlying various estimation and test methods. Last part
describes Theil-Sen regression
Adjustment for covariates
Alley, W.M. 1988. Using exogenous variables in testing for monotonic trends in hydrological
time series. Water Resources Research 24:1955-1961.
Proposes an adjustment to Kendall’s tau to make it more like a partial regression coefficient
and improve power when adjusting for a covariate.
Smith, E.P. and Rose, K.A. 1991. Trend detection in the presence of covariates: stagewise versus
multiple regression. Environmetrics 2:153-168.
Lo(w)ess smoothing
Cleveland, R.B., Cleveland, W.S., McRae, J.E, and Termpenning, I. 1990. STL: A seasonaltrend decomposition procedure based on loess. Journal of Official Statistics 6:3-73 (with
discussion)
Method using loess to decompose a sequence into trend, seasonal and remainder components.
Cleveland, W.S. and Devlin, S.J. 1988. Locally-weighted regression: an approach to regression
analysis by local fitting. J. Am. Stat. Assoc. 83:596-610.
Original paper describing loess / lowess regression
Cleveland, W.S., Grosse, E. and Shyu, W.M. 1992. Local regression models. Chapter 8 of
Statistical Models in S, Chambers, J.M. and Hastie, T.J. (eds.) Wadsworth & Brooks/Cole.
Less technical description of the lowess/loess algorithm with examples using S code (should
be equiv. to R code).
Nonparametric regression
Hatfield, J.S., Gould, W.R. IV, Hoover, B.A, Fuller, M.R., and Lindquist, E.L. 1996. Detecting trends in raptor counts: power and Type I error rates of various statistical tests.
Wildlife Society Bulletin 24:505-515
One (of many possible) examples of a simulation comparion of ols regression and nonparametric tests for trend.
Helsel, D.R. and Hirsch, R.M. 1988. Discussion: Applicability of the t-test for detecting trends
in water quality variables. Water Resources Bulletin 24:201-204.
Half of a discussion (with reference back the original paper) on parametric vs. nonparametric
methods
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Hess, A., Iyer, H., and Malm, W. 2001. Linear trend analysis: a comparison of methods.
Atmospheric Environment 35:5211-5222.
An especially complete set of methods in a simulation assessment of type I error rate and power.
Hirsch, R.M. and Slack, J.R. 1984. A nonparametric trend test for seasonal data with serial
dependence. Water Resources Research 20:727-732.
Modification of seasonal Kendall’s tau to account for correlation between seasons within
year.
Hirsch, R.M., Slack, J.R., and Smith, R.A. 1982. Techniques of trend analysis for monthly water
quality data. Water Reources Research 18:107-121.
Original paper on the seasonal Kendall’s tau approach.
Kendall, M.G. 1938. A new measure of rank correlation. Biometrika 30:81-93
Original paper on Kendall’s tau as a test of indepedendence in a bivariate distribution.
Mann, H.B. 1945. Nonparametric tests against trend. Econometrika 13:245-259.
Extension of Kendall’s tau correlation to a test for trend. Theoretical properties (moments
and asymptotic distribution, bias and consistency).
vanBelle, G. and Hughes, J.P. 1984. Nonparametric tests for trend in water quality. Water
Resources Research 20:127-136.
Extension of seasonal Kendall’s tau to data from multiple stations.
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