*Andrew J. Connolly, Jacob T. VanderPlas, Alexander Gray, Andrew J. Connolly, Jacob T. VanderPlas, and Alexander Gray*

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691151687
- eISBN:
- 9781400848911
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691151687.003.0008
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

Regression is a special case of the general model fitting and selection procedures discussed in chapters 4 and 5. It can be defined as the relation between a dependent variable, y, and a set of ...
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Regression is a special case of the general model fitting and selection procedures discussed in chapters 4 and 5. It can be defined as the relation between a dependent variable, y, and a set of independent variables, x, that describes the expectation value of y given x: E [y¦x]. The purpose of obtaining a “best-fit” model ranges from scientific interest in the values of model parameters (e.g., the properties of dark energy, or of a newly discovered planet) to the predictive power of the resulting model (e.g., predicting solar activity). This chapter starts with a general formulation for regression, list various simplified cases, and then discusses methods that can be used to address them, such as regression for linear models, kernel regression, robust regression and nonlinear regression.Less

Regression is a special case of the general model fitting and selection procedures discussed in chapters 4 and 5. It can be defined as the relation between a dependent variable, *y*, and a set of independent variables, *x*, that describes the expectation value of *y* given *x*: *E* [*y*¦*x*]. The purpose of obtaining a “best-fit” model ranges from scientific interest in the values of model parameters (e.g., the properties of dark energy, or of a newly discovered planet) to the predictive power of the resulting model (e.g., predicting solar activity). This chapter starts with a general formulation for regression, list various simplified cases, and then discusses methods that can be used to address them, such as regression for linear models, kernel regression, robust regression and nonlinear regression.

*Timo Teräsvirta, Dag Tjøstheim, and W. J. Granger*

- Published in print:
- 2010
- Published Online:
- May 2011
- ISBN:
- 9780199587148
- eISBN:
- 9780191595387
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199587148.003.0011
- Subject:
- Economics and Finance, Econometrics

Long memory, unit root models and cointegration are important in linear modelling of nonstationary processes, not the least in econometrics. Recently, nonlinear generalizations of these concepts have ...
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Long memory, unit root models and cointegration are important in linear modelling of nonstationary processes, not the least in econometrics. Recently, nonlinear generalizations of these concepts have been attempted. The framework is mathematically demanding, requiring tools that can handle both nonstationarity and nonlinearity. Two such tools are local times and null recurrent Markov chains. These are reviewed in parametric and non‐parametric cases.Less

Long memory, unit root models and cointegration are important in linear modelling of nonstationary processes, not the least in econometrics. Recently, nonlinear generalizations of these concepts have been attempted. The framework is mathematically demanding, requiring tools that can handle both nonstationarity and nonlinearity. Two such tools are local times and null recurrent Markov chains. These are reviewed in parametric and non‐parametric cases.

*James B. Elsner and Thomas H. Jagger*

- Published in print:
- 2013
- Published Online:
- November 2020
- ISBN:
- 9780199827633
- eISBN:
- 9780197563199
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199827633.003.0011
- Subject:
- Earth Sciences and Geography, Meteorology and Climatology

Here in Part II, we focus on statistical models for understanding and predicting hurricane climate. This chapter shows you how to model hurricane occurrence. This is done using the annual count of ...
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Here in Part II, we focus on statistical models for understanding and predicting hurricane climate. This chapter shows you how to model hurricane occurrence. This is done using the annual count of hurricanes making landfall in the United States. We also consider the occurrence of hurricanes across the basin and by origin. We begin with exploratory analysis and then show you how to model counts with Poisson regression. Issues of model fit, interpretation, and prediction are considered in turn. The topic of how to assess forecast skill is examined including how to perform cross-validation. Alternatives to the Poisson regression model are considered. Logistic regression and receiver operating characteristics (ROCS) are also covered. You use the data set US.txt which contains a list of tropical cyclone counts by year (see Chapter 2). The counts indicate the number of hurricanes hitting in the United States (excluding Hawaii). Input the data, save them as a data frame object, and print out the first six lines by typing . . . > H = read.table("US.txt", header=TRUE) > head(H) . . . The columns include year Year, number of U.S. hurricanes All, number of major U.S. hurricanes MUS, number of U.S. Gulf coast hurricanes G, number of Florida hurricanes FL, and number of East coast hurricanes E. Save the total number of years in the record as n and the average number hurricanes per year as rate. . . . > n = length(H$Year); rate = mean(H$All) > n; rate [1] 160 [1] 1.69 . . . The average number of U.S. hurricanes is 1.69 per year over these 160 years. First plot a time series and a distribution of the annual counts. Together, the two plots provide a nice summary of the information in your data relevant to any modeling effort. . . . > par(las=1) > layout(matrix(c(1, 2), 1, 2, byrow=TRUE), + widths=c(3/5, 2/5)) > plot(H$Year, H$All, type="h", xlab="Year", + ylab="Hurricane Count") > grid() > mtext("a", side=3, line=1, adj=0, cex=1.1) > barplot(table(H$All), xlab="Hurricane Count", + ylab="Number of Years", main="") > mtext("b", side=3, line=1, adj=0, cex=1.1) . . . The layout function divides the plot page into rows and columns as specified in the matrix function (first argument).
Less

Here in Part II, we focus on statistical models for understanding and predicting hurricane climate. This chapter shows you how to model hurricane occurrence. This is done using the annual count of hurricanes making landfall in the United States. We also consider the occurrence of hurricanes across the basin and by origin. We begin with exploratory analysis and then show you how to model counts with Poisson regression. Issues of model fit, interpretation, and prediction are considered in turn. The topic of how to assess forecast skill is examined including how to perform cross-validation. Alternatives to the Poisson regression model are considered. Logistic regression and receiver operating characteristics (ROCS) are also covered. You use the data set US.txt which contains a list of tropical cyclone counts by year (see Chapter 2). The counts indicate the number of hurricanes hitting in the United States (excluding Hawaii). Input the data, save them as a data frame object, and print out the first six lines by typing . . . > H = read.table("US.txt", header=TRUE) > head(H) . . . The columns include year Year, number of U.S. hurricanes All, number of major U.S. hurricanes MUS, number of U.S. Gulf coast hurricanes G, number of Florida hurricanes FL, and number of East coast hurricanes E. Save the total number of years in the record as n and the average number hurricanes per year as rate. . . . > n = length(H$Year); rate = mean(H$All) > n; rate [1] 160 [1] 1.69 . . . The average number of U.S. hurricanes is 1.69 per year over these 160 years. First plot a time series and a distribution of the annual counts. Together, the two plots provide a nice summary of the information in your data relevant to any modeling effort. . . . > par(las=1) > layout(matrix(c(1, 2), 1, 2, byrow=TRUE), + widths=c(3/5, 2/5)) > plot(H$Year, H$All, type="h", xlab="Year", + ylab="Hurricane Count") > grid() > mtext("a", side=3, line=1, adj=0, cex=1.1) > barplot(table(H$All), xlab="Hurricane Count", + ylab="Number of Years", main="") > mtext("b", side=3, line=1, adj=0, cex=1.1) . . . The layout function divides the plot page into rows and columns as specified in the matrix function (first argument).