Syllabus
Simple regression models, assumptions, least square regression parameter estimates. Residual analysis, heteroscedasticity. Analysis of variance, coefficient of determination, goodness-of-fit measures, tests and confidence intervals for the regression parameters, confidence bounds for the mean of the response variable, confidence intervals for the response variable. Outliers, trimmed regression. Multiple regression, multiple correlation coefficient, partial correlation. Verification of the linear regression model assumptions, multicolinearity, overfitting, stepwise regression. Nonlinear regression.
Principal-component analysis (EOF) analysis, covariance and correlation matrix, eigenvalues, eigenvectors, eigenvectors elements, principal components, principal-component elements, rotation of the eigenvectors, application of PCA to meteorological fields. Cluster analysis, application in meteorology.
Stochastic processes, basic definitions, autocovariance, autocorrelation and cross-correlation function, stationary process, ergodicity. Spectral analysis, periodogram, white noise.
Time series, homogeneity tests, tests for randomness, smoothing (robust locally weighted regression), auto-regressive processes, the Yule-Walker equations, moving average processes.
Annotation
Introduction to techniques of statistical analysis of multivariate data and time series (multiple linear regression, principal component analysis, canonical correlation analysis, discriminant analysis, cluster analysis; Fourier and wavelet transforms, Markov chains, autoregressive models)