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Name of QuantLet: TVRPchangeSQR | ||
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Published in : 'Unpublished; Theoretically description of Time Varying | ||
Penalization method.' | ||
Published in : submitted to N/A | ||
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Description : 'Performs LASSO regression in a moving window by using BIC criterion to | ||
choose penalty parameter (lambda). The simulated data contains a break | ||
point after which the cardinality of active set q changes. Plots time series | ||
of lambda in LASSO regression. Furthermore, the cardinality of the active | ||
set q, the L2-norm of the residuals, the L1-norm of the parameter beta | ||
and the condition number of the squared design matrix [t(X)X] are plotted. | ||
All of the plots contain results from a number of simulations and the | ||
average over all of them.' | ||
Description : 'Performs the Lasso regression with two distinct algorithms. The first one uses moving window method and the Bayesian information criterion (BIC) or the generalized cross-validation (GCV) to calibrate the penalty parameter (lambda), and the second is called the real-time adaptive penalization (RAP). The simulated data contains a break point, after which a combination of changes of the variance of the error term, the correlation structure of the design matrix | ||
and/or the number of active parameters, q, in the model is simulated. The code plots the relative changes of the Lasso parameter in dependence on the relative changes in the specific model parameters and a time series of the average lambda in the Lasso regression. The average values are taken over the specified number of simulations.' | ||
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Keywords : 'LASSO, lasso shrinkage, L1-norm penalty, change point, bic, | ||
euclidean-norm, regression, simulation, plot, visualization, | ||
historical moving window, time-series, estimation, L1-norm, error, beta, | ||
multi-dimensional, multivariate normal' | ||
Keywords : 'Lasso, shrinkage, L1-norm penalty, change point, bic, gcv, adaptive penalization, regression, simulation, plot, moving window, time-series, beta, linear model, heatmap’ | ||
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See also : 'TVPvariance, TVPdesign, MVAgrouplasso, MVAlassocontour, MVAlassoregress, | ||
SMSlassocar, SMSlassoridge, quantilelasso' | ||
See also : 'TVRPchangeB, TVRPchangefmri, TVRPfrm, XFGTVP_BetaChange, XFGTVP_FRM, XFGTVP_LambdaSim, MVAgrouplasso, MVAlassocontour, MVAlassoregress, SMSlassocar, SMSlassoridge, quantilelasso' | ||
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Author : Lenka Zbonakova | ||
Author : Lenka Zboňáková | ||
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Submitted: | ||
Submitted: 9 October 2018 by Lenka Zboňáková | ||
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Input: | ||
- n.obs : Number of observations to simulate | ||
- n.param : Number of parameters to simulate | ||
- n.sim : Number of simulations | ||
- w : Size of each moving window | ||
- seed1 : Seed to simulate design matrix X | ||
- seed2 : Seed to simulate error terms | ||
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Example: | ||
- Lambda | ||
- Cardinality of q | ||
- L2-norm of the residuals | ||
- L1-norm of the beta | ||
- Condition number of the squared design matrix [t(X)X] | ||
- n.obs: Number of observations to simulate | ||
- n.param: Number of parameters to simulate | ||
- n.sim: Number of scenarios | ||
- w: Size of the moving window | ||
- w.rap: Burn-in period for the RAP algorithm | ||
- seed1: Seed to simulate the design matrix X | ||
- seed2: Seed to simulate the error term | ||
- sd.start: Standard deviation of error term before the change point | ||
- sd.end: Standard deviation of error term after the change point | ||
- q.start: Number of nonzero parameters before the change point | ||
- q.end: Number of nonzero parameters after the change point | ||
- r.start: Correlation coefficient for design before the change point | ||
- r.end: Correlation coefficient for design after the change point | ||
- m.type: Type of the method to calibrate lambda (“BIC” or “GCV”) | ||
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