Tests For Constancy Of Model Parameters Over Time

By Nils Lid Hjort, A. Koning. 2002

89 citations recorded by the source corpus.

Suppose that a sequence of data points follows a distribution of a certain parametric form, but that one or more of the underlying parameters may change over time. This paper addresses various natural questions in such a framework. We construct canonical monitoring processes which under the hypothesis of no change converge in distribution to independent Brownian bridges, and use these to construct natural goodness-of-fit statistics. Weighted versions of these are also studied, and optimal weight functions are derived to give maximum local power against alternatives of interest. We also discuss how our results can be used to pinpoint where and what type of changes have occurred, in the event that initial screening tests indicate that such exist. Our unified large-sample methodology is quite general and applies to all regular parametric models, including regression, Markov chain and time series situations.

Subfields: Finance, Statistics and Probability

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Citations in the corpus

Generalized random forests (2016, methodology): “A Central Limit Theorem for Generalized Random Forests. Given these assumptions, we are now ready to provide an asymptotic characterization of generalzed random forests. In doing so, we note that existing asymptotic analyses of regression forests, including Mentch and Hooker (2016), Scornet, Biau an”
Gaining insight with recursive partitioning of generalized linear models (2013, methodology): “For continuous Z j the supLM statistic (Andrews 1993) is used and for categorical covariates (factors) we employ the χ 2 statistic by Hjort and Koning (2002).”
Generalized Measurement Invariance Tests with Application to Factor Analysis (2011, methodology): “The asymptotic distribution of this test statistic is then easily obtained by applying the same aggregation to the asymptotic process B 0 (Hjort and Koning 2002; Zeileis and Hornik 2007), so that corresponding p values can be derived.”
A Unified Approach to Structural Change Tests Based on ML Scores, F Statistics, and OLS Residuals (2005, methodology): “Common choices for time are the absolute maximum, the mean or the range, and typical functionals comp include the maximum norm (or L∞ norm, denoted as ‖ · ‖∞) or the squared Euclidean norm (or L2 norm, denoted as ‖ · ‖22); see Hjort and Koning (2002) and Zeileis and Hornik (2003) for more examples.”
Generalized M‐fluctuation tests for parameter instability (2007, methodology): “Further discussion of the choice of functionals for fluctuation tests—in particular of different optimal weighting schemes—can be found in Hjort and Koning (2002).”
Model-Based Recursive Partitioning (2008, methodology): “The test statistic is then the weighted sum of the squared L 2 norm of the increments which has an asymptotic χ 2 distribution with k · ( C − 1) degrees of freedom from which the corresponding p value p j can be computed (Hjort and Koning 2002).”