Page 151 - Contributed Paper Session (CPS) - Volume 3

CPS1973 Matúš M. et al.
• the robustness property of the conditional quantile estimation is proved
with respect to outlying observations and heavy tailed distributions (for
instance, Cauchy distribution);
Due to the strict page limitation all theoretical assumptions, technical details
and complete proofs can be found in Maciak and Mizera (2016), Ciuperca and
Maciak (2018) and Maciak and Mizera (2019).

4. Discussion and Conclusion
Similarly as standard LASSO approaches the proposed methodology does
not yield the oracle properties. Indeed, different values of the regularization
parameter > 0 in (3) are needed to achieve the consistency of the

changepoint detection or the consistency of the model estimation. From the
empirical point of view, various techniques can be used to improve the finite
sample properties especially for small sample sizes (for instance, de-biasing,
relaxed LASSO, or two-stage estimation). However, the proposed
methodology can effectively deal with changepoint detection and estimation
problem within nonparametric regression setups and it is especially suitable
for situations where no prior knowledge on any changepoint structure is
known in advance. An extensive Monte Carlo simulation study is proposed to
closely investigate finite sample properties and various model selection
options. The overall suitability of the proposed regularized changepoint
detection in nonparametric models is also illustrated on some practical
examples.

References
1. Antoch, J., Gregoire, G., and Huˇskov´a M. (2006), “Test for Continuity of
Regression Function.” Journal for Statistical Planning and Inference 137,
753 – 777.
2. Antoch, J. and Jaruˇskov´a, D. (2013), “Testing for Multiple Change-
points.” Journal of Computational Statistics 28, 2161 – 2183.
3. Aue, A., Hotv´ath, L., Huˇskov´a M. and Kokoszka, P. (2008), “Testing for
Changes in Polynomial Regression.” Bernoulli, Volume 13, No.3, 637 –
660.
4. Ciuperca, G. and Maciak, M. (2018), “Change-point detection in a linear
model by adaptive fused quantile method.” Scandinavian Journal of
Statistic, (submitted).
5. Cs¨org¨o, M., and Hotv´ath, L. (1997), “Limit Theorems in Change-Point
Analysis.” Wiley Series in Probability & Statistics, Chichester, England.
6. Efron, B., Hastie, T., Johnstone, I. and Tibshirani, R. (2004), “Least Angle
Regression.” The Annals of Statistics, 32, No.2, 407 – 499.

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