Fabian Dunker, Konstantin Eckle, Katharina Proksch, Johannes Schmidt-Hieber
arXiv 4 Apr 2017 · Statistics — Methodology · publishedElectronic Journal of Statistics (2019) · 15 citations (OpenAlex)
arXiv:1704.01066 · PDF · DOI · OpenAlex · Extracted main text
The random coefficients model is an extension of the linear regression model that allows for unobserved heterogeneity in the population by modeling the regression coefficients as random variables. Given data from this model, the statistical challenge is to recover information about the joint density of the random coefficients which is a multivariate and ill-posed problem. Because of the curse of dimensionality and the ill-posedness, pointwise nonparametric estimation of the joint density is difficult and suffers from slow convergence rates. Larger features, such as an increase of the density along some direction or a well-accentuated mode can, however, be much easier detected from data by means of statistical tests. In this article, we follow this strategy and construct tests and confidence statements for qualitative features of the joint density, such as increases, decreases and modes. We propose a multiple testing approach based on aggregating single tests which are designed to extract shape information on fixed scales and directions. Using recent tools for Gaussian approximations of multivariate empirical processes, we derive expressions for the critical value. We apply our method to simulated and real data.
appendix boundary found by appendix_command · 49% of the source is main text. Read the extracted text to check this.
The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Helgason, S (2011) Integral geometry and Radon transforms | 0.811 | 4 | 2 | 100% |
| 2 | Hoderlein, S., Klemelä, J., and Mammen, E (2010) Analyzing the random coefficient model nonparametrically | 0.811 | 4 | 2 | 100% |
| 3 | Eckle, K., Bissantz, N., and Dette, H (2017) Multiscale inference for multivariate deconvolution self | 0.737 | 4 | 4 | 50% |
| 4 | Adler, R. J. and Taylor, J. E (2007) Random fields and geometry | 0.644 | 3 | 2 | 67% |
| 5 | Beran, R., Feuerverger, A., and Hall, P (1996) On nonparametric estimation of intercept and slope distributions in random coefficient regression | 0.644 | 2 | 2 | 100% |
| 6 | Breunig, C. and Hoderlein, S (2018) Specification Testing in Random Coefficient Models | 0.644 | 2 | 2 | 100% |
| 7 | Hoderlein, S., Holzmann, H., and Meister, A (2015) The triangular model with random coefficients | 0.644 | 2 | 2 | 100% |
| 8 | Schmidt-Hieber, J., Munk, A., and Dümbgen, L (2013) Multiscale methods for shape constraints in deconvolution: confidence statements for qualitative features self | 0.644 | 2 | 2 | 100% |
| 9 | Dümbgen, L. and Spokoiny, V. G (2001) Multiscale testing of qualitative hypotheses | 0.511 | 5 | 2 | 20% |
| 10 | Chernozhukov, V., Chetverikov, D., and Kato, K (2017) Central limit theorems and bootstrap in high dimensions | 0.511 | 2 | 2 | 50% |
Showing the top 10 of 44 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | A sliced Wasserstein and diffusion approach to random coefficient models | 0.644 | 2 | 2 |