Consistency for the negative binomial regression with fixed covariate

Weißbach, Rafael; Radloff, Lucas

doi:10.1007/s00184-019-00750-5

Cited by 12 publications

(7 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…• (C.2): We assume the identifiability condition that X T i (β + δ) = X T i β implies and Radloff (2019) shows the consistency for the NBR with fixed covariates under the assumption that all possible parameters and regressor are in the compact space.…”

Section: Q -Estimation Error Via Compatibility Factormentioning

confidence: 99%

Elastic-net Regularized High-dimensional Negative Binomial Regression: Consistency and Weak Signal Detection

Zhang¹,

Jia²

2022

STAT SINICA

View full text Add to dashboard Cite

We study sparse negative binomial regression (NBR) for count data by showing non-asymptotic merits of the Elastic-net estimator. Two types of oracle inequalities are derived for the Elastic-net estimates of NBR by utilizing Compatibility Factor or Stabil Condition. The second-type oracle inequality is for random design which can be extended to many 1 + 2 regularized M-estimation with the corresponding empirical process having stochastic Lipschitz properties. To show some high probability events, we derive concentration inequality for suprema empirical processes for the weighted sum of negative binomial variables. For applications, we show the sign consistency provided that the non-zero components in sparse true vector are larger than a proper choice of the weakest signal detection threshold; and the second application is that we show the grouping effect inequality with high probability; thirdly, under some assumptions of design matrix, we can recover the true variable set with high probability if the weakest signal detection threshold is large than the turning parameter up to a known constant; at last, we briefly discuss the de-biased Elastic-net estimator and numerical studies are given to support the proposal.

show abstract

Section: Q -Estimation Error Via Compatibility Factormentioning

confidence: 99%

Elastic-net Regularized High-dimensional Negative Binomial Regression: Consistency and Weak Signal Detection

Zhang¹,

Jia²

2022

STAT SINICA

View full text Add to dashboard Cite

show abstract

“…without being able to exploit cross-sectional independence and relies on the same result from the 1960s from Robert Jennrich. So do Weißbach and Radloff (2020) who again use the cross-sectional independence in a panel model.…”

Section: Discussionmentioning

confidence: 99%

A consistent nonparametric test of the effect of dementia duration on mortality

Radloff,

Weissbach,

Reinke

et al. 2021

Preprint

View full text Add to dashboard Cite

A continuous-time multi-state history is semi-Markovian, if an intensity to migrate from one state into another, depends on the duration in the first state.Such duration can be formalised as covariate, entering the intensity process of the transition counts. We derive the integrated intensity process, prove its predictability and the martingale property of the residual. In particular, we verify the usual conditions for the respective filtration. As a consequence, according to Nielsen and Linton (1995), a kernel estimator of the transition intensity, including the duration dependence, converges point-wise at a slow rate, compared to the Markovian kernel estimator, i.e when ignoring dependence. By using the rate discrepancy, we follow Gozalo (1993) and show that the (properly scaled) maximal difference of the two kernel estimators on a random grid of points is asymptotically χ 2 1 -distributed. As a data example, for a sample of 130,000 German women observed over a period of nine years, we model the mortality after dementia onset, potentially dependent on the disease duration. As usual, the models under both hypotheses need to be enlarged to allow for independent right-censoring. We find a significant effect of dementia duration, nearly independent of the bandwidth.

show abstract

“…The usual formula of introductory statistics that the density for a collection of independent persons is the product of the persons' densities relies on the equal (and parameter-independent) dominating measure (usually being Lebesgues). Unconditionally, such fixed covariate regression could be analysed as Weißbach and Radloff (2020). To achieve equal dominating measures for all persons, we follow Examples IV.1.7 and VI.1.4 of Andersen et al (1993) in using a random U .…”

Section: Discussionmentioning

confidence: 99%

Left-Truncated Health Insurance Claims Data: Theoretical Review and Empirical Application

Rafael¹,

Dörre²,

Wied³

et al. 2021

Preprint

View full text Add to dashboard Cite

We observe a quarter million people over a period of nine years and are interested in the effect of a stroke on the probability of dementia onset. Randomly lefttruncated has a person been that was already deceased before the period. The ages at a stroke event or dementia onset are conditionally fixed right-censored, when either event may still occur, but after the period. We incorporate death and model the history of the three events by a homogeneous Markov process.The compensator for the respective counting processes is derived and Jacod's formula yields the likelihood contribution, conditional on observation. An Appendix is devoted to the role of filtrations in deriving the likelihood, for the simplification of merged non-dead states. Asymptotic normality of the estimated intensities is derived by martingale theory, relative to the size of the sample including the truncated persons. The data of a German health insurance reveals that after a stroke, the intensity of dementia onset is increased from 0.02 to 0.07, for Germans born in the first half on the 20 th century. The intensity difference has a 95%-confidence interval of [0.048, 0.051] and the difference halves when we extent to an age-inhomogeneous model due to Simpson's paradox.

show abstract

Consistency for the negative binomial regression with fixed covariate

Cited by 12 publications

References 17 publications

Elastic-net Regularized High-dimensional Negative Binomial Regression: Consistency and Weak Signal Detection

Elastic-net Regularized High-dimensional Negative Binomial Regression: Consistency and Weak Signal Detection

A consistent nonparametric test of the effect of dementia duration on mortality

Left-Truncated Health Insurance Claims Data: Theoretical Review and Empirical Application

Contact Info

Product

Resources

About