Andrey Akinshin's Blog

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Andrey is a Ph.D. in computer science. He is involved in a research project at the Sobolev Institute of Mathematics SB RAS related to the mathematical biology and bifurcation theory. Previously, he worked as a postdoctoral research fellow at the Weizmann Institute of Science.

Andrey Akinshin's Blog

5M ago

In this short case study, we explore a few more plots with Gaussian efficiency plots for the trimmed and winsorized mean estimators against the sample median ..read more

Andrey Akinshin's Blog

6M ago

Let us consider xkcd.com/2435: While this strip may look like a joke, it contains an interesting idea for [[research-rldr]]. The classic “simple” estimators typically have poor resistance against low-density regions around the breakdown point. The wider the low-density region, the lower the corresponding statistical efficiency. Any kind of aggregation allows mitigate the error magnitude when we hit a low-density region. Potentially, it can reduce the overall efficiency in high-density regions, but I doubt that we would experience a noticeable efficiency loss in majority of simple cases. The ge ..read more

Andrey Akinshin's Blog

6M ago

In the world of mathematical statistics, there is a constant confrontation between adepts of different paradigms. This is a constant source of confusion for many researchers who struggle to pick out the proper approach to follow. For example, how to choose between the frequentist and Bayesian approaches? Since these paradigms may produce inconsistent results (e.g., see Lindley’s paradox), some choice has to be made. The easiest way to conduct research is to pick a single paradigm and stick to it. The right way to conduct research is to carefully think ..read more

Andrey Akinshin's Blog

6M ago

For a sample $\mathbf{x} = (x_1, x_2, \ldots, x_n)$, the tau measure of location is defined as follows (described in [[wilcox-introduction-to-robust-estimation-and-hypothesis-testing]], Edition 5, Section 3.8.1):
$$ \hat{\mu}_{\tau}(\mathbf{x}) = \left( \sum_{i=1}^n w_i x_i \right) / \left( \sum_{i=1}^n w_i \right), $$
where
$$ w_i(\mathbf{x}) = W_c \left( \frac{x_i - \operatorname{median}(\mathbf{x})}{\operatorname{MAD}(\mathbf{x})} \right), \quad W_c(x) = \left( 1 - (x/c)^2 \right)^2 \cdot I(|x| \leq c), $$
where $I$ is the indicator function, $\operatorname{MAD}$ is the median absolute devi ..read more

Andrey Akinshin's Blog

6M ago

We continue exploring various use cases of the [[lowland-multimodality-detection]]. In this post, we will consider a brief example of using weighted samples ..read more

Andrey Akinshin's Blog

6M ago

We continue exploring various corner cases for the Lowland multimodality detection. In this post, we consider an example that illustrates the usefulness of THDQE ..read more

Andrey Akinshin's Blog

7M ago

When researchers focus on model design, they often worry whether the model is correct or not. I believe that we should accept the fact that all the models are wrong. The world is too complex to be captured by a single model: we are never able to acknowledge all the variables. Therefore, the answer to the question “Is the model correct?” is always “No”. It should not bother us: from the pragmatic perspective, it is irrelevant whether the model is correct or not. If we embrace the model misspecification, we can switch our attention to the question “What is the impact of deviations from the model ..read more

Andrey Akinshin's Blog

7M ago

I have just published a preprint of a paper ‘Quantile-Respectful Density Estimation Based on the Harrell-Davis Quantile Estimator’. It is based on a series of my research notes.
The paper preprint is available on arXiv: arXiv:2404.03835 [stat.ME]. The paper source code is available on GitHub: AndreyAkinshin/paper-qrdehd. You can cite it as follows:
Andrey Akinshin (2024) “Quantile-Respectful Density Estimation Based on the Harrell-Davis Quantile Estimator” arXiv:2404.03835
Abstract:
Traditional density and quantile estimators are often inconsistent with each other. Their simultaneous usage ..read more

Andrey Akinshin's Blog

7M ago

In A better jittering approach for discretization acknowledgment in density estimation, I discussed the jittering approach that improves Quantile-Respectful Density Estimation for discrete distributions and continuous-discrete mixtures. In this post, I will show a brief example of how such an approach improves the accuracy of the Lowland multimodality detection ..read more

Andrey Akinshin's Blog

7M ago

I continue the topic of Quantile-Respectful Density Estimation in the context of Multimodality Detection. In this post, we briefly discuss the handling of the QRDE boundary spikes in order to correctly detect the near-border modes ..read more