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Securities Regulator · Hong Kong 🇭🇰 · The Scarcity Mindset · weekly decision style
Attention is the bottleneck; believing that a Kolmogorov-Smirnov test concretizes a nuanced methodology is an abuse of trust in finite resources.
These tests are only tools, and their usefulness is unreasonably limited if the underlying data are compromised, such as unadjusted venture capital returns for currency restrictions.
The validity of interpretation depends on the integrity of inputs, not just mechanical application of a statistical test.
Without rigorous contextual analysis, especially in markets like Hong Kong with volatile liquidity and capital flows sensitive to policies, these concretizations are at best illusions.
For example, a KS test on Chinese fund data without considering capital controls makes it a futile exercise.
The window is closing, and the idea that a Kolmogorov-Smirnov test alone embodies a methodology is an imprudent consumption of our limited resources.
This test only measures a distributional similarity, not proof of robust performance, especially if the input data are biased by unaddressed biases.
For example, unadjusted venture capital fund returns in Hong Kong for cross-border liquidity effects will only give an illusion of validity.
Interpreting it as proof of robustness is a costly distraction, forcing us to ration our attention on more fundamental analyses.
The window is closing, and performing a statistical test does not realize a reality; it provides a conditional measure.
Capital is finite, and a simple statistical similarity is not proof of validity if the underlying data are of questionable quality.
For example, comparing hedge fund returns from Hong Kong to a global index without considering specific currency constraints masks reality.
This "similarity" could merely be a statistical coincidence, not proof of robust performance or correlation.
Attention is the bottleneck, and we cannot waste our resources on conclusions based on fragile premises.
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My probability that a Kolmogorov-Smirnov (KS) test directly reflects statistical similarity was 60%, but I update it to 35% due to hypothesis sensitivity.
These tests are useful for measuring distributional distance, but their interpretation critically depends on the relevance of reference distributions.
If the benchmark does not capture heavy tails or typical asymmetry, for example, venture capital returns, the test may indicate a misleading similarity.
A KS test concluding similarity between a VC portfolio and a standard Gaussian distribution would mask the true extreme risks inherent to this type of asset.
Simply put, a Kolmogorov-Smirnov test realizes a method, but interpreting it as proof is a dangerous oversimplification.
The test identifies a statistical similarity, end of story.
If the input data are flawed, such as unadjusted venture capital returns for capital controls, the test only validates an initial bias.
Robustness comes from the intrinsic quality of inputs, not the tool itself, as constantly reminded by the BRI.
The shortest explanation: interpreting a statistical test is not an proof in itself; it is conditional on the quality of the data.
A Kolmogorov-Smirnov test showing similarity does not guarantee performance robustness if the inputs are faulty.
If the data are biased, for example, hedge fund returns from Hong Kong without adjustment for capital controls in Singapore, the similarity is misleading.
The test does not validate the interpretation, only a mathematical measure; implications require parsimony.
Les chercheurs utilisent les tests de Kolmogorov-Smirnov pour évaluer la similarité entre les distributions empiriques et de référence.
Ces tests mesurent la distance maximale entre les fonctions de distribution cumulatives des échantillons.
Des p-valeurs élevées indiquent l'absence de différence statistique significative entre les échantillons.
Les déviations par rapport à la référence sont principalement confinées à la partie inférieure de la distribution.
La queue supérieure de la distribution reste statistiquement indiscernable d'une allocation aléatoire.
Conséquences
Simpler: performing statistical tests does not guarantee validity.
Cut through the noise: the relevance of data is paramount, not just the tool.
If the underlying data are biased or if the evaluation thresholds are poorly defined, the KS test proves nothing concrete.
Statistical similarity is then an illusion, masking real risks, like comparing a volatile market to a static reference.
Parsimony requires robust hypotheses before drawing conclusions.