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Maximum simulated likelihood: don't stop believin'?

Schrey Christopher

Annals of Computer Science and Information Systems

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2021

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Vol. 26

175--180

EN

Unobserved heterogeneity may complicate model estimation in econometrics. To integrate out the effect of unobserved heterogeneity via maximum simulated likelihood (MSL) estimation, assumptions regarding the underlying distribution need to be made. Researchers seldomly discuss these assumptions. This raises the question, to what extent estimation results in the MSL-context are robust to potential distributional mismatch. This work-in-progress derives the research question from the literature. A simulation study is conducted that underpins the relevance of this matter, where results imply that mismatch may introduce significant bias. Intended future work to properly address and answer this question is defined and discussed.

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Revisiting the optimal probability estimator from small samples for data mining

Cestnik Bojan

International Journal of Applied Mathematics and Computer Science

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2019

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Vol. 29, no. 4

783--796

EN

Estimation of probabilities from empirical data samples has drawn close attention in the scientific community and has been identified as a crucial phase in many machine learning and knowledge discovery research projects and applications. In addition to trivial and straightforward estimation with relative frequency, more elaborated probability estimation methods from small samples were proposed and applied in practice (e.g., Laplace’s rule, the m-estimate). Piegat and Landowski (2012) proposed a novel probability estimation method from small samples Eph√2 that is optimal according to the mean absolute error of the estimation result. In this paper we show that, even though the articulation of Piegat’s formula seems different, it is in fact a special case of the m-estimate, where pa = 1/2 and m = √2. In the context of an experimental framework, we present an in-depth analysis of several probability estimation methods with respect to their mean absolute errors and demonstrate their potential advantages and disadvantages. We extend the analysis from single instance samples to samples with a moderate number of instances. We define small samples for the purpose of estimating probabilities as samples containing either less than four successes or less than four failures and justify the definition by analysing probability estimation errors on various sample sizes.

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Optimal estimator of hypothesis probability for data mining problems with small samples

Piegat A, Landowski M.

International Journal of Applied Mathematics and Computer Science

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2012

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Vol. 22, no. 3

629-645

EN

The paper presents a new (to the best of the authors' knowledge) estimator of probability called the "[...] completeness estimator" along with a theoretical derivation of its optimality. The estimator is especially suitable for a small number of sample items, which is the feature of many real problems characterized by data insufficiency. The control parameter of the estimator is not assumed in an a priori, subjective way, but was determined on the basis of an optimization criterion (the least absolute errors).The estimator was compared with the universally used frequency estimator of probability and with Cestnik's m-estimator with respect to accuracy. The comparison was realized both theoretically and experimentally. The results show the superiority of the [...] completeness estimator over the frequency estimator for the probability interval ph (0.1, 0.9). The frequency estimator is better for ph [0, 0.1] and ph [0.9, 1].