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Applications of Relative Entropy
In this chapter we first introduce the concept of the relative entropy and prove the entropy projection theorem for probability measures. Then, as an...
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Mathematical Expectation
This chapter introduces random variables and mathematical expectation. Discrete and continuous random variables and their basic properties are...
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Asymptotically Normal Estimators for Zipf’s Law
We study an infinite urn scheme with probabilities corresponding to a power function. Urns here represent words from an infinitely large vocabulary....
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Weighted likelihood methods for robust fitting of wrapped models for p-torus data
We consider, robust estimation of wrapped models to multivariate circular data that are points on the surface of a p -torus based on the weighted...
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Minimum Hellinger Distance Estimation for Discretely Observed Stochastic Processes Using Recursive Kernel Density Estimator
The paper deals with the estimation of the parameters of stochastic processes that are discretely observed. We construct estimator of the parameters...
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Probability distribution as a path and its action integral
To describe the convergence in law of a sequence of probability distributions, “the principle of least action” is introduced nonparametrically into...
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Reflections on Civic Statistics: A Triangulation of Citizen, State and Statistics: Past, Present and Future
The chapter aims to develop four lines of discussion on people’s relationships with statistics. A first line problematizes historical aspects related...
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Flat rent price prediction in Berlin with web scra**
Internet data pose a challenge to the traditional system of official statistics, which relies on more conventional sources such as surveys and...
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An effective method for identifying clusters of robot strengths
In the analysis of qualification stage data from FIRST Robotics Competition (FRC) championships, the ratio (1.67–1.68) of the number of observations...
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Worldview Statistics
Today, the role of official statistics as a science of the state and that of the statistician is viewed rather critically due to the many negative...
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A non-classical parameterization for density estimation using sample moments
Probability density estimation is a core problem in statistics and data science. Moment methods are an important means of density estimation, but...
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Minimum Divergence Method
This chapter provides a general framework of the minimum divergence method for a statistical model. In particular, we explore the U-minimum...
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Likelihood Ratio Test for Homogeneity
Despite the successful application of the C( \(\alpha \) )...
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An Analysis of Extremes: Semiparametric Efficiency in Regression
Let Y denote a response variable and X denote a covariate. We consider statistical inferences in semiparametric regression models, where the...
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Statistical applications of contrastive learning
The likelihood function plays a crucial role in statistical inference and experimental design. However, it is computationally intractable for several...
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Bayesian Reliability Estimation and Prediction
It is often the case that information is available on the parameters of the life distributions from prior experiments or prior analysis of failure...
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Non-Parametric MLE and Its Consistency
In Chapter 2 , our primary focus lies on nonparametric mixture models. In contrast to some existing...
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Predicting the popularity of tweets using internal and external knowledge: an empirical Bayes type approach
The problem of tweet popularity prediction, or forecasting the total number of retweets stemming from an ancestral tweet, has attracted considerable...
