Statistics

In this paper we study the problem of statistical inference on the parameters of the semiparametric variance-mean mixtures. This class of mixtures has recently become rather popular in statistical and financial modelling. We design a semiparametric estimation procedure that first estimates the mean of the underlying normal distribution and then recovers nonparametrically the density of the corresponding mixing distribution. We illustrate the performance of our procedure on simulated and real data.

Starting from the pioneering works of Shannon and Weiner in 1948, a plethora of works have been reported on entropy in different directions. Entropy-related review work in the direction of statistics, reliability and information science, to the best of our knowledge, has not been reported so far. Here we have tried to collect all possible works in this direction during the period 1948-2018 so that people interested in entropy, specially the new researchers, get benefited.

A fundamental class of inferential problems are those characterised by there having been a substantial degree of pre-data (or prior) belief that the value of a model parameter was equal or lay close to a specified value, which may, for example, be the value that indicates the absence of an effect. Standard ways of tackling problems of this type, including the Bayesian method, are often highly inadequate in practice. To address this issue, an inferential framework called bispatial inference is put forward, which can be viewed as both a generalisation and radical reinterpretation of existing approaches to inference that are based on P values. It is shown that to obtain an appropriate post-data density function for a given parameter, it is often convenient to combine a special type of bispatial inference, which is constructed around one-sided P values, with a previously outlined form of fiducial inference. Finally, by using what are called post-data opinion curves, this bispatial-fiducial theory is naturally extended to deal with the general scenario in which any number of parameters may be unknown. The application of the theory is illustrated in various examples, which are especially relevant to the analysis of clinical trial data.

This dissertation examines three distinct big data analytics problems related to the social aspects of consumers' choices. The main goal of this line of research is to help two sided platform firms to target their marketing policies given the great heterogeneity among their customers. In three essays, I combined structural modeling and machine learning approaches to first understand customers' responses to intrinsic and extrinsic factors, using unique data sets I scraped from the web, and then explore methods to optimize two sided platforms' firms' reactions accordingly. The first essay examines "social learning" in the mobile app store context, controlling for intrinsic value of hedonic and utilitarian mobile apps, price, advertising, and number of options available. The second essay investigates bidders' anticipated winner and loser regret in the context of the eBay online auction platform. Using a large data set from eBay and empirical Bayesian estimation method, I quantify the bidders' anticipation of regret in various product categories, and investigate the role of experience in explaining the bidders' regret and learning behaviors. The third essay investigates the effects of Gamification incentive mechanisms in an online platform for user generated content. I use an ensemble method over LDA, mixed normal and k-mean clustering methods to segment users into competitors, collaborators, achievers, explorers and uninterested users. These findings help the Gamification platform to target its users. The simulation counterfactual analysis suggests that a two sided platform can increase the number of user contributions, by making earning badges more difficult.

Conventional wisdom assumes that the indefinite integral of the probability density function for the standard normal distribution cannot be expressed in finite elementary terms. While this is true, there is an expression for this anti-derivative in infinite elementary terms that, when being differentiated, directly yields the standard normal density function. We derive this function using infinite partial integration and review its relation to the cumulative distribution function for the standard normal distribution and the error function.

This paper deals with two-sample Kolmogorov-Smirnov test and its biasedness. This test is not unbiased in general in case of different sample sizes. We found out most biased distribution for some values of significance level α . Moreover we discovered that there exists number of observation and significance level α such that this test is unbiased at level α .

In this paper, we consider the problem of obtaining the best k -sparse solution of Ax=y subject to the constraint that the columns of A are orthogonal. The naive approach for obtaining a solution to this problem has exponential complexity and there exist l 1 regularization methods such as Lasso to obtain approximate solutions. In this paper, we show that we can obtain an exact solution to the problem, with much less computational effort compared to the brute force search when the columns of A are orthogonal.

We develop a class of exponential-family point processes based on a latent social space to model the coevolution of social structure and behavior over time. Temporal dynamics are modeled as a discrete Markov process specified through individual transition distributions for each actor in the system at a given time. We prove that these distributions have an analytic closed form under certain conditions and use the result to develop likelihood-based inference. We provide a computational framework to enable both simulation and inference in practice. Finally, we demonstrate the value of these models by analyzing alcohol and drug use over time in the context of adolescent friendship networks.

This study demonstrates how to use "spmoran", an R package estimating spatial additive mixed models and other spatial regression models for Gaussian and non-Gaussian data. Moran eigenvectors are used to an approximate Gaussian process modeling which is interpretable in terms of the Moran coefficient. The GP is used for modeling the spatial processes in residuals and regression coefficients. All these models are estimated computationally efficiently. For the sample code used in this paper, see this https URL.

OBJECTIVES: Estimates of the basic reproduction number (R0) of COVID-19 vary across countries. This paper aims to characterise the spatial variability in R0 across the first six months of the global COVID-19 outbreak, and to explore social factors that impact R0 estimates at national and regional level. METHODS: We searched PubMed, LitCOVID and the WHO COVID-19 database from January to June 2020. Peer-reviewed English-language papers were included that provided R0 estimates. For each study, the value of the estimate, country under study and publication month were extracted. The median R0 value was calculated per country, and the median and variance were calculated per region. For each country with an R0 estimate, the Human Development Index (HDI), Sustainable Mobility Index (SMI), median age, population density and development status were obtained from external sources. RESULTS: A total of 81 studies were included in the analysis. These studies provided at least one estimate of R0, along with sufficient methodology to explain how the value was calculated. Values of R0 ranged between 0.48 and 14.8, and between 0.48 and 6.7 when excluding outliers. CONCLUSIONS: This systematic review provides a comprehensive overview of the estimates of the basic reproduction number of COVID-19 globally and highlights the spatial heterogeneity in R0. Higher values were recorded in more developed countries, and countries with an older population or more sustainable mobility. Countries with higher population density had lower R0 estimates. For most regions, variability in R0 spiked initially before reducing and stabilising as more estimates became available.