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Both in science and in practical affairs we reason by combining facts only inconclusively supported by evidence. Building on an abstract understanding of this process of combination, this book constructs a new theory of epistemic probability. The theory draws on the work of A. P. Dempster but diverges from Depster's viewpoint by identifying his "lower probabilities" as epistemic probabilities and taking his rule for combining "upper and lower probabilities" as fundamental. The book opens with a critique of the well-known Bayesian theory of epistemic probability. It then proceeds to develop an alternative to the additive set functions and the rule of conditioning of the Bayesian theory: set functions that need only be what Choquet called "monotone of order of infinity." and Dempster's rule for combining such set functions. This rule, together with the idea of "weights of evidence," leads to both an extensive new theory and a better understanding of the Bayesian theory. The book concludes with a brief treatment of statistical inference and a discussion of the limitations of epistemic probability. Appendices contain mathematical proofs, which are relatively elementary and seldom depend on mathematics more advanced that the binomial theorem.

Probabilities. --- Mathematical statistics. --- Evidence. --- Bayesian belief functions. --- Granger, Thomas. --- Hacking, Ian. --- Jeffrey, Richard. --- Keynes, John Maynard. --- assessment of evidence. --- chance density. --- confidence sets. --- decision theory. --- degree of belief. --- dissonance. --- epistemology. --- exponential function. --- judgment and evidence. --- likelihood. --- linear models. --- orthogonal sum. --- plausibility. --- proposition. --- quasi support function. --- scientific hypotheses. --- statistical estimation. --- test statistic. --- upper probability.

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The scope of the contributions to this book will be to present new and original research papers based on MPHIE, MHD, and MDPDE, as well as test statistics based on these estimators from a theoretical and applied point of view in different statistical problems with special emphasis on robustness. Manuscripts given solutions to different statistical problems as model selection criteria based on divergence measures or in statistics for high-dimensional data with divergence measures as loss function are considered. Reviews making emphasis in the most recent state-of-the art in relation to the solution of statistical problems base on divergence measures are also presented.

Research & information: general --- classification --- Bayes error rate --- Henze–Penrose divergence --- Friedman–Rafsky test statistic --- convergence rates --- bias and variance trade-off --- concentration bounds --- minimal spanning trees --- composite likelihood --- composite minimum density power divergence estimators --- model selection --- minimum pseudodistance estimation --- Robustness --- estimation of α --- monitoring --- numerical minimization --- S-estimation --- Tukey’s biweight --- integer-valued time series --- one-parameter exponential family --- minimum density power divergence estimator --- density power divergence --- robust change point test --- Galton-Watson branching processes with immigration --- Hellinger integrals --- power divergences --- Kullback-Leibler information distance/divergence --- relative entropy --- Renyi divergences --- epidemiology --- COVID-19 pandemic --- Bayesian decision making --- INARCH(1) model --- GLM model --- Bhattacharyya coefficient/distance --- time series of counts --- INGARCH model --- SPC --- CUSUM monitoring --- MDPDE --- contingency tables --- disparity --- mixed-scale data --- pearson residuals --- residual adjustment function --- robustness --- statistical distances --- Hellinger distance --- large deviations --- divergence measures --- rare event probabilities --- n/a --- Henze-Penrose divergence --- Friedman-Rafsky test statistic --- Tukey's biweight

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This book presents new and original research in Statistical Information Theory, based on minimum divergence estimators and test statistics, from a theoretical and applied point of view, for different statistical problems with special emphasis on efficiency and robustness. Divergence statistics, based on maximum likelihood estimators, as well as Wald’s statistics, likelihood ratio statistics and Rao’s score statistics, share several optimum asymptotic properties, but are highly non-robust in cases of model misspecification under the presence of outlying observations. It is well-known that a small deviation from the underlying assumptions on the model can have drastic effect on the performance of these classical tests. Specifically, this book presents a robust version of the classical Wald statistical test, for testing simple and composite null hypotheses for general parametric models, based on minimum divergence estimators.

n/a --- mixture index of fit --- Kullback-Leibler distance --- relative error estimation --- minimum divergence inference --- Neyman Pearson test --- influence function --- consistency --- thematic quality assessment --- asymptotic normality --- Hellinger distance --- nonparametric test --- Berstein von Mises theorem --- maximum composite likelihood estimator --- 2-alternating capacities --- efficiency --- corrupted data --- statistical distance --- robustness --- log-linear models --- representation formula --- goodness-of-fit --- general linear model --- Wald-type test statistics --- Hölder divergence --- divergence --- logarithmic super divergence --- information geometry --- sparse --- robust estimation --- relative entropy --- minimum disparity methods --- MM algorithm --- local-polynomial regression --- association models --- total variation --- Bayesian nonparametric --- ordinal classification variables --- Wald test statistic --- Wald-type test --- composite hypotheses --- compressed data --- hypothesis testing --- Bayesian semi-parametric --- single index model --- indoor localization --- composite minimum density power divergence estimator --- quasi-likelihood --- Chernoff Stein lemma --- composite likelihood --- asymptotic property --- Bregman divergence --- robust testing --- misspecified hypothesis and alternative --- least-favorable hypotheses --- location-scale family --- correlation models --- minimum penalized ?-divergence estimator --- non-quadratic distance --- robust --- semiparametric model --- divergence based testing --- measurement errors --- bootstrap distribution estimator --- generalized renyi entropy --- minimum divergence methods --- generalized linear model --- ?-divergence --- Bregman information --- iterated limits --- centroid --- model assessment --- divergence measure --- model check --- two-sample test --- Wald statistic --- Hölder divergence

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Econometric Modeling provides a new and stimulating introduction to econometrics, focusing on modeling. The key issue confronting empirical economics is to establish sustainable relationships that are both supported by data and interpretable from economic theory. The unified likelihood-based approach of this book gives students the required statistical foundations of estimation and inference, and leads to a thorough understanding of econometric techniques. David Hendry and Bent Nielsen introduce modeling for a range of situations, including binary data sets, multiple regression, and cointe.

Econometric models. --- Econometrics. --- Accuracy and precision. --- Asymptotic distribution. --- Autocorrelation. --- Autoregressive conditional heteroskedasticity. --- Autoregressive model. --- Bayesian statistics. --- Bayesian. --- Bernoulli distribution. --- Bias of an estimator. --- Calculation. --- Central limit theorem. --- Chow test. --- Cointegration. --- Conditional expectation. --- Conditional probability distribution. --- Confidence interval. --- Confidence region. --- Correlation and dependence. --- Correlogram. --- Count data. --- Cross-sectional data. --- Cross-sectional regression. --- Distribution function. --- Dummy variable (statistics). --- Econometric model. --- Empirical distribution function. --- Equation. --- Error term. --- Estimation. --- Estimator. --- Exogeny. --- Exploratory data analysis. --- F-distribution. --- F-test. --- Fair coin. --- Forecast error. --- Forecasting. --- Granger causality. --- Heteroscedasticity. --- Inference. --- Instrumental variable. --- Joint probability distribution. --- Law of large numbers. --- Least absolute deviations. --- Least squares. --- Likelihood function. --- Likelihood-ratio test. --- Linear regression. --- Logistic regression. --- Lucas critique. --- Marginal distribution. --- Markov process. --- Mathematical optimization. --- Maximum likelihood estimation. --- Model selection. --- Monte Carlo method. --- Moving-average model. --- Multiple correlation. --- Multivariate normal distribution. --- Nonparametric regression. --- Normal distribution. --- Normality test. --- One-Tailed Test. --- Opportunity cost. --- Orthogonalization. --- P-value. --- Parameter. --- Partial correlation. --- Poisson regression. --- Probability. --- Probit model. --- Quantile. --- Quantity. --- Quasi-likelihood. --- Random variable. --- Regression analysis. --- Residual sum of squares. --- Round-off error. --- Seemingly unrelated regressions. --- Selection bias. --- Simple linear regression. --- Skewness. --- Standard deviation. --- Standard error. --- Stationary process. --- Statistic. --- Student's t-test. --- Sufficient statistic. --- Summary statistics. --- T-statistic. --- Test statistic. --- Time series. --- Type I and type II errors. --- Unit root test. --- Unit root. --- Utility. --- Variable (mathematics). --- Variance. --- Vector autoregression. --- White test.