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One of the most widely known and important applications of probability and statistics is scientific polling to forecast election results. In 1936, Gallup predicted correctly the victory of Roosevelt over Landon in the US presidential election, using scientific sampling of a few thousand persons, whereas the Literary Digest failed using 2.4 million answers to 10 million mailed questionnaires to automobile and telephone owners. Since then, polls have grown to be a multibillion flourishing and very influential and important industry, spreading around the world. Polls have mostly been accurate in the US presidential elections, with a few exceptions. Their two most notable failures were their wrong predictions of the US 1948 and 2016 presidential elections. Most polls failed too in the 2016 UK Referendum, in the 2014 and 2019 India Lok Sabha elections, and in the US 2020 presidential election, even though in the latter three they did predict the winner. We discuss these polls in the present paper. The failure in 1948 was due to non-random sampling. In 2016 and 2020 it was mainly due to the problem of non-response, despite weighting adjustments, and possible biases of the pollsters. In 2014 and 2019 it was due to non-response and political biases of the polling agencies and news outlets that produced the polls.

KEYWORDS: Central limit theorem; confidence interval; Gallup poll; Biden; Trump; Truman; Roosevelt

The possibility of characterizing classical bivariate normality via regression conditions is discussed. Some additional assumptions are required. It has been suggested that a further assumption of constant conditional variance would suffice, but even this is not adequate. It is shown that an additional assumption of conditional normality of X given Y = y for all y will yield the desired characterization. Related characterization problems are also considered. The analogous trivariate problem is discussed but is unresolved.

KEYWORDS: Bivariate normal; Conditional normal; Linear regression; Moment generating function; Variance-covariance matrix

Using random, nonrandom and mixed normings, the paper obtains uniform rates of weak convergence to the standard normal distribution of the distribution of several approximate Bayes estimators and approximate maximum a posteriori estimators of the drift parameter in the discretely observed Ornstein-Uhlenbeck process from high frequency data.

KEYWORDS: Approximate Bayes estimator; Approximate maximum a posteriori estimator; Bayesian computation; Discrete observations; High frequency data; Ito stochastic differential equation; Monte Carlo method; Ornstein-Uhlenbeck process; Rate of weak convergence; Uniform Berry-Esseen type bound.

The aim of the present paper is to examine a multivariate extension of the Spearman dependence coefficient which can be deployed in the framework of regression analysis. The coefficient describes how well a response random variable can be approximated by a multivariate monotonously increasing function of a certain number of regressors. We introduce estimators of the dependence coefficient and prove their convergence rate and asymptotic normality.

KEYWORDS: Dependence measures, Spearman’s ?, Spearman’s footrule, estimators for dependence measures

In this paper we present a short review and discussion of some characterizations of almost unbiased ratio type estimators constructed at estimation stage . In such estimators the bias of O(1/n) is removed and the ultimate bias becomes of O(1/n2) ,where n is the sample size.

KEYWORDS: Almost Unbiased estimators; Finite population; Ratio type estimators; Simple random sampling

In this paper, the focus is on Multinomial document model which is similar to the Bernoulli model, but the presence flag in the former is replaced with the frequentist method which takes into account the number of times the tokens occur in the text. The application of Na¨?ve Bayes approach is discussed for the document models. Estimators in Na¨?ve Bayes and Multinomial setup have been derived. Illustration and R code snippets for implementation are included.

KEYWORDS: Sections; lists; figures; tables; references; appendices