Central limit theorem for directional statistics
In probability theory, the central limit theorem states conditions under which the average of a sufficiently large number of independent random variables, each with finite mean and variance, will be a
Large deviations theory
In probability theory, the theory of large deviations concerns the asymptotic behaviour of remote tails of sequences of probability distributions. While some basic ideas of the theory can be traced to
Markov chain central limit theorem
In the mathematical theory of random processes, the Markov chain central limit theorem has a conclusion somewhat similar in form to that of the classic central limit theorem (CLT) of probability theor
Law of the iterated logarithm
In probability theory, the law of the iterated logarithm describes the magnitude of the fluctuations of a random walk. The original statement of the law of the iterated logarithm is due to A. Ya. Khin
Slutsky's theorem
In probability theory, Slutsky’s theorem extends some properties of algebraic operations on convergent sequences of real numbers to sequences of random variables. The theorem was named after Eugen Slu
Central limit theorem
In probability theory, the central limit theorem (CLT) establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distri
Consistent estimator
In statistics, a consistent estimator or asymptotically consistent estimator is an estimator—a rule for computing estimates of a parameter θ0—having the property that as the number of data points used
Asymptotic theory (statistics)
In statistics, asymptotic theory, or large sample theory, is a framework for assessing properties of estimators and statistical tests. Within this framework, it is often assumed that the sample size n
U-statistic
In statistical theory, a U-statistic is a class of statistics that is especially important in estimation theory; the letter "U" stands for unbiased. In elementary statistics, U-statistics arise natura
Dvoretzky–Kiefer–Wolfowitz inequality
In the theory of probability and statistics, the Dvoretzky–Kiefer–Wolfowitz–Massart inequality (DKW inequality) bounds how close an empirically determined distribution function will be to the distribu
Local asymptotic normality
In statistics, local asymptotic normality is a property of a sequence of statistical models, which allows this sequence to be asymptotically approximated by a normal location model, after a rescaling
Stochastic equicontinuity
In estimation theory in statistics, stochastic equicontinuity is a property of estimators (estimation procedures) that is useful in dealing with their asymptotic behaviour as the amount of data increa
Consistency (statistics)
In statistics, consistency of procedures, such as computing confidence intervals or conducting hypothesis tests, is a desired property of their behaviour as the number of items in the data set to whic
Law of large numbers
In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results
Asymptotic distribution
In mathematics and statistics, an asymptotic distribution is a probability distribution that is in a sense the "limiting" distribution of a sequence of distributions. One of the main uses of the idea
V-statistic
V-statistics are a class of statistics named for Richard von Mises who developed their asymptotic distribution theory in a fundamental paper in 1947. V-statistics are closely related to U-statistics (
Glivenko–Cantelli theorem
In the theory of probability, the Glivenko–Cantelli theorem (sometimes referred to as the Fundamental Theorem of Statistics), named after Valery Ivanovich Glivenko and Francesco Paolo Cantelli, determ