Wald testIn statistics, the Wald test (named after Abraham Wald) assesses constraints on statistical parameters based on the weighted distance between the unrestricted estimate and its hypothesized value under the null hypothesis, where the weight is the precision of the estimate. Intuitively, the larger this weighted distance, the less likely it is that the constraint is true. While the finite sample distributions of Wald tests are generally unknown, it has an asymptotic χ2-distribution under the null hypothesis, a fact that can be used to determine statistical significance.
Quantile functionIn probability and statistics, the quantile function outputs the value of a random variable such that its probability is less than or equal to an input probability value. Intuitively, the quantile function associates with a range at and below a probability input the likelihood that a random variable is realized in that range for some probability distribution. It is also called the percentile function (after the percentile), percent-point function or inverse cumulative distribution function (after the cumulative distribution function).
Sample mean and covarianceThe sample mean (sample average) or empirical mean (empirical average), and the sample covariance or empirical covariance are statistics computed from a sample of data on one or more random variables. The sample mean is the average value (or mean value) of a sample of numbers taken from a larger population of numbers, where "population" indicates not number of people but the entirety of relevant data, whether collected or not. A sample of 40 companies' sales from the Fortune 500 might be used for convenience instead of looking at the population, all 500 companies' sales.
Normal distributionIn statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter is its standard deviation. The variance of the distribution is . A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate.
Statistical dispersionIn statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range. For instance, when the variance of data in a set is large, the data is widely scattered. On the other hand, when the variance is small, the data in the set is clustered. Dispersion is contrasted with location or central tendency, and together they are the most used properties of distributions.
One- and two-tailed testsIn statistical significance testing, a one-tailed test and a two-tailed test are alternative ways of computing the statistical significance of a parameter inferred from a data set, in terms of a test statistic. A two-tailed test is appropriate if the estimated value is greater or less than a certain range of values, for example, whether a test taker may score above or below a specific range of scores. This method is used for null hypothesis testing and if the estimated value exists in the critical areas, the alternative hypothesis is accepted over the null hypothesis.
Mathematical statisticsMathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure theory. Statistical data collection is concerned with the planning of studies, especially with the design of randomized experiments and with the planning of surveys using random sampling.
Ratio distributionA ratio distribution (also known as a quotient distribution) is a probability distribution constructed as the distribution of the ratio of random variables having two other known distributions. Given two (usually independent) random variables X and Y, the distribution of the random variable Z that is formed as the ratio Z = X/Y is a ratio distribution. An example is the Cauchy distribution (also called the normal ratio distribution), which comes about as the ratio of two normally distributed variables with zero mean.
Doctor of SciencesDoctor of Sciences (доктор наук, abbreviated д-р наук or д. н.; доктор наук; доктор на науките; доктар навук) is a higher doctoral degree in the Russian Empire, Soviet Union and many post-Soviet countries, which may be earned after the Candidate of Sciences. The "Doctor of Sciences" degree was introduced in the Russian Empire in 1819 and abolished in 1917. Later it was revived in the USSR on January 13, 1934, by a decision of the Council of People's Commissars of the USSR.
EctodomainAn ectodomain is the domain of a membrane protein that extends into the extracellular space (the space outside a cell). Ectodomains are usually the parts of proteins that initiate contact with surfaces, which leads to signal transduction. A notable example of an ectodomain is the S protein, commonly known as the spike protein, of the viral particle responsible for the COVID-19 pandemic. The ectodomain region of the spike protein (S) is essential for attachment and eventual entry of the viral protein into the host cell.
Candidate of SciencesA Candidate of Sciences (кандидат наук) is the first of two doctoral level scientific degrees in Russia and the Commonwealth of Independent States. It is formally classified as UNESCO's ISCED level 8, "doctoral or equivalent." It may be recognized as a Doctor of Philosophy, usually in natural sciences, by scientific institutions in other countries. Former Soviet countries also have a more advanced degree, Doctor of Sciences.
Convex functionIn mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above the graph between the two points. Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set. A twice-differentiable function of a single variable is convex if and only if its second derivative is nonnegative on its entire domain.
