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Missing Data
In statistics, missing data, or missing values, occur when no data value is stored for the variable in an observation. Missing data are a common occurrence and can have a significant effect on the conclusions that can be drawn from the data. Missing data can occur because of nonresponse: no information is provided for one or more items or for a whole unit ("subject"). Some items are more likely to generate a nonresponse than others: for example items about private subjects such as income. Attrition is a type of missingness that can occur in longitudinal studies—for instance studying development where a measurement is repeated after a certain period of time. Missingness occurs when participants drop out before the test ends and one or more measurements are missing. Data often are missing in research in economics, sociology, and political science because governments or private entities choose not to, or fail to, report critical statistics, or because the information is not avai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments. When census data (comprising every member of the target population) cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix Completion
Matrix completion is the task of filling in the missing entries of a partially observed matrix, which is equivalent to performing data imputation in statistics. A wide range of datasets are naturally organized in matrix form. One example is the movie-ratings matrix, as appears in the Netflix problem: Given a ratings matrix in which each entry (i,j) represents the rating of movie j by customer i, if customer i has watched movie j and is otherwise missing, we would like to predict the remaining entries in order to make good recommendations to customers on what to watch next. Another example is the document-term matrix: The frequencies of words used in a collection of documents can be represented as a matrix, where each entry corresponds to the number of times the associated term appears in the indicated document. Without any restrictions on the number of degrees of freedom in the completed matrix, this problem is underdetermined since the hidden entries could be assigned arbitrary ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Latent Variable
In statistics, latent variables (from Latin: present participle of ) are variables that can only be inferred indirectly through a mathematical model from other observable variables that can be directly observed or measured. Such '' latent variable models'' are used in many disciplines, including engineering, medicine, ecology, physics, machine learning/artificial intelligence, natural language processing, bioinformatics, chemometrics, demography, economics, management, political science, psychology and the social sciences. Latent variables may correspond to aspects of physical reality. These could in principle be measured, but may not be for practical reasons. Among the earliest expressions of this idea is Francis Bacon's polemic the ''Novum Organum'', itself a challenge to the more traditional logic expressed in Aristotle's Organon: In this situation, the term ''hidden variables'' is commonly used, reflecting the fact that the variables are meaningful, but not observable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inverse Probability Weighting
Inverse probability weighting is a statistical technique for estimating quantities related to a population other than the one from which the data was collected. Study designs with a disparate sampling population and population of target inference (target population) are common in application. There may be prohibitive factors barring researchers from directly sampling from the target population such as cost, time, or ethical concerns. A solution to this problem is to use an alternate design strategy, e.g. stratified sampling. Weighting, when correctly applied, can potentially improve the efficiency and reduce the bias of unweighted estimators. One very early weighted estimator is the Horvitz–Thompson estimator of the mean. When the sampling probability is known, from which the sampling population is drawn from the target population, then the inverse of this probability is used to weight the observations. This approach has been generalized to many aspects of statistics under vario ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indicator Variable
In regression analysis, a dummy variable (also known as indicator variable or just dummy) is one that takes a binary value (0 or 1) to indicate the absence or presence of some categorical effect that may be expected to shift the outcome. For example, if we were studying the relationship between biological sex and income, we could use a dummy variable to represent the sex of each individual in the study. The variable could take on a value of 1 for males and 0 for females (or vice versa). In machine learning this is known as one-hot encoding. Dummy variables are commonly used in regression analysis to represent categorical variables that have more than two levels, such as education level or occupation. In this case, multiple dummy variables would be created to represent each level of the variable, and only one dummy variable would take on a value of 1 for each observation. Dummy variables are useful because they allow us to include categorical variables in our analysis, which w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expectation–maximization Algorithm
In statistics, an expectation–maximization (EM) algorithm is an iterative method to find (local) maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models, where the model depends on unobserved latent variables. The EM iteration alternates between performing an expectation (E) step, which creates a function for the expectation of the log-likelihood evaluated using the current estimate for the parameters, and a maximization (M) step, which computes parameters maximizing the expected log-likelihood found on the ''E'' step. These parameter-estimates are then used to determine the distribution of the latent variables in the next E step. It can be used, for example, to estimate a mixture of gaussians, or to solve the multiple linear regression problem. History The EM algorithm was explained and given its name in a classic 1977 paper by Arthur Dempster, Nan Laird, and Donald Rubin. They pointed out that the method had been "proposed man ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Censoring (statistics)
In statistics, censoring is a condition in which the Value (mathematics), value of a measurement or observation is only partially known. For example, suppose a study is conducted to measure the impact of a drug on mortality rate. In such a study, it may be known that an individual's age at death is ''at least'' 75 years (but may be more). Such a situation could occur if the individual withdrew from the study at age 75, or if the individual is currently alive at the age of 75. Censoring also occurs when a value occurs outside the range of a measuring instrument. For example, a bathroom scale might only measure up to 140 kg, after which it rolls over 0 and continues to count up from there. If a 160 kg individual is weighed using the scale, the observer would only know that the individual's weight is 20 modulo, mod 140 kg (in addition to 160kg, they could weigh 20kg, 300kg, 440kg, and so on). The problem of censored data, in which the observed value of some variable is partially kn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Markov Chain
In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happens next depends only on the state of affairs ''now''." A countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain (CTMC). Markov processes are named in honor of the Russian mathematician Andrey Markov. Markov chains have many applications as statistical models of real-world processes. They provide the basis for general stochastic simulation methods known as Markov chain Monte Carlo, which are used for simulating sampling from complex probability distributions, and have found application in areas including Bayesian statistics, biology, chemistry, economics, fin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joint Probability Distribution
A joint or articulation (or articular surface) is the connection made between bones, ossicles, or other hard structures in the body which link an animal's skeletal system into a functional whole.Saladin, Ken. Anatomy & Physiology. 7th ed. McGraw-Hill Connect. Webp.274/ref> They are constructed to allow for different degrees and types of movement. Some joints, such as the knee, elbow, and shoulder, are self-lubricating, almost frictionless, and are able to withstand compression and maintain heavy loads while still executing smooth and precise movements. Other joints such as suture (joint), sutures between the bones of the skull permit very little movement (only during birth) in order to protect the brain and the sense organs. The connection between a tooth and the jawbone is also called a joint, and is described as a fibrous joint known as a gomphosis. Joints are classified both structurally and functionally. Joints play a vital role in the human body, contributing to movement, sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annual Review Of Economics
The ''Annual Review of Economics'' is a peer-reviewed academic journal that publishes an annual volume of review articles relevant to economics. It was established in 2009 and is published by Annual Reviews. The co-editors are Philippe Aghion and Hélène Rey. As of 2023, it is being published as open access, under the Subscribe to Open model. History The ''Annual Review of Economics'' was first published in 2009 by the nonprofit publisher Annual Reviews. Its founding editors were Timothy Bresnahan and Nobel laureate Kenneth J. Arrow. As of 2021, it is published both in print and online. Scope and indexing The ''Annual Review of Economics'' defines its scope as covering significant developments in economics; specific subdisciplines included are macroeconomics; microeconomics; international, social, behavioral, cultural, institutional, education, and network economics; public finance; economic growth, economic development; political economy; game theory; and social choice ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Identification
In statistics and econometrics, set identification (or partial identification) extends the concept of identifiability (or "point identification") in statistical models to environments where the model and the distribution of observable variables are not sufficient to determine a unique value for the model parameters, but instead constrain the parameters to lie in a strict subset of the parameter space. Statistical models that are set (or partially) identified arise in a variety of settings in economics, including game theory and the Rubin causal model. Unlike approaches that deliver point-identification of the model parameters, methods from the literature on partial identification are used to obtain set estimates that are valid under weaker modelling assumptions. History Early works containing the main ideas of set identification included and . However, the methods were significantly developed and promoted by Charles Manski, beginning with and . Partial identification contin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
