Stress testing with misspecified models
... the pointwise mean of a variable on whose path one conditions combined with a pointwise restriction on the variance (to be zero) then a natural loosening is to impose a mean path, but allow for a non-degenerate distribution around it. This sort of restriction may capture the fact that regulators ha ...
... the pointwise mean of a variable on whose path one conditions combined with a pointwise restriction on the variance (to be zero) then a natural loosening is to impose a mean path, but allow for a non-degenerate distribution around it. This sort of restriction may capture the fact that regulators ha ...
PredictionWorks: Data Mining Glossary
... continuous or categorical variables. Chi square test is used to test the significance between the column and the row frequencies, that is, whether the frequencies of one of the variables depends on the other. Control Group Study (a.k.a. Randomized Controlled Study): Click here for more information. ...
... continuous or categorical variables. Chi square test is used to test the significance between the column and the row frequencies, that is, whether the frequencies of one of the variables depends on the other. Control Group Study (a.k.a. Randomized Controlled Study): Click here for more information. ...
Neural Networks and Statistical Models
... layer neuron. This initialises the processing step. For example, if the input member of the first training pair is (0.20, 0.6). Thus, the output signal of the 1st neuron in the first layer is 0.20, and the signal of the 2nd neuron is 0.60. Each neuron in the next layer receives an "input signal" fro ...
... layer neuron. This initialises the processing step. For example, if the input member of the first training pair is (0.20, 0.6). Thus, the output signal of the 1st neuron in the first layer is 0.20, and the signal of the 2nd neuron is 0.60. Each neuron in the next layer receives an "input signal" fro ...
lecture2
... The prior p(.) encodes our prior knowledge about the domain © Eric Xing @ CMU, 2006-2010 ...
... The prior p(.) encodes our prior knowledge about the domain © Eric Xing @ CMU, 2006-2010 ...
An introduction to modern missing data analyses
... Association Task Force on Statistical Inference, 1999, p. 598) that stated that deletion methods “are among the worst methods available for practical applications.” It is not a surprise that substantive researchers routinely employ missing data handling techniques that methodologists criticize. For ...
... Association Task Force on Statistical Inference, 1999, p. 598) that stated that deletion methods “are among the worst methods available for practical applications.” It is not a surprise that substantive researchers routinely employ missing data handling techniques that methodologists criticize. For ...
Applying Finite Mixture Models
... 2.8 Provision of Standard Errors One way of obtaining standard errors of the estimates of the parameters in a mixture model is to approximate the covariance matrix of ̂ by the inverse of the observed information matrix, which is given by the negative of the Hessian matrix of the log likelihood ev ...
... 2.8 Provision of Standard Errors One way of obtaining standard errors of the estimates of the parameters in a mixture model is to approximate the covariance matrix of ̂ by the inverse of the observed information matrix, which is given by the negative of the Hessian matrix of the log likelihood ev ...
Bayesian Framework for Least-Squares Support
... defining, in a straightforward way the effective number of parameters γef f in section 4. In the LS-SVM formulation, the bias term is considered a model parameter and is obtained on the first level of inference. As in ordinary ridge regression (Brown, 1997), no regularization is applied on the bias ...
... defining, in a straightforward way the effective number of parameters γef f in section 4. In the LS-SVM formulation, the bias term is considered a model parameter and is obtained on the first level of inference. As in ordinary ridge regression (Brown, 1997), no regularization is applied on the bias ...
1-Way Analysis of Variance
... • Dummy (Indicator) Variables: Variables that take on the value 1 if observation comes from a particular group, 0 if not. • If there are I groups, we create I-1 dummy variables. • Individuals in the “baseline” group receive 0 for all dummy variables. • Statistical software packages typically assign ...
... • Dummy (Indicator) Variables: Variables that take on the value 1 if observation comes from a particular group, 0 if not. • If there are I groups, we create I-1 dummy variables. • Individuals in the “baseline” group receive 0 for all dummy variables. • Statistical software packages typically assign ...
Low-Frequency Econometrics ∗ Ulrich K. Müller and Mark W. Watson Princeton University
... than average growth? And, what is the value of the population mean growth rate of GDP? The plot for inflation shows large persistent variation in its trends over the past sixty years. Does this suggest that the inflation process is (1)? Or is this behavior consistent with an (0) process? Alternati ...
... than average growth? And, what is the value of the population mean growth rate of GDP? The plot for inflation shows large persistent variation in its trends over the past sixty years. Does this suggest that the inflation process is (1)? Or is this behavior consistent with an (0) process? Alternati ...
1 Statistical Models for Proportional Outcomes Abstract For many
... To better illustrate how to employ these five models in the practice, we would apply them to a use case of modeling the financial leverage ratio defined in the interval of [0, 1) with the point mass at 0 implying zero debt in the corporate capital structure. All information including both the respon ...
... To better illustrate how to employ these five models in the practice, we would apply them to a use case of modeling the financial leverage ratio defined in the interval of [0, 1) with the point mass at 0 implying zero debt in the corporate capital structure. All information including both the respon ...
The Bisquare Weighted Analysis of Variance: A Technique for Nonnormal Distributions
... (bANOVA) is a technique that we have developed for comparing the weighted means of several groups where the weights are designed to reduce the influence of, or completely eliminate, outliers (Stine & Regeth, In preparation). Unlike the analysis of variance (ANOVA), the bANOVA maintains high power wi ...
... (bANOVA) is a technique that we have developed for comparing the weighted means of several groups where the weights are designed to reduce the influence of, or completely eliminate, outliers (Stine & Regeth, In preparation). Unlike the analysis of variance (ANOVA), the bANOVA maintains high power wi ...
STAT 515 fa 2016 Lec 06 Random Variables, Expected Value
... 1. There is more than one possible outcome. 2. It is known in advance what the possible outcomes are. 3. The outcome to be generated cannot be predicted with certainty. Suppose we define X to be a numeric encoding of the outcome of a statistical experiment. We call X a random variable. A random vari ...
... 1. There is more than one possible outcome. 2. It is known in advance what the possible outcomes are. 3. The outcome to be generated cannot be predicted with certainty. Suppose we define X to be a numeric encoding of the outcome of a statistical experiment. We call X a random variable. A random vari ...
Linear regression
In statistics, linear regression is an approach for modeling the relationship between a scalar dependent variable y and one or more explanatory variables (or independent variables) denoted X. The case of one explanatory variable is called simple linear regression. For more than one explanatory variable, the process is called multiple linear regression. (This term should be distinguished from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.)In linear regression, data are modeled using linear predictor functions, and unknown model parameters are estimated from the data. Such models are called linear models. Most commonly, linear regression refers to a model in which the conditional mean of y given the value of X is an affine function of X. Less commonly, linear regression could refer to a model in which the median, or some other quantile of the conditional distribution of y given X is expressed as a linear function of X. Like all forms of regression analysis, linear regression focuses on the conditional probability distribution of y given X, rather than on the joint probability distribution of y and X, which is the domain of multivariate analysis.Linear regression was the first type of regression analysis to be studied rigorously, and to be used extensively in practical applications. This is because models which depend linearly on their unknown parameters are easier to fit than models which are non-linearly related to their parameters and because the statistical properties of the resulting estimators are easier to determine.Linear regression has many practical uses. Most applications fall into one of the following two broad categories: If the goal is prediction, or forecasting, or error reduction, linear regression can be used to fit a predictive model to an observed data set of y and X values. After developing such a model, if an additional value of X is then given without its accompanying value of y, the fitted model can be used to make a prediction of the value of y. Given a variable y and a number of variables X1, ..., Xp that may be related to y, linear regression analysis can be applied to quantify the strength of the relationship between y and the Xj, to assess which Xj may have no relationship with y at all, and to identify which subsets of the Xj contain redundant information about y.Linear regression models are often fitted using the least squares approach, but they may also be fitted in other ways, such as by minimizing the ""lack of fit"" in some other norm (as with least absolute deviations regression), or by minimizing a penalized version of the least squares loss function as in ridge regression (L2-norm penalty) and lasso (L1-norm penalty). Conversely, the least squares approach can be used to fit models that are not linear models. Thus, although the terms ""least squares"" and ""linear model"" are closely linked, they are not synonymous.