number selection strategy of lotto players
... that lotto players shift their selection strategies. In the second stage, we compute the expected values before and after the break date found previously. Comparing the expected value in these two periods helps us to explain why lotto players change their behavior. Last, we estimate the demand funct ...
... that lotto players shift their selection strategies. In the second stage, we compute the expected values before and after the break date found previously. Comparing the expected value in these two periods helps us to explain why lotto players change their behavior. Last, we estimate the demand funct ...
Applied Statistical Methods - UF-Stat
... For numeric variables, there are two commonly reported types of descriptive measures: location and dispersion. Measures of location describe the level of the ‘typical’ measurement. Two measures widely studied are the mean (µ) and the median. The mean represents the arithmetic average of all measurem ...
... For numeric variables, there are two commonly reported types of descriptive measures: location and dispersion. Measures of location describe the level of the ‘typical’ measurement. Two measures widely studied are the mean (µ) and the median. The mean represents the arithmetic average of all measurem ...
Recursive partitioning and Bayesian inference on
... distribution has richer structure, i.e. less uniform in shape. This is essentially a “model selection” feature, particularly important in higher dimensional settings where an even division across the entire sample space is undesirable both computationally and statistically due to the “curse of dimen ...
... distribution has richer structure, i.e. less uniform in shape. This is essentially a “model selection” feature, particularly important in higher dimensional settings where an even division across the entire sample space is undesirable both computationally and statistically due to the “curse of dimen ...
THE COUNTRY-PRODUCT-DUMMY (CPD) METHOD AND
... computing purchasing power parities (PPPs) of currencies. PPPs are essentially spatial price index numbers that provide measures of price level differences across countries or regions within a country. The Country Product Dummy (CPD) method represents a simple regression approach to measure price le ...
... computing purchasing power parities (PPPs) of currencies. PPPs are essentially spatial price index numbers that provide measures of price level differences across countries or regions within a country. The Country Product Dummy (CPD) method represents a simple regression approach to measure price le ...
Regularization and variable selection via the elastic net
... variable selection method. Moreover, the lasso is not well defined unless the bound on the L1 -norm of the coefficients is smaller than a certain value. (b) If there is a group of variables among which the pairwise correlations are very high, then the lasso tends to select only one variable from the ...
... variable selection method. Moreover, the lasso is not well defined unless the bound on the L1 -norm of the coefficients is smaller than a certain value. (b) If there is a group of variables among which the pairwise correlations are very high, then the lasso tends to select only one variable from the ...
Chapter 2 - Yale Economics
... Let us take the demand shifters (xn and n ) and cost shifters (wn and ωn ) as the “primitives” of the model and assume for now that they are distributed i.i.d. across markets. The temptation for early researchers was to estimate the demand equation by OLS, regressing a time series of log output qua ...
... Let us take the demand shifters (xn and n ) and cost shifters (wn and ωn ) as the “primitives” of the model and assume for now that they are distributed i.i.d. across markets. The temptation for early researchers was to estimate the demand equation by OLS, regressing a time series of log output qua ...
Matching a Distribution by Matching Quantiles
... Basel III is a global regulatory standard on bank capital adequacy, stress testing and market liquidity risk put forward by the Basel Committee on Banking Supervision in 2010–2011, in response to the deficiencies in risk management revealed by the late-2000s financial crisis. One of the mandated req ...
... Basel III is a global regulatory standard on bank capital adequacy, stress testing and market liquidity risk put forward by the Basel Committee on Banking Supervision in 2010–2011, in response to the deficiencies in risk management revealed by the late-2000s financial crisis. One of the mandated req ...
The SURVEYLOGISTIC Procedure
... used in practice are the probit function and the complementary log-log function. The SURVEYLOGISTIC procedure enables you to choose one of these link functions, resulting in fitting a broad class of binary response models of the form g./ D ˛ C xˇ For ordinal response models, the response Y of an in ...
... used in practice are the probit function and the complementary log-log function. The SURVEYLOGISTIC procedure enables you to choose one of these link functions, resulting in fitting a broad class of binary response models of the form g./ D ˛ C xˇ For ordinal response models, the response Y of an in ...
price competition in pharmaceuticals: the case of anti
... considers competition among sellers of closely related molecules. Ellison et al. (1997) examine cross-product price competition in cephalosporins, and find mixed evidence of price competition across products for these closely related antibiotics. In contrast, Stern (1994) finds that in two of his fo ...
... considers competition among sellers of closely related molecules. Ellison et al. (1997) examine cross-product price competition in cephalosporins, and find mixed evidence of price competition across products for these closely related antibiotics. In contrast, Stern (1994) finds that in two of his fo ...
Evaluation criteria for statistical editing and imputation
... we shall not attempt to distinguish between evaluation of logical editing performance and evaluation of statistical editing performance in this report. We shall only be concerned with evaluation of overall editing performance (i.e. detection of data fields with errors). We also distinguish editing f ...
... we shall not attempt to distinguish between evaluation of logical editing performance and evaluation of statistical editing performance in this report. We shall only be concerned with evaluation of overall editing performance (i.e. detection of data fields with errors). We also distinguish editing f ...
Measures and mensuration
... • Interpret the results of an experiment using the language of probability; appreciate that random processes are unpredictable • Know that if the probability of an event occurring is p, then the probability of it not occurring is 1-p; use diagrams and tables to record in a systematic way all possibl ...
... • Interpret the results of an experiment using the language of probability; appreciate that random processes are unpredictable • Know that if the probability of an event occurring is p, then the probability of it not occurring is 1-p; use diagrams and tables to record in a systematic way all possibl ...
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.