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Why We Should Shift to Symmetric Regression

Rein Taagepera

in Making Social Sciences More Scientific: The Need for Predictive Models

When data are scattered, Ordinary Least-Squares (OLS) regression produces two quite distinct regression lines – one for y versus x and another for x versus y – and both may differ appreciably from ... More

When data are scattered, Ordinary Least-Squares (OLS) regression produces two quite distinct regression lines – one for y versus x and another for x versus y – and both may differ appreciably from what your eyes tell you. If data are scattered, OLS regression of y against x will disconfirm a model that actually fits; thus good statistics can be death of good science. Standard OLS equations cannot form a system of interlocking models, because they are unidirectional and nontransitive. Scale-independent symmetric regression avoids these problems of OLS, offering a single reversible and transitive equation.Less

Business Forecasting and Credit Decisions

Hrishikes Bhattacharya

in Banking Strategy, Credit Appraisal, and Lending Decisions: A Risk–Return Framework

This chapter discusses one of the most reliable and commonly used techniques of business forecasting, and develops an appraisal methodology by applying this technique. Of the various statistical ... More

This chapter discusses one of the most reliable and commonly used techniques of business forecasting, and develops an appraisal methodology by applying this technique. Of the various statistical techniques used for forecasting, the least square regression analysis has stood the test of time. The standard error of estimate aided by the ‘t’ distribution table enables a decision maker to take a position within a range depending upon the risk profile of the customer, and that of the lending organization.Less

The Problem of Index Revisions

Robert J. Shiller

in Macro Markets: Creating Institutions for Managing Society's Largest Economic Risks

Most published economic indices are revised after they are first published—information does not come in all at once, and timely publication dictates that the preliminary index numbers be later ... More

Most published economic indices are revised after they are first published—information does not come in all at once, and timely publication dictates that the preliminary index numbers be later revised. The repeated‐measures indices developed in the preceding chapters are vulnerable to revisions after especially long intervals of time, since they have the property that, unless the repeated measures come sequentially (which they do not necessarily), there will be revisions in the indices after the index numbers are first produced, even if the raw data used then were perfectly accurate and complete. There are other index number construction methods, such as ordinary‐least‐squares regression‐per‐period hedonic regressions, that do not normally produce revisions; this would at first seem to be an advantage, but an index number construction method that does not produce revisions is not a virtue if new information tends to arrive that implies revisions and is just ignored. This chapter addresses the whole problem of index number revisions in the following sections: Variance components in regression‐per‐period hedonics; Interval‐linked indices; Indices that are derived by conditioning on lagged index values. The final section of the chapter draws some sort of interpretation of what has gone before.Less

Function Approximation

Masashi Sugiyama and Motoaki Kawanabe

in Machine Learning in Non-Stationary Environments: Introduction to Covariate Shift Adaptation

This chapter discusses function learning methods under covariate shift. Ordinary empirical risk minimization learning is not consistent under covariate shift for misspecified models, and this ... More

This chapter discusses function learning methods under covariate shift. Ordinary empirical risk minimization learning is not consistent under covariate shift for misspecified models, and this inconsistency issue can be resolved by considering importance-weighted loss functions. Here, various importance-weighted empirical risk minimization methods are introduced, including least squares and Huber’s method for regression, and Fisher discriminant analysis, logistic regression, support vector machines, and boosting for classification. Their adaptive and regularized variants are also described. The numerical behavior of these importance-weighted learning methods is illustrated through experiments.Less

From Sample to Population

in Introductory Econometrics: Intuition, Proof, and Practice

This chapter discusses the reasons why we can generalize from what we observe in one sample to what we might expect in others. It defines the population, distinguishes between parameters and ... More

This chapter discusses the reasons why we can generalize from what we observe in one sample to what we might expect in others. It defines the population, distinguishes between parameters and estimators, and discusses why we work with samples when populations are what we are interested in. It demonstrates that, with the appropriate assumptions about the structure of the population, a and b, as calculated in Chapter 4, are best linear unbiased (BLU) estimators of the corresponding parameters in the population relationship. Under these population assumptions, regression is frequently known as ordinary least squares (OLS) regression.Less

Estimation of Stationary Time Series Processes

M. Hashem Pesaran

in Time Series and Panel Data Econometrics

This chapter begins with the problem of estimating the mean and autocovariances of a stationary process. It then considers the estimation of autoregressive and moving average processes as well as the ... More

This chapter begins with the problem of estimating the mean and autocovariances of a stationary process. It then considers the estimation of autoregressive and moving average processes as well as the estimation of spectral density functions. The analysis is also related to the standard ordinary least squares (OLS) regression models. It shows that when the errors are serially correlated, the OLS estimators of models with lagged dependent variables are inconsistent, and derives an asymptotic expression for the bias. Exercises are provided at the end of the chapter.Less