/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Offering a unifying theoretical perspective not readily available in any other text, this innovative guide to econometrics uses simple geometrical arguments to develop students' intuitive understanding of basic and advanced topics, emphasizing throughout the practical applications of modern theory and nonlinear techniques of estimation. One theme of the text is the use of artificial regressions for estimation, reference, and specification testing of nonlinear models, including diagnostic tests for parameter constancy, serial correlation, heteroscedasticity, and other types of mis-specification. Explaining how estimates can be obtained and tests can be carried out, the authors go beyond a mere algebraic description to one that can be easily translated into the commands of a standard econometric software package. Covering an unprecedented range of problems with a consistent emphasis on those that arise in applied work, this accessible and coherent guide to the most vital topics in econometrics today is indispensable for advanced students of econometrics and students of statistics interested in regression and related topics. It will also suit practising econometricians who want to update their skills. Flexibly designed to accommodate a variety of course levels, it offers both complete coverage of the basic material and separate chapters on areas of specialized interest.

Estimation and Inference in Econometrics

Considering the fundamental role played by small and medium sized enterprises (SMEs) in the economy of many countries and the considerable attention placed on SMEs in the new Basel Capital Accord, we develop a distress prediction model specifically for the SME sector and to analyze its effectiveness compared to a generic corporate model. The behavior of financial measures for SMEs is analyzed and the most significant variables in predicting the entities' credit worthiness are selected in order to construct a default prediction model. Using a logit regression technique on a panel of over 2,000 US firms (with sales less than $65 million) over the period 1994-2002, we develop a one-year default prediction model. This model has an out of sample prediction power which is almost 30% higher than a generic corporate model. An associated objective is to observe our model's ability to lower bank capital requirements considering the new Basel Capital Accord's rules for SMEs.

https://papers.ssrn.com/sol3/Delivery.cfm/abac_234.pdf?abstractid=1007548&mirid=1

Modeling Credit Risk for SMEs: Evidence from the US Market

Considering the fundamental role played by small and medium sized enterprises (SMEs) in the economy of many countries and the considerable attention placed on SMEs in the new Basel Capital Accord, we develop a distress prediction model specifically for the SME sector and to analyse its effectiveness compared to a generic corporate model. The behaviour of financial measures for SMEs is analysed and the most significant variables in predicting the entities’ credit worthiness are selected in order to construct a default prediction model. Using a logit regression technique on panel data of over 2,000 U.S. firms (with sales less than $65 million) over the period 1994–2002, we develop a one-year default prediction model. This model has an out-of-sample prediction power which is almost 30 per cent higher than a generic corporate model. An associated objective is to observe our model's ability to lower bank capital requirements considering the new Basel Capital Accord's rules for SMEs.

/pdf/modelling-credit-risk-for-smes-evidence-from-the-u-s-market-3huffey3xm.pdf

Modelling Credit Risk for SMEs: Evidence from the U.S. Market

Considering the fundamental role played by small and medium sized enterprises (SMEs) in the economy of many countries and the considerable attention placed on SMEs in the new Basel Capital Accord, we develop a distress prediction model specifically for the SME sector and to analyze its effectiveness compared to a generic corporate model. The behavior of financial measures for SMEs is analyzed and the most significant variables in predicting the entities' credit worthiness are selected in order to construct a default prediction model. Using a logit regression technique on a panel of over 2,000 US firms (with sales less than $65 million) over the period 1994–2002, we develop a one-year default prediction model. This model has an out of sample prediction power which is almost 30 percent higher than a generic corporate model. An associated objective is to observe our model's ability to lower bank capital requirements considering the new Basel Capital Accord's rules for SMEs.

MODELING CREDIT RISK FOR SMEs: EVIDENCE FROM THE US MARKET

We examine model performance measures in four contexts: Discrete Probability, Continuous Probability, Conditional Discrete Probability and Conditional Probability Density Models. We consider the model performance question from the point of view of an investor who evaluates models based on the performance of the (optimal) strategies that the models suggest. Under this new paradigm, the investor selects the model with the highest estimated expected utility. We interpret our performance measures in information theoretic terms and provide new generalizations of entropy and Kullback-Leibler relative entropy. We show that the relative performance measure is independent of the market prices if and only if the investor's utility function is a member of a logarithmic family that admits a wide range of possible risk aversions. In this case, we show that the relative performance measure is equivalent to the (easily understood) differential expected growth of wealth or the (familiar) likelihood ratio. We state conditions under which relative performance measures for general utilities are well approximated by logarithmic-family-based relative performance measures. Some popular probability model performance measures (including ROC methods) are not consistent with our framework. We demonstrate that rank based performance measures can suggest model selections that are disastrous under various popular utilities.

Model Performance Measures for Expected Utility Maximizing Investors

We review a decision theoretic, i.e., utility-based, motivation for entropy and Kullback-Leibler relative entropy, the natural generalizations that follow, and various properties of thesegeneralized quantities. We then consider these generalized quantities in an easily interpreted spe-cial case. We show that the resulting quantities, share many of the properties of entropy andrelative entropy, such as the data processing inequality and the second law of thermodynamics.We formulate an important statistical learning problem – probability estimation – in terms of ageneralized relative entropy. The solution of this problem reflects general risk preferences via theutility function; moreover, the solution is optimal in a sense of robust absolute performance.

/pdf/a-utility-based-approach-to-some-information-measures-18lndiu3jn.pdf

A Utility-Based Approach to Some Information Measures

We consider the problem of learning a probabilistic model from the viewpoint of an expected utility maximizing decision maker/investor who would use the model to make decisions (bets), which result in well defined payoffs. In our new approach, we seek good out-of-sample model performance by considering a one-parameter family of Pareto optimal models, which we define in terms of consistency with the training data and consistency with a prior (benchmark) model. We measure the former by means of the large-sample distribution of a vector of sample-averaged features, and the latter by means of a generalized relative entropy. We express each Pareto optimal model as the solution of a strictly convex optimization problem and its strictly concave (and tractable) dual. Each dual problem is a regularized maximization of expected utility over a well-defined family of functions. Each Pareto optimal model is robust: maximizing worst-case outperformance relative to the benchmark model. Finally, we select the Pareto optimal model with maximum (out-of-sample) expected utility. We show that our method reduces to the minimum relative entropy method if and only if the utility function is a member of a three-parameter logarithmic family.

Learning Probabilistic Models: An Expected Utility Maximization Approach

Model performance measures for expected utility maximizing investors

/pdf/learning-probabilistic-models-an-expected-utility-33zefmqeow.pdf

Sven Sandow

Papers

Model Performance Measures for Expected Utility Maximizing Investors

A Utility-Based Approach to Some Information Measures

Learning Probabilistic Models: An Expected Utility Maximization Approach

Model performance measures for expected utility maximizing investors

Learning probabilistic models: an expected utility maximization approach