Cressie Read Family Research Articles

Assessing Misspecifications in Asset Pricing Models with Nonlinear Projections of Pricing Kernels

We develop a new approach to identify model misspecifications based on Minimum Discrepancy (MD) projections that correct asset pricing models with the use of nonlinear functions of basis assets returns. These nonlinear corrections make our method more effective than the Hansen and Jagannathan distance in detecting sources of model specifications, especially in economies where nonlinear risk is priced. A theoretical example illustrates our point, with an economy where the true SDF prices coskewness risk with respect to the market portfolio (Kraus and Litzemberger (1976)). We suggest diagnosing the CAPM model under this economy, and show that while the HJ distance can not identify the exact source of model misspecification (a quadratic term in the market return), there are nonlinear projections in the class of MD problems that correctly capture this term. We also derive the asymptotic distributions of the estimators for the Cressie Read family of discrepancies, and illustrate their use with an empirical assessment of the CCAPM.

φ -Divergence empirique et vraisemblance empirique généralisée

In this paper, we generalize the results obtained with the Kullback distance (corresponding to empirical likelihood) and Cressie-Read metrics (generalized empirical likelihood) to general Phi*-discrepancies, for some convex functions Phi satisfying a few regularity properties. In particular, we introduce a new Bartlett correctable family of empirical discrepancies, the Quasi-Kullback, out of Cressie-Read family, which possess interesting finite sample properties. We conclude this work with some simulations in the multidimensional case for different discrepancies.

Efficient Exact <I>p</I>-Value Computation for Small Sample, Sparse, and Surprising Categorical Data

A major obstacle in applying various hypothesis testing procedures to datasets in bioinformatics is the computation of ensuing p-values. In this paper, we define a generic branchand- bound approach to efficient exact p-value computation and enumerate the required conditions for successful application. Explicit procedures are developed for the entire Cressie–Read family of statistics, which includes the widely used Pearson and likelihood ratio statistics in a one-way frequency table goodness-of-fit test. This new formulation constitutes a first practical exact improvement over the exhaustive enumeration performed by existing statistical software. The general techniques we develop to exploit the convexity of many statistics are also shown to carry over to contingency table tests, suggesting that they are readily extendible to other tests and test statistics of interest. Our empirical results demonstrate a speed-up of orders of magnitude over the exhaustive computation, significantly extending the practical range for performing exact tests. We also show that the relative speed-up gain increases as the null hypothesis becomes sparser, that computation precision increases with increase in speed-up, and that computation time is very moderately affected by the magnitude of the computed p-value. These qualities make our algorithm especially appealing in the regimes of small samples, sparse null distributions, and rare events, compared to the alternative asymptotic approximations and Monte Carlo samplers. We discuss several established bioinformatics applications, where small sample size, small expected counts in one or more categories (sparseness), and very small p-values do occur. Our computational framework could be applied in these, and similar cases, to improve performance.

Efficient Exact p-Value Computation for Small Sample, Sparse, and Surprising Categorical Data

A major obstacle in applying various hypothesis testing procedures to datasets in bioinformatics is the computation of ensuing p-values. In this paper, we define a generic branch-and-bound approach to efficient exact p-value computation and enumerate the required conditions for successful application. Explicit procedures are developed for the entire Cressie-Read family of statistics, which includes the widely used Pearson and likelihood ratio statistics in a one-way frequency table goodness-of-fit test. This new formulation constitutes a first practical exact improvement over the exhaustive enumeration performed by existing statistical software. The general techniques we develop to exploit the convexity of many statistics are also shown to carry over to contingency table tests, suggesting that they are readily extendible to other tests and test statistics of interest. Our empirical results demonstrate a speed-up of orders of magnitude over the exhaustive computation, significantly extending the practical range for performing exact tests. We also show that the relative speed-up gain increases as the null hypothesis becomes sparser, that computation precision increases with increase in speed-up, and that computation time is very moderately affected by the magnitude of the computed p-value. These qualities make our algorithm especially appealing in the regimes of small samples, sparse null distributions, and rare events, compared to the alternative asymptotic approximations and Monte Carlo samplers. We discuss several established bioinformatics applications, where small sample size, small expected counts in one or more categories (sparseness), and very small p-values do occur. Our computational framework could be applied in these, and similar cases, to improve performance.