Nonparametric Evaluation of Quantitative Traits in Population-Based Association Studies when the Genetic Model is Unknown

Statistical association between a single nucleotide polymorphism (SNP) genotype and a quantitative trait in genome-wide association studies is usually assessed using a linear regression model, or, in the case of non-normally distributed trait values, using the Kruskal-Wallis test. While linear regression models assume an additive mode of inheritance via equi-distant genotype scores, Kruskal-Wallis test merely tests global differences in trait values associated with the three genotype groups. Both approaches thus exhibit suboptimal power when the underlying inheritance mode is dominant or recessive. Furthermore, these tests do not perform well in the common situations when only a few trait values are available in a rare genotype category (disbalance), or when the values associated with the three genotype categories exhibit unequal variance (variance heterogeneity). We propose a maximum test based on Marcus-type multiple contrast test for relative effect sizes. This test allows model-specific testing of either dominant, additive or recessive mode of inheritance, and it is robust against variance heterogeneity. We show how to obtain mode-specific simultaneous confidence intervals for the relative effect sizes to aid in interpreting the biological relevance of the results. Further, we discuss the use of a related all-pairwise comparisons contrast test with range preserving confidence intervals as an alternative to Kruskal-Wallis heterogeneity test. We applied the proposed maximum test to the Bogalusa Heart Study dataset, and gained a remarkable increase in the power to detect association, particularly for rare genotypes. Our simulation study also demonstrated that the proposed non-parametric tests control family-wise error rate in the presence of non-normality and variance heterogeneity contrary to the standard parametric approaches. We provide a publicly available R library nparcomp that can be used to estimate simultaneous confidence intervals or compatible multiplicity-adjusted p-values associated with the proposed maximum test.

Estimation of dynamic latent variable models using simulated nonparametric moments

Given a model that can be simulated, conditional moments at a trial parameter value can be calculated with high accuracy by applying kernel smoothing methods to a long simulation. With such conditional moments in hand, standard method of moments techniques can be used to estimate the parameter. Since conditional moments are calculated using kernel smoothing rather than simple averaging, it is not necessary that the model be simulable subject to the conditioning information that is used to define the moment conditions. For this reason, the proposed estimator is applicable to general dynamic latent variable models. Monte Carlo results show that the estimator performs well in comparison to other estimators that have been proposed for estimation of general DLV models.

Modeling U.S. Inflation Dynamics: A Bayesian Nonparametric Approach

This paper uses an infinite hidden Markov model (IIHMM) to analyze U.S. inflation dynamics with a particular focus on the persistence of inflation. The IHMM is a Bayesian nonparametric approach to modeling structural breaks. It allows for an unknown number of breakpoints and is a flexible and attractive alternative to existing methods. We found a clear structural break during the recent financial crisis. Prior to that, inflation persistence was high and fairly constant.

Estimation of dynamic latent variable models using simulated nonparametric moments

Abstract. Given a model that can be simulated, conditional moments at a trial parameter value can be calculated with high accuracy by applying kernel smoothing methods to a long simulation. With such conditional moments in hand, standard method of moments techniques can be used to estimate the parameter. Because conditional moments are calculated using kernel smoothing rather than simple averaging, it is not necessary that the model be simulable subject to the conditioning information that is used to define the moment conditions. For this reason, the proposed estimator is applicable to general dynamic latent variable models. It is shown that as the number of simulations diverges, the estimator is consistent and a higher-order expansion reveals the stochastic difference between the infeasible GMM estimator based on the same moment conditions and the simulated version. In particular, we show how to adjust standard errors to account for the simulations. Monte Carlo results show how the estimator may be applied to a range of dynamic latent variable (DLV) models, and that it performs well in comparison to several other estimators that have been proposed for DLV models.

Augmented myocardial methionine-enkephalin in a murine model of cardiac angiotensin II-overexpression.

INTRODUCTION: The endogenous opioid system has been reported to interact with both the cardiac sympathetic and renin-angiotensin systems in exerting a local regulatory action on the heart. The goal of this investigation was to examine how cardiac levels of enkephalin production are altered in the development of normotensive primary hypertrophy due to elevated intra-cardiac angiotensin II (Ang II) production. METHODS: Atrial and ventricular methionine-enkephalin (ME) levels were measured by quantitative radioimmunoassay in 14 and 28-week-old male transgenic mice (TG1306/1R) and control mice. The TG1306/1R exhibit cardiac specific Ang II overexpression and cardiac hypertrophy, but not hypertension. RESULTS: TG1306/1R mice had significantly higher heart/body weight ratios (15-20%) than control littermates at both 14 (p=0.02) and 28 weeks (p=0.04). Relative to controls, ME content was significantly elevated (approximately two-fold) in atria and ventricles in the older 28-week TG1306/1R mice only. A significant inverse correlation between heart size and ME level was observed for 28-week TG1306/1R only. CONCLUSIONS: We have provided evidence that a marked elevation of myocardial enkephalin level is observed in the established (but not early) phase of cardiac hypertrophy associated with cardiac-specific Ang II-overexpression. This study identifies a potentially important relationship between two endogenous peptidergic signalling systems involved in the regulation of growth and function of the hypertrophic heart.

Interleukin-17 is a critical mediator of vaccine-induced reduction of Helicobacter infection in the mouse model.

BACKGROUND & AIMS: Despite the proven ability of immunization to reduce Helicobacter infection in mouse models, the precise mechanism of protection has remained elusive. This study explores the possibility that interleukin (IL)-17 plays a role in the reduction of Helicobacter infection following vaccination of wild-type animals or in spontaneous reduction of bacterial infection in IL-10-deficient mice. METHODS: In mice, reducing Helicobacter infection, the levels and source of IL-17 were determined and the role of IL-17 in reduction of Helicobacter infection was probed by neutralizing antibodies. RESULTS: Gastric IL-17 levels were strongly increased in mice mucosally immunized with urease plus cholera toxin and challenged with Helicobacter felis as compared with controls (654 +/- 455 and 34 +/- 84 relative units for IL-17 messenger RNA expression [P < .01] and 6.9 +/- 8.4 and 0.02 +/- 0.04 pg for IL-17 protein concentration [P < .01], respectively). Flow cytometry analysis showed that a peak of CD4(+)IL-17(+) T cells infiltrating the gastric mucosa occurred in immunized mice in contrast to control mice (4.7% +/- 0.3% and 1.4% +/- 0.3% [P < .01], respectively). Gastric mucosa-infiltrating CD4(+)IL-17(+) T cells were also observed in IL-10-deficient mice that spontaneously reduced H felis infection (4.3% +/- 2.3% and 2% +/- 0.6% [P < .01], for infected and noninfected IL-10-deficient mice, respectively). In wild-type immunized mice, intraperitoneal injection of anti-IL-17 antibodies significantly inhibited inflammation and the reduction of Helicobacter infection in comparison with control antibodies (1 of 12 mice vs 9 of 12 mice reduced Helicobacter infection [P < .01], respectively). CONCLUSIONS: IL-17 plays a critical role in the immunization-induced reduction of Helicobacter infection from the gastric mucosa.

Optimal capital structure: a trade-off model and its empirical testing

In the present research we have set forth a new, simple, Trade-Off model that would allow us to calculate how much debt and, by default, how much equity a company should have, using easily available information and calculating the cost of debt dynamically on the basis of the effect that the capital structure of the company has on the risk of bankruptcy; in an attempt to answer this question. The proposed model has been applied to the companies that make up the Dow Jones Industrial Average (DJIA) in 2007. We have used consolidated financial data from 1996 to 2006, published by Bloomberg. We have used simplex optimization method to find the debt level that maximizes firm value. Then, we compare the estimated debt with real debt of companies using statistical nonparametric Mann-Whitney. The results indicate that 63% of companies do not show a statistically significant difference between the real and the estimated debt.

Using a Bayesian model for bankruptcy prediction : a comparative approach

The purpose of this study is to examine the impact of the choice of cut-off points, sampling procedures, and the business cycle on the accuracy of bankruptcy prediction models. Misclassification can result in erroneous predictions leading to prohibitive costs to firms, investors and the economy. To test the impact of the choice of cut-off points and sampling procedures, three bankruptcy prediction models are assessed- Bayesian, Hazard and Mixed Logit. A salient feature of the study is that the analysis includes both parametric and nonparametric bankruptcy prediction models. A sample of firms from Lynn M. LoPucki Bankruptcy Research Database in the U. S. was used to evaluate the relative performance of the three models. The choice of a cut-off point and sampling procedures were found to affect the rankings of the various models. In general, the results indicate that the empirical cut-off point estimated from the training sample resulted in the lowest misclassification costs for all three models. Although the Hazard and Mixed Logit models resulted in lower costs of misclassification in the randomly selected samples, the Mixed Logit model did not perform as well across varying business-cycles. In general, the Hazard model has the highest predictive power. However, the higher predictive power of the Bayesian model, when the ratio of the cost of Type I errors to the cost of Type II errors is high, is relatively consistent across all sampling methods. Such an advantage of the Bayesian model may make it more attractive in the current economic environment. This study extends recent research comparing the performance of bankruptcy prediction models by identifying under what conditions a model performs better. It also allays a range of user groups, including auditors, shareholders, employees, suppliers, rating agencies, and creditors' concerns with respect to assessing failure risk.

The Seemingly Unrelated Dynamic Cointegration Regression Model and Testing for Purching Power Parity.

This paper studies seemingly unrelated linear models with integrated regressors and stationary errors. By adding leads and lags of the first differences of the regressors and estimating this augmented dynamic regression model by feasible generalized least squares using the long-run covariance matrix, we obtain an efficient estimator of the cointegrating vector that has a limiting mixed normal distribution. Simulation results suggest that this new estimator compares favorably with others already proposed in the literature. We apply these new estimators to the testing of purchasing power parity (PPP) among the G-7 countries. The test based on the efficient estimates rejects the PPP hypothesis for most countries.

Exact Nonparametric Two-Sample Homogeneity Tests for Possibly Discrete Distributions.

In this paper, we study several tests for the equality of two unknown distributions. Two are based on empirical distribution functions, three others on nonparametric probability density estimates, and the last ones on differences between sample moments. We suggest controlling the size of such tests (under nonparametric assumptions) by using permutational versions of the tests jointly with the method of Monte Carlo tests properly adjusted to deal with discrete distributions. We also propose a combined test procedure, whose level is again perfectly controlled through the Monte Carlo test technique and has better power properties than the individual tests that are combined. Finally, in a simulation experiment, we show that the technique suggested provides perfect control of test size and that the new tests proposed can yield sizeable power improvements.

Nonparametric Instrumental Regression

The focus of the paper is the nonparametric estimation of an instrumental regression function P defined by conditional moment restrictions stemming from a structural econometric model : E[Y-P(Z)|W]=0 and involving endogenous variables Y and Z and instruments W. The function P is the solution of an ill-posed inverse problem and we propose an estimation procedure based on Tikhonov regularization. The paper analyses identification and overidentification of this model and presents asymptotic properties of the estimated nonparametric instrumental regression function.

Inference for nonparametric high-frequency estimators with an application to time variation in betas

We consider the problem of conducting inference on nonparametric high-frequency estimators without knowing their asymptotic variances. We prove that a multivariate subsampling method achieves this goal under general conditions that were not previously available in the literature. We suggest a procedure for a data-driven choice of the bandwidth parameters. Our simulation study indicates that the subsampling method is much more robust than the plug-in method based on the asymptotic expression for the variance. Importantly, the subsampling method reliably estimates the variability of the Two Scale estimator even when its parameters are chosen to minimize the finite sample Mean Squared Error; in contrast, the plugin estimator substantially underestimates the sampling uncertainty. By construction, the subsampling method delivers estimates of the variance-covariance matrices that are always positive semi-definite. We use the subsampling method to study the dynamics of financial betas of six stocks on the NYSE. We document significant variation in betas within year 2006, and find that tick data captures more variation in betas than the data sampled at moderate frequencies such as every five or twenty minutes. To capture this variation we estimate a simple dynamic model for betas. The variance estimation is also important for the correction of the errors-in-variables bias in such models. We find that the bias corrections are substantial, and that betas are more persistent than the naive estimators would lead one to believe.

CAMCR: Computer assisted mixture model analysis for capture-recapture count data

Population size estimation with discrete or nonparametric mixture models is considered, and reliable ways of construction of the nonparametric mixture model estimator are reviewed and set into perspective. Construction of the maximum likelihood estimator of the mixing distribution is done for any number of components up to the global nonparametric maximum likelihood bound using the EM algorithm. In addition, the estimators of Chao and Zelterman are considered with some generalisations of Zelterman’s estimator. All computations are done with CAMCR, a special software developed for population size estimation with mixture models. Several examples and data sets are discussed and the estimators illustrated. Problems using the mixture model-based estimators are highlighted.

CAMCR: Computer-Assisted Mixture model analysis for Capture–Recapture count data

Population size estimation with discrete or nonparametric mixture models is considered, and reliable ways of construction of the nonparametric mixture model estimator are reviewed and set into perspective. Construction of the maximum likelihood estimator of the mixing distribution is done for any number of components up to the global nonparametric maximum likelihood bound using the EM algorithm. In addition, the estimators of Chao and Zelterman are considered with some generalisations of Zelterman’s estimator. All computations are done with CAMCR, a special software developed for population size estimation with mixture models. Several examples and data sets are discussed and the estimators illustrated. Problems using the mixture model-based estimators are highlighted.

Geostatistical radar-raingauge combination with nonparametric correlograms: methodological considerations and application in Switzerland

Modelling spatial covariance is an essential part of all geostatistical methods. Traditionally, parametric semivariogram models are fit from available data. More recently, it has been suggested to use nonparametric correlograms obtained from spatially complete data fields. Here, both estimation techniques are compared. Nonparametric correlograms are shown to have a substantial negative bias. Nonetheless, when combined with the sample variance of the spatial field under consideration, they yield an estimate of the semivariogram that is unbiased for small lag distances. This justifies the use of this estimation technique in geostatistical applications. Various formulations of geostatistical combination (Kriging) methods are used here for the construction of hourly precipitation grids for Switzerland based on data from a sparse realtime network of raingauges and from a spatially complete radar composite. Two variants of Ordinary Kriging (OK) are used to interpolate the sparse gauge observations. In both OK variants, the radar data are only used to determine the semivariogram model. One variant relies on a traditional parametric semivariogram estimate, whereas the other variant uses the nonparametric correlogram. The variants are tested for three cases and the impact of the semivariogram model on the Kriging prediction is illustrated. For the three test cases, the method using nonparametric correlograms performs equally well or better than the traditional method, and at the same time offers great practical advantages. Furthermore, two variants of Kriging with external drift (KED) are tested, both of which use the radar data to estimate nonparametric correlograms, and as the external drift variable. The first KED variant has been used previously for geostatistical radar-raingauge merging in Catalonia (Spain). The second variant is newly proposed here and is an extension of the first. Both variants are evaluated for the three test cases as well as an extended evaluation period. It is found that both methods yield merged fields of better quality than the original radar field or fields obtained by OK of gauge data. The newly suggested KED formulation is shown to be beneficial, in particular in mountainous regions where the quality of the Swiss radar composite is comparatively low. An analysis of the Kriging variances shows that none of the methods tested here provides a satisfactory uncertainty estimate. A suitable variable transformation is expected to improve this.