Goodness-of-fit statistics for location-scale distributions

This dissertation is concerned with the problem of assessing the fit of a hypothesized parametric family of distributions to data. A nontraditional use of the chi-square and likelihood ratio statistics is considered in which the number of cells is allowed to increase as the sample size increases. A new goodness-of-fit statistic k(\u272), based on the Pearson correlation coefficient of points of a P-P (percent versus percent) probability plot, is developed for testing departures from the normal, Gumbel, and exponential distributions. A statistic r(\u272) based on the Pearson correlation coefficient of points on a Q-Q (quantile versus quantile) probability plot is also considered. A new qualitative method based on the P-P probability plot is developed, for assessing the goodness of fit of nonhypothesized probability models to data. This method is not limited to location-scale distributions. Curves were fitted through the Monte Carlo percentiles to obtain formulas for the percentiles of k(\u272) and r(\u272) Statistics and Probability; An extensive Monte Carlo power comparison was performed for the normal, Gumbel, and exponential distributions. The statistics examined included those mentioned earlier, statistics based on the moments, statistics based on the empirical distribution function, and the commonly used Shapiro-Wilk statistic. The results of the power study are summarized, and general recommendations are given for the use of these Statistics and Probability

Testing for stochastic dominance in social networks

Also can be found at https://ideas.repec.org/p/adl/wpaper/2017-02.htmlThis paper illustrates how stochastic dominance criteria can be used to rank social networks in terms of efficiency, and develops statistical inference procedures for as- sessing these criteria. The tests proposed can be viewed as extensions of a Pearson goodness-of-fit test and a studentized maximum modulus test often used to partially rank income distributions and inequality measures. We establish uniform convergence of the empirical size of the tests to the nominal level, and show their consistency under the usual conditions that guarantee the validity of the approximation of a multinomial distribution to a Gaussian distribution. Furthermore, we propose a bootstrap method that enhances the finite-sample properties of the tests. The performance of the tests is illustrated via Monte Carlo experiments and an empirical application to risk sharing networks in rural IndiaFirmin Doko Tchatoka, Robert Garrard and Virginie Masso

Flexible specification testing in quantile regression models

We propose three novel consistent specification tests for quantile regression models which generalize former tests in three ways. First, we allow the covariate effects to be quantile-dependent and nonlinear. Second, we allow parameterizing the conditional quantile functions by appropriate basis functions, rather than parametrically. We are thereby able to test for general functional forms, while retaining linear effects as special cases. In both cases, the induced class of conditional distribution functions is tested with a Cramér–von Mises type test statistic for which we derive the theoretical limit distribution and propose a bootstrap method. Third, a modified test statistic is derived to increase the power of the tests. We highlight the merits of our tests in a detailed MC study and two real data examples. Our first application to conditional income distributions in Germany indicates that there are not only still significant differences between East and West but also across the quantiles of the conditional income distributions, when conditioning on age and year. The second application to data from the Australian national electricity market reveals the importance of using interaction effects for modeling the highly skewed and heavy-tailed distributions of energy prices conditional on day, time of day and demand.Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659Peer Reviewe

Additive Cox proportional hazards models for next-generation sequencing data

Eighty-Nine Non-Small Cell Lung Cancer (NSCLC) patients experience chromosomal rearrangements called Copy Number Alteration (CNA), where the cells have abnormal number of copies in one or more regions in their genome, this genetic alteration are known to drive cancer development. An important aim of this thesis is to propose a way to combine the clinical covariate as fixed predictors with CNAs genomics windows as smoothing terms using the penalized additive Cox Proportional Hazards (PH) model. Most of the proposed prediction methods assume linearity of the CNAs genomic windows along with the clinical covariates. However, the continuous covariates can affect the hazard via more complicated nonlinear functional forms. Therefore, Cox PH model with continuous covariate are likely misspecified, because it is not fitting the correct functional form for the continuous covariates. Some reports of the work on combining the clinical covariates with high-dimensional genomic data in a clinical genomic prediction are based on standard Cox PH model. Most of them focus on applying variable selection to high-dimensional CNA genomic data. Our main interest is to propose a variable selection procedure to select important nonlinear effects from CNAs genomic-windows. Two different approaches of feature selection are presented which are discrete and shrinkage. Discrete feature selection is based on penalized univariate variable selection, which identify the subset of the CNAs genomic-windows have the strongest effects on the survival time, while feature selection by shrinkage works by adding a second penalty to the penalized partial log-likelihood, that leads to penalizing the smoothing coefficients in the model, as a result some of the smoothing coefficient are being set to the zero. For the NSCLC dataset, we find that the size of the tumor cells and spread cancer into the lymph nodes are significant factors that increase the hazard of the patients survival, and the estimate of the smooth log hazard ratio curves identify that some of the significant CNA genomic-windows contribute a higher or lower hazard of death to the survival of some significant CNA genomic-windows across the genome

Sensitivity Analysis using Approximate Moment Condition Models

We consider inference in models defined by approximate moment conditions. We show that near-optimal confidence intervals (CIs) can be formed by taking a generalized method of moments (GMM) estimator, and adding and subtracting the standard error times a critical value that takes into account the potential bias from misspecification of the moment conditions. In order to optimize performance under potential misspecification, the weighting matrix for this GMM estimator takes into account this potential bias, and therefore differs from the one that is optimal under correct specification. To formally show the near-optimality of these CIs, we develop asymptotic efficiency bounds for inference in the locally misspecified GMM setting. These bounds may be of independent interest, due to their implications for the possibility of using moment selection procedures when conducting inference in moment condition models. We apply our methods in an empirical application to automobile demand, and show that adjusting the weighting matrix can shrink the CIs by a factor of 3 or more

Sensitivity Analysis using Approximate Moment Condition Models

We consider inference in models defined by approximate moment conditions. We show that near-optimal confidence intervals (CIs) can be formed by taking a generalized method of moments (GMM) estimator, and adding and subtracting the standard error times a critical value that takes into account the potential bias from misspecification of the moment conditions. In order to optimize performance under potential misspecification, the weighting matrix for this GMM estimator takes into account this potential bias, and therefore differs from the one that is optimal under correct specification. To formally show the near-optimality of these CIs, we develop asymptotic efficiency bounds for inference in the locally misspecified GMM setting. These bounds may be of independent interest, due to their implications for the possibility of using moment selection procedures when conducting inference in moment condition models. We apply our methods in an empirical application to automobile demand, and show that adjusting the weighting matrix can shrink the CIs by a factor of 3 or more