![]() ![]() " Optimal Capital Structure with Endogenous Default and Volatility Risk,"Ģ012-02, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa. Swiss Finance Institute Research Paper Seriesġ5-08, Swiss Finance Institute, revised Mar 2015. " Pricing and Disentanglement of American Puts in the Hyper-Exponential Jump-Diffusion Model," Markus LEIPPOLD & Nikola VASILJEVIC, 2015.The simulation studies lend further support to our theoretical claims and additionally show excellent finite-sample size and power properties of the proposed test. ![]() Moreover, the proposed method is asymptotically exact and has satisfactory power properties for testing very general functionals of the high-dimensional parameters. This is especially significant given the fact that the former is a fundamental condition underlying most of the theoretical development in high-dimensional statistics, while the latter is a key condition used to establish variable selection properties. For example, we can directly conduct inference on the sparsity level of the model parameters and the minimum signal strength. This projection automatically takes into account the structure of the null hypothesis and allows us to study formal inference for a number of long-standing problems. The proposed inference is centered around a new class of estimators defined as l 1 projection of the initial guess of the unknown onto the space defined by the null. We propose a new inference method developed around the hypothesis adaptive projection pursuit framework, which solves the testing problems in the most general case. However, the problem of testing general and complex hypotheses remains widely open. ![]() Existing literature has considered less than a handful of hypotheses, such as testing individual coordinates of the model parameter. This article develops a framework for testing general hypothesis in high-dimensional models where the number of variables may far exceed the number of observations. Simulation studies illustrate finite sample properties of our procedure. The main technical result are the development of a Bahadur representation of the debiasing estimator that is uniform over a range of quantiles and uniform convergence of the quantile process to the Brownian bridge process, which are of independent interest. Furthermore, we develop a Kolmogorov-Smirnov test in a location-shift high-dimensional models and confidence sets that are uniformly valid for many quantile values. We develop high-dimensional regression rank scores and show how to use them to estimate the sparsity function, as well as how to adapt them for inference involving the quantile regression process. In this paper we consider a debiasing approach for the uniform testing problem. Additionally, inference in quantile regression requires estimation of the so called sparsity function, which depends on the unknown density of the error. However, it is frequently desirable to formulate tests based on the quantile regression process, as this leads to more robust tests and more stable confidence sets. The theory of debiased estimators can be developed in the context of quantile regression models for a fixed quantile value. Hypothesis tests in models whose dimension far exceeds the sample size can be formulated much like the classical studentized tests only after the initial bias of estimation is removed successfully. ![]()
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