外部非局部自相似先验的图像去噪

针对在噪声水平比较高的情况下难以从噪声图像本身提取准确先验信息的问题,提出一种从外部干净图像数据集学习非局部自相似先验信息的图像去噪方法。首先用高斯混合模型学习外部干净图像的非局部自相似先验信息,其次利用最大后验概率估计的方法找到与噪声图像块最匹配的外部先验信息,最后利用外部先验对噪声图像块进行稀疏表示。实验对比表明,所提算法在去除噪声的同时可以较好地保留图像的细节信息,使图像数据集的平均峰值信噪比提高0.18 dB以上。     

Implicit expectiles and measures of implied volatility

It is well known that the normal distribution is inadequate in capturing the skewed and heavy-tailed behaviour of exchange rate returns. To this end, various flexible distributions that are capable of modelling the asymmetric and tailed behaviour of returns have been proposed. In this paper, we investigate the performance of the generalized lambda distribution (GLD) to capture the skewed and leptokurtic behaviour of exchange rate returns. We do this by conducting a comprehensive numerical study to compare the performance of the GLD against the performances of the skewed t distribution, the unbounded Johnson family of distributions and the normal inverse Gaussian (NIG) distribution. Our results suggest that in terms of the value-at-risk and expected shortfall, the GLD shows at least similar performance to the skewed t distribution and the NIG distribution. Considering the ease in GLD’s use for random variate generation in Monte Carlo simulations, we conclude that the GLD can be a good alternative in various financial applications where modelling of the heavy tail behaviour is critical.     

GEFCom2012 hierarchical load forecasting: Gradient boosting machines and Gaussian processes

This report discusses methods for forecasting hourly loads of a US utility as part of the load forecasting track of the Global Energy Forecasting Competition 2012 hosted on Kaggle. The methods described (gradient boosting machines and Gaussian processes) are generic machine learning/regression algorithms, and few domain-specific adjustments were made. Despite this, the algorithms were able to produce highly competitive predictions, which can hopefully inspire more refined techniques to compete with state-of-the-art load forecasting methodologies.     

Copula Gaussian graphical models with penalized ascent Monte Carlo EM algorithm

Typical data that arise from surveys, experiments, and observational studies include continuous and discrete variables. In this article, we study the interdependence among a mixed (continuous, count, ordered categorical, and binary) set of variables via graphical models. We propose an ?₁‐penalized extended rank likelihood with an ascent Monte Carlo expectation maximization approach for the copula Gaussian graphical models and establish near conditional independence relations and zero elements of a precision matrix. In particular, we focus on high‐dimensional inference where the number of observations are in the same order or less than the number of variables under consideration. To illustrate how to infer networks for mixed variables through conditional independence, we consider two datasets: one in the area of sports and the other concerning breast cancer.     

FAST SWAPTION PRICING IN GAUSSIAN TERM STRUCTURE MODELS

We propose a fast and accurate numerical method for pricing European swaptions in multifactor Gaussian term structure models. Our method can be used to accelerate the calibration of such models to the volatility surface. The pricing of an interest rate option in such a model involves evaluating a multidimensional integral of the payoff of the claim on a domain where the payoff is positive. In our method, we approximate the exercise boundary of the state space by a hyperplane tangent to the maximum probability point on the boundary and simplify the multidimensional integration into an analytical form. The maximum probability point can be determined using the gradient descent method. We demonstrate that our method is superior to previous methods by comparing the results to the price obtained by numerical integration.     

Predicting recovery rates using logistic quantile regression with bounded outcomes

Logistic quantile regression (LQR) is used for studying recovery rates. It is developed using monotone transformations. Using Moody’s Ultimate Recovery Database, we show that the recovery rates in different partitions of the estimation sample have different distributions, and thus for predicting recovery rates, an error-minimizing quantile point over each of those partitions is determined for LQR. Using an expanding rolling window approach, the empirical results confirm that LQR with the error-minimizing quantile point has better and more robust out-of-sample performance than its competing alternatives, in the sense of yielding more accurate predicted recovery rates. Thus, LQR is a useful alternative for studying recovery rates.     

Unit root tests for panel MTAR model with cross-sectionally dependent error

Unit root tests are constructed for dynamic panels whose component series are momentum threshold autoregressive processes. Gaussian null asymptotics are established for the proposed tests. A Monte–Carlo experiment is conducted to compare finite sample properties of the proposed tests. The tests are illustrated by a real data set.     

Analysis of failure time using threshold regression with semi‐parametric varying coefficients

Many new statistical models may enjoy better interpretability and numerical stability than traditional models in survival data analysis. Specifically, the threshold regression (TR) technique based on the inverse Gaussian distribution is a useful alternative to the Cox proportional hazards model to analyse lifetime data. In this article we consider a semi‐parametric modelling approach for TR and contribute implementational and theoretical details for model fitting and statistical inferences. Extensive simulations are carried out to examine the finite sample performance of the parametric and non‐parametric estimates. A real example is analysed to illustrate our methods, along with a careful diagnosis of model assumptions.     

CONTINUOUSLY MONITORED BARRIER OPTIONS UNDER MARKOV PROCESSES

In this paper, we present an algorithm for pricing barrier options in one‐dimensional Markov models. The approach rests on the construction of an approximating continuous‐time Markov chain that closely follows the dynamics of the given Markov model. We illustrate the method by implementing it for a range of models, including a local Lévy process and a local volatility jump‐diffusion. We also provide a convergence proof and error estimates for this algorithm.     

Gaussian risk models with financial constraints

In this paper, we investigate Gaussian risk models which include financial elements, such as inflation and interest rates. For some general models for inflation and interest rates, we obtain an asymptotic expansion of the finite-time ruin probability for Gaussian risk models. Furthermore, we derive an approximation of the conditional ruin time by an exponential random variable as the initial capital tends to infinity.