Student-t Distribution Research Articles

Forecasting VaRs via hybrid EVT with normal and non-normal filters: A comparative analysis from the Chinese stock market

This paper studies the performance of hybrid methods combining normal and non-normal GARCH-type filters with extreme value theory (EVT) in predicting Value-at-Risk (VaR) for four major stock indices in the Chinese stock market. Based on the out-of-sample VaR forecasts results over the 24 models considered, we find that the hybrid EVT approaches illustrate substantial advantage over the corresponding GARCH-type models with parametric distributions, especially in the lower tail and extremal VaR evaluations (1% and 0.5% VaRs). Overall, the hybrid EVT methods with heavy-tailed filters (std-EVT, sstd-EVT) perform the best, followed by the hybrid EVT approaches with light-tailed filters (norm-EVT, snorm-EVT), and then the GARCH-type models with skewed student-t distribution. The conditional normal, skewed normal and student-t models are rejected and excluded from the Model Confidence Set (MCS) in predicting extremal VaRs for most cases, particularly for the lower tail. Additionally, we find that the results for alternative models in predicting VaRs vary sharply among alternative innovation specifications, but present trivial differences across the volatility models. Furthermore, our results based on the MCS tests and comparative backtests also indicate that the scoring function effectively discriminates predictive performance across methods for the lower tail, in contrast to showing less disparity for the upper tail. This emphasizes the importance of model selection in VaR forecasting performance for the lower tail. The above findings are robust to alternative threshold selections and the rolling-step chosen to update parameters. Similar analyses concerning the out-of-sample performance of the 24 models in predicting the Expected Shortfall (ES) show consistent results overall.

Classification Methods for the Serological Status Based on Mixtures of Skew-Normal and Skew-t Distributions

Gaussian mixture models are widely employed in serological data analysis to discern between seropositive and seronegative individuals. However, serological populations often exhibit significant skewness, making symmetric distributions like Normal or Student-t distributions unreliable. In this study, we propose finite mixture models based on Skew-Normal and Skew-t distributions for serological data analysis. Although these distributions are well established in the literature, their application to serological data needs further exploration, with emphasis on the determination of the threshold that distinguishes seronegative from seropositive populations. Our previous work proposed three methods to estimate the cutoff point when the true serological status is unknown. This paper aims to compare the three cutoff techniques in terms of their reliability to estimate the true threshold value. To attain this goal, we conducted a Monte Carlo simulation study. The proposed cutoff points were also applied to an antibody dataset against four SARS-CoV-2 virus antigens where the true serological status is known. For this real dataset, we also compared the performance of our estimated cutoff points with the ROC curve method, commonly used in situations where the true serological status is known.

Investigating the Impact of Consumption Distribution on CRRA Estimation: Quantile-CCAPM-Based Approach

Abstract Using quantile maximization decision theory, this paper considers a quantile-based Euler equation that states that the asset price is a function of the quantiles of the payoff, consumption growth, the stochastic discount factor, risk aversion, and the distribution of the consumption growth rate. We use a more general distribution assumption (log-elliptical distributions) than the log-normality of the consumption growth rate assumed in the literature. The simulation results show that: (1) the higher the downside risk aversion, the lower the constant relative risk aversion; (2) the heavier the tails of the Student-t distribution, the higher the risk aversion for each level of downside risk aversion; and (3) the curve of the relationship between risk aversion and downside risk aversion shifts upward when the normality assumption is dropped, and the magnitude of this shift is high even for high degrees of freedom of the Student-t distribution. Our results suggest that using normally distributed errors to model stock returns and consumption growth rates could lead to an underestimation of the risk aversion coefficient.

An upper bound and a characterization for Gini’s mean difference based on correlated random variables

In this paper, we obtain an upper bound for the Gini mean difference based on mean, variance and correlation for the case when the variables are correlated. We also derive some closed-form expressions for the Gini mean difference when the random variables have an absolutely continuous joint distribution. We then examine some particular examples based on elliptically contoured distributions, and specifically with multivariate normal and Student-t distributions.

Force-Directed Graph Layouts Revisited: A New Force Based on the T-Distribution.

In this article, we propose the t-FDP model, a force-directed placement method based on a novel bounded short-range force (t-force) defined by Student's t-distribution. Our formulation is flexible, exerts limited repulsive forces for nearby nodes and can be adapted separately in its short- and long-range effects. Using such forces in force-directed graph layouts yields better neighborhood preservation than current methods, while maintaining low stress errors. Our efficient implementation using a Fast Fourier Transform is one order of magnitude faster than state-of-the-art methods and two orders faster on the GPU, enabling us to perform parameter tuning by globally and locally adjusting the t-force in real-time for complex graphs. We demonstrate the quality of our approach by numerical evaluation against state-of-the-art approaches and extensions for interactive exploration.

End-to-End Label Uncertainty Modeling in Speech Emotion Recognition using Bayesian Neural Networks and Label Distribution Learning

To train machine learning algorithms to predict emotional expressions in terms of arousal and valence, annotated datasets are needed. However, as different people perceive others' emotional expressions differently, their annotations are subjective. To account for this, annotations are typically collected from multiple annotators and averaged to obtain ground-truth labels. However, when exclusively trained on this averaged ground-truth, the model is agnostic to the inherent subjectivity in emotional expressions. In this work, we therefore propose an end-to-end Bayesian neural network capable of being trained on a distribution of annotations to also capture the subjectivity-based label uncertainty. Instead of a Gaussian, we model the annotation distribution using Student's t-distribution, which also accounts for the number of annotations available. We derive the corresponding Kullback-Leibler divergence loss and use it to train an estimator for the annotation distribution, from which the mean and uncertainty can be inferred. We validate the proposed method using two in-the-wild datasets. We show that the proposed t-distribution based approach achieves state-of-the-art uncertainty modeling results in speech emotion recognition, and also consistent results in cross-corpora evaluations. Furthermore, analyses reveal that the advantage of a t-distribution over a Gaussian grows with increasing inter-annotator correlation and a decreasing number of annotations available.

Application of Copula Methods in Financial Risk Management: Case of the Zimbabwe Stock Exchange and the Victoria Falls Stock Exchange.

In order to minimize risks and create a safe investing environment, financial risk management is becoming more and more crucial for individuals, financial organizations, and even entire nations. Accurately assessing financial risks and using that information to inform wise investment choices can give an investor a competitive edge as well as significant returns. In actuality, real-world financial variables limit the ability to estimate financial risks. On the other hand, a wealth of data indicates that financial variables typically have asymmetric dependency, skewness, and fat tails. In three ways, the conventional approaches to financial risk management based on normally distributed hypotheses are put to the test by these stylized characteristics of financial variables. First, the univariate normal distribution or other elliptical distributions are unable to adequately fit the distribution of the univariate variable. Second, despite their straightforward tractability, multivariate variables’ extra kurtosis and skewness are not captured by their normal distribution. As a result, the dependence risks associated with multivariate financial variables may be underestimated. Finally, when the joint distribution of various variables is non-elliptical, linear correlation which is typically employed to characterize the dependence of various variables in traditional portfolio risk management is likewise insufficient. This research uses a promising technique based on copulas in conjunction with GARCH and realized volatility models to examine the risks associated with multivariate financial variables in order to address these issues. The multivariate distributions are constructed using copulas in conjunction with GARCH and Realized Volatility models which are then utilized to evaluate portfolio risks in financial market. The findings demonstrate that copula-based models outperform conventional models in fitting financial data. Second, a variety of marginal models have a notable impact on the value at risk of the portfolio, including the GARCH and realized volatility models. Lastly, both the dependence structure and the marginal distribution exhibit notable skewness. Consequently, compared to the normal or Student-t distribution, the skewed Student-t distribution fits some datasets better.

Binary regression model with misclassification and Berkson-type measurement error with student-t distribution

In this article, we introduce a regression model tailored for fitting binary data affected by misclassification in the response variable and Berkson-type measurement error in the covariate. The conventional assumption of a normal distribution for measurement error may inadequately represent atypical observations present in the dataset. To address this limitation, our model incorporates misclassification in the response variable and Berksontype measurement error, employing the Student-t distribution for more robust modeling of these atypical observations. We utilize the cumulative distribution function from the Student-t distribution as the link function, enhancing our ability to capture the dataset’s unique characteristics. Model parameters are estimated via the maximum likelihood method. We conduct a comprehensive Monte Carlo simulation study to thoroughly assess the impact of measurement errors and misclassification. Additionally, we apply the proposed model to a real-world dataset of survivors from the atomic bombing in Japan, showcasing its adaptability and suitability in practical scenarios. Our findings highlight the robustness and flexibility of this model in effectively handling complex binary regression scenarios involving measurement errors and misclassification.

Quantile estimation in fractional Levy Ornstein-Uhlenbeck processes

First we study estimation of the drift parameter in the fractional Ornstein-Uhlenbeck process whose marginal distribution is Student t-distribution. We obtain Spearman’s correlation based estimator, quantile estimator and Brownian excursion based estimator of the drift parameter. Then we study method of moments estimator and quantile estimator in fractional inverse Gaussian and fractional gamma Ornstein-Uhlenbeck processes.

Forecasting risk of European carbon emissions trading market with DySco-SKST model

Influenced by energy prices, macroeconomic factors and policy factors, the price of the European carbon emissions trading market has changed significantly. Effective measurement of price risk of the European carbon emissions trading market is of practical importance for market participants. Two measures Value at Risk (VaR) and Expected shortfall (ES) are used to assess price risk. Based on the dynamic score (DySco) model and skewed Student-t (SKST) distribution, the DySco-SKST model is constructed and used to predict the price risk. The unconditional/conditional coverage tests, dynamic quantile test, Actual over Expected ratio, mean and maximum Absolute Deviation, quantile loss and FZ loss are used to evaluate the VaR and ES prediction performance. The daily spot closing prices of EUAs from January 3, 2013 to November 23, 2018 are used. The empirical results show that the VaR and ES prediction performance of the DySco-SKST model is better than that of the DySco-N and DySco-ST models. The VaR and ES prediction performance is affected by the parameter re-estimation scheme, but not by the parameter re-estimation frequency. The DySco-SKST model is better at predicting VaR and ES under the rolling window than under the expanding window.

EEG based emotion recognition by hierarchical bayesian spectral regression framework

Spectral regression (SR), a graph-based learning regression model, can be used to extract features from graphs to realize efficient dimensionality reduction. However, due to the SR method remains a regularized least squares problem and being defined in L2-norm space, the effect of artifacts in EEG signals cannot be efficiently resisted. In this work, to further improve the robustness of the graph-based regression models, we propose to utilize the prior distribution estimation in the Bayesian framework and develop a robust hierarchical Bayesian spectral regression framework (named HB-SR), which is designed with the hierarchical Bayesian ensemble strategies. In the proposed HB-SR, the impact of noises can be effectively reduced by the adaptive adjustment approach in model parameters with the data-driven manner. Specifically, in the current work, three different distributions have been elaborately designed to enhance the universality of the proposed HB-SR, i.e., Gaussian distribution, Laplace distribution, and Student-t distribution. To objectively evaluate the performance of the HB-SR framework, we conducted both simulation studies and emotion recognition experiments based on emotional EEG signals. Experimental results have consistently indicated that compared with other existing spectral regression methods, the proposed HB-SR can effectively suppress the influence of noises and achieve robust EEG emotion recognition.

A review of recent researches for student t-distribution

The t-distribution, often known as the student t-distribution, can be referred to simply as the t-distribution. The development of the aforementioned concept was initially documented by William Gosse in the year 1908, during his tenure at the renowned Guinness Distillery located in Dublin. Due to the author's inability to publish under his own name, the piece employed the pseudonym "Student". The t-test and its associated theories were further advanced by Ronald Fisher, who referred to this particular distribution as the student distribution. In the field of statistics, the t-distribution is employed to make estimations regarding the mean value of a population that conforms to a normal distribution with an unknown variance. This work employs a literature review methodology to examine the historical development of research on the t-distribution. Additionally, it investigates recent advancements in t-distribution research and its use in many domains. This work aims to offer readers a comprehensive understanding of the various implications associated with the t-distribution, thereby shedding light on potential avenues for future research in this area.

Design and Performance of a Low-Cost, Portable Platelet Counter for Point-of-Care and at-Home Use

Background Patients with recurrent or chronic moderate-to-severe thrombocytopenia can experience a marked reduction in quality of life due to the need for regular blood draws, frequent contact with the health care system, and potential for bleeding complications requiring emergency department visits and/or hospital admissions. To improve quality of life while maintaining effective platelet monitoring, we introduce a portable, point-of-care platelet counter that can be used in any health care setting or at home. Methods Obtaining a platelet count requires three components: a counter, staining modality, and erythrocyte lysing agent. The counting device described here is the Athelas One, a small cylindrical device containing a miniaturized microscope embedded with a control board. A strip containing a stained microfluidic channel approximately 10µm tall and thus suitable for a monolayer of blood cells houses the sample. An ammonium oxalate solution is used to lyse the erythrocytes in the capillary sample. Images of the blood sample are acquired and then analyzed using a convolutional neural network to yield platelet counts. To use the device, a patient pricks his or her finger and collects 20µL of blood in a K2EDTA-coated minivette. The blood is mixed with the lysing agent and inserted into the strip, which in turn is inserted into the device. A platelet count is obtained within 5 minutes. In this observational study, we enrolled 233 adults at least 21 years of age with normal platelet counts at a single teaching hospital. Non-hematological illness was allowed. Each patient's platelet count was obtained using both capillary samples processed on Athelas One and paired anticoagulated venous samples processed on a standard hematology analyzer, the Sysmex XS-1000i (SX). Platelet counts from Athelas One and SX were compared using a Passing-Bablok regression model with a Pearson correlation coefficient. Bland-Altman analysis was also performed. Confidence intervals (CI) were calculated using a Student's t-distribution. Least squares regression modeled the relationship between time necessary to collect capillary samples and bias between Athelas One and SX. Analyses were conducted in R. Results A strong linear relationship was observed between Athelas One and SX: Passing-Bablok regression revealed a slope of 0.98 and a y-intercept estimate of -16.45 (Figure), and the Pearson correlation-coefficient was 0.70. Bland-Altman statistics revealed an average percent difference of -8.66% (95% CI: -6.55% to -10.77%), reflecting a bias of Athelas One to undercount as compared with SX. In an effort to explain the predilection for undercounting, device performance was analyzed as a function of sample collection time. Least squares regression revealed a slope of -1.08 (95% CI: -1.55 to -0.61) and a y-intercept estimate of 8.16 (95% CI: -12.15 to 28.47). The Pearson correlation-coefficient was 0.54. Conclusion Athelas One compared favorably with SX. The bias for undercounting may be a consequence of a pseudothrombocytopenia phenomenon due to platelet activation and clot formation prior to sample collection, which sequesters platelets out of solution. This hypothesis is supported by the fact that longer time needed to collect the capillary sample correlated with larger negative bias between Athelas One and SX. To improve agreement, a number of methods in the counting procedure, namely sample collection, could be altered. A potential solution involves wiping the finger with an anticoagulant prior to sample collection to discourage clot formation. This proof-of-concept analysis demonstrates the plausibility of point-of-care platelet monitoring. Future work will focus on validating Athelas One in thrombocytopenic and thrombocytotic samples.

Modeling and Forecasting Exchange Rate Volatility in West Africa using GARCH models

Abstract This study empirically investigates the nature of exchange rate volatility in the context of West Africa. The study uses daily data on the exchange rates of the West African CFA franc (XOF) in terms of US Dollar. The empirical analysis has been carried out for the period from 13-11-2009 to 18-09-2023, for a total of 5058 observations. We excluded the last 25% of observations in order to evaluate the forecasting accuracy. The exchange rate volatility of the West African CFA franc against the US Dollar is estimated using GARCH models based on normal and student’s t-distribution of innovations. Results show that the ARMA(3,1)-GARCH(1,2) model with student-t distribution is well adequate model to capture the mean and the volatility process of USD-CFA exchange rate log returns. Keywords: Exchange rates, normal and student-t distribution, ARMA-GARCH.

Consistency factor for the MCD estimator at the Student-t distribution

It is well known that trimmed estimators of multivariate scatter, such as the Minimum Covariance Determinant (MCD) estimator, are inconsistent unless an appropriate factor is applied to them in order to take the effect of trimming into account. This factor is widely recommended and applied when uncontaminated data are assumed to come from a multivariate normal model. We address the problem of computing a consistency factor for the MCD estimator in a heavy-tail scenario, when uncontaminated data come from a multivariate Student-t distribution. We derive a remarkably simple computational formula for the appropriate factor and show that it reduces to an even simpler analytic expression in the bivariate case. Exploiting our formula, we then develop a robust Monte Carlo procedure for estimating the usually unknown number of degrees of freedom of the assumed and possibly contaminated multivariate Student-t model, which is a necessary ingredient for obtaining the required consistency factor. Finally, we provide substantial simulation evidence about the proposed procedure and apply it to data from image processing and financial markets.

Hyaluronic Acid Rectal Spacer Stability during Radiation Therapy for Localized Prostate Cancer: An Intercontinental Study.

Despite IGRT and IMRT current techniques, rectal toxicity remains a significant problem after prostate cancer radiation therapy but implanted rectal spacers have successfully reduced toxicity rates. We are reporting the results of an intercontinental prospective rectal spacer trial performed at 13 centers in Spain, Australia, and USA. Our hypothesis was that the separation created between the prostate and anterior rectal wall was stable between the time of implant and a 3-month follow-up. Our prospective multicenter study was approved by the corresponding IRBs and patients signed informed consent. It was performed between February - June 2021. Patients were imaged using T2 MRI immediately post-implant (MRI-1) and at 3 months (MRI-2). We analyzed the dimensions of hyaluronic acid (HA) rectal spacer inserted for low - intermediate risk prostate cancer treated with EBRT. The rectal displacement was determined by measuring the separation at 3 different levels: prostate midline, midgland +1cm (superior), and midgland -1 cm (inferior), from the posterior prostate capsule to the anterior rectal wall. The core laboratory performed the measurement for all sites. The confidence interval (CI) was computed using a Student's t-distribution. A total of 136 patients randomized to the Barrigel arm underwent HA rectal spacing with 100% placement success rate. There were no device failures or surgical complications. Of these, 6 were lost to follow-up. The averages of the remaining 130 patients at the 3 perirectal distances were 13.04 mm +/- 3.1 mm and 12.79 mm +/- 3.5 mm for MRI-1 and MRI-2, respectively with an average difference of -0.17 mm +/- 3.48 mm. Additional parameters are listed on the table. The results demonstrate the stability of the HA-created separation at the three different prostatic levels for up to 3 months. These findings show dimensional stability well within standard clinical margins. This indicates reliability for HA use in most clinics, as the results are relevant in the setting of dose escalation or ultra-hypofractionation schedules, as well as conventional fractionation.

Modelling and Forecasting Volatility on Electric Power Exchange SEEPEX

Research Question: The launch and the beginning of trade on the South East Electric Power Exchange (SEEPEX) in Belgrade, early in 2016, opened the issue of forecasting volatility and price movements in the market. Motivation: The issue is of vital importance for all market actors for the purpose of maximising profits, reducing risks, planning production and making investment decisions. Forecasting volatility and price movements in electric power markets is important for traders with profit maximisation and yield-to-risk ratio optimisation in mind and, equally, for producers, large industrial consumers, investors and portfolio managers. Idea: Exploring models and techniques to forecast volatility in electricity markets and subsequently testing statistical methods based on time series data, the ARMA-GARCH being the preferred model, with a view to identifying optimal methods for this market. The volatility of the power market and price movements have been tested during a given period. The results can be used to gauge market parameters and opportunities to extrapolate future volatility and movements in electricity prices. Data: For the purposes of this analysis, a time series involving price movements and trade volumes were used, covering a period between the SEEPEX trade launch and the end of 2019. Tools: In the empirical part of the paper, "Stata 13" statistical and econometric software was used to explore stylised facts and model the volatility of SEEPEX electricity price returns. Findings: The authors offer an overview of different methods used in the research, having selected different specifications of the ARMA-GARCH model as the most reliable in predicting volatility in the given market. The exponential GARCH model with student-t error distribution is believed to have provided the best overall performance in modelling the SEEPEX return volatility, as well as the best volatility forecast. Contribution: This is one of the first empirical studies of the Serbian power market that deals with risk modelling. Forecasting time-varying electricity exchange volatility is important for all market participants interested in variance forecasts to be used to calculate risk and hedging measures.

BIT ERROR PERFORMANCE ENHANCEMENT FOR UNDERWATER ACOUSTIC NOISE CHANNEL BY USING CHANNEL CODING

The harm that underwater noise pollution poses to aquatic ecosystems and the resources that support it are being acknowledged on a worldwide scale. Fisheries and ecotourism are only two of the important businesses that are impacted by noise pollution. Reducing underwater impact noise is a major challenge for underwater acoustic communication systems. However, the implementation of noise reduction measures (noise abatement) remains limited. Most communication systems assume that the noise is both additive and Gaussian. Underwater Acoustic Noise (UWAN) systems generally perform poorly because of the often large non-Gaussian components in intermittent noise in the ocean. This study presents an experimental model (Dolphin-EAR DE200 Series) sound channel noise underwater at Lake Diyala Hamrin, Iraq, using a hydrophone model. Low data volume, multipath propagation, low bandwidth, and higher bit error rate (BER) of received data are major issues for underwater communication systems. In this paper, the Underwater Acoustic Channel (UWAC) aspect is evaluated and an error performance term is determined from the noise in the Student's t-distribution. In addition, Signals using binary phase-shift keying (BPSK) and quadrature phase-shift keying (QPSK) are used to generate error power analysis.

Laplace Distribution Based Online Identification of Linear Systems With Robust Recursive Expectation–Maximization Algorithm

The robust online identification problem of linear systems is considered in this paper using a faster robust recursive expectation-maximization (RREM) framework. To improve the convergence rate, the outliers, which would deteriorate the identified models, are accommodated with a Laplace distribution instead of Student's t-distribution. Then, the recursive transformation of the maximum likelihood function is realized with a recursive Q-function. The extensively recognized autoregressive exogenous (ARX) models are used for the description of general linear systems. As a result, the unknown parameters, including the regression coefficient vector of the ARX models, the variance of the noise without outliers, and the scale parameter of the Laplace distribution, are determined in a recursive manner. The performance of the proposed approach is tested with a simulated continuous fermentation reactor (CFR) system example and a coupled-tank experiment.

Design of restricted normalizing flow towards arbitrary stochastic policy with computational efficiency

This paper proposes a new design method for a stochastic control policy using a normalizing flow (NF). In reinforcement learning (RL), the policy is usually modeled as a distribution model with trainable parameters. When this parameterization has less expressiveness, it would fail to acquiring the optimal policy. A mixture model has capability of a universal approximation, but it with too much redundancy increases the computational cost, which can become a bottleneck when considering the use of real-time robot control. As another approach, NF, which is with additional parameters for invertible transformation from a simple stochastic model as a base, is expected to exert high expressiveness and lower computational cost. However, NF cannot compute its mean analytically due to complexity of the invertible transformation, and it lacks reliability because it retains stochastic behaviors after deployment for robot controller. This paper therefore designs a restricted NF (RNF) that achieves an analytic mean by appropriately restricting the invertible transformation. In addition, the expressiveness impaired by this restriction is regained using bimodal student-t distribution as its base, so-called Bit-RNF. In RL benchmarks, Bit-RNF policy outperformed the previous models. Finally, a real robot experiment demonstrated the applicability of Bit-RNF policy to real world.