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Essays in Distributed High-Dimensional Statistics and Limit Order Book.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Essays in Distributed High-Dimensional Statistics and Limit Order Book./
作者:	Yang, Zhuoyi.
面頁冊數:	1 online resource (182 pages)
附註:	Source: Dissertations Abstracts International, Volume: 83-11, Section: B.
Contained By:	Dissertations Abstracts International83-11B.
標題:	Statistics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29067648click for full text (PQDT)
ISBN:	9798438750017

Essays in Distributed High-Dimensional Statistics and Limit Order Book.
Yang, Zhuoyi.

Essays in Distributed High-Dimensional Statistics and Limit Order Book. - 1 online resource (182 pages)

Source: Dissertations Abstracts International, Volume: 83-11, Section: B.

Thesis (Ph.D.)--New York University, 2022.

Includes bibliographical references

The development of modern technology brings great opportunity and challenges to data analysis and statistical estimation. On example is the capability of acquisition of data with unprecedented size that cannot be fit into a single machine, which calls for the development of distributed estimation and inferential approaches. Another example is the transition from old quote-driven markets to order-driven markets with high frequency data. In this dissertation we address several challenges in distributed statistics and limit order modeling in high frequency trading.Despite a vast literature on support vector machine (SVM), much less is known about the inferential properties of SVM, especially in a distributed setting. We propose a multi-round distributed linear-type (MDL) estimator for conducting inference for linear SVM. The proposed estimator is computationally efficient. In particular, it only requires an initial SVM estimator and then successively refines the estimator by solving simple weighted least squares problem. Theoretically, we establish the Bahadur representation of the estimator. Based on the representation, the asymptotic normality is further derived, which shows that the MDL estimator achieves the optimal statistical efficiency, i.e., the same efficiency as the classical linear SVM applying to the entire data set in a single machine setup. Moreover, our asymptotic result avoids the condition on the number of machines or data batches, which is commonly assumed in distributed estimation literature, and allows the case of diverging dimension. We provide simulation studies to demonstrate the performance of the proposed MDL estimator.The estimation and support recovery for high-dimensional linear regression model with heavy-tailed noise is a challenge problem, especially in a distributed setting. To deal with heavy-tailed noise whose variance can be infinite, we adopt the quantile regression loss function instead of the commonly used squared loss. However, the non-smooth quantile loss poses new challenges to high-dimensional distributed estimation in both computation and theoretical development. To address the challenge, we transform the response variable and establish a new connection between quantile regression and ordinary linear regression. Then, we provide a distributed estimator that is both computationally and communicationally efficient, where only the gradient information is communicated at each iteration. Theoretically, we show that, after a constant number of iterations, the proposed estimator achieves a near-oracle convergence rate without any restriction on the number of machines. Moreover, we establish the theoretical guarantee for the support recovery. The simulation analysis is provided to demonstrate the effectiveness of our method. With the help of limit order book and high frequency data, all agents who want to buy or sell equity can post their offers at whatever prices and quantities they choose. The main challenge is to tractably model the complex micro-structure and evolution of the limit order book. We model the order book as two coupled measure-valued stochastic processes where the limit and market orders arrive at the book according to independent Poisson processes. We assume that the price at which the limit orders are placed follows a distribution that depends on the current best price on both sides. We consider a high frequency regime where the rates of the incoming orders are large and the limit orders are placed close to the current best price, and study the asymptotic behavior of the limit order book in this setting. We provide both the price and measure processes in the asymptotic setting as solution to stochastic differential equations.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798438750017Subjects--Topical Terms:

517247
Statistics.
Subjects--Index Terms:

High-dimensional statisticsIndex Terms--Genre/Form:

542853
Electronic books.

Essays in Distributed High-Dimensional Statistics and Limit Order Book.
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504 $a Includes bibliographical references
520 $a The development of modern technology brings great opportunity and challenges to data analysis and statistical estimation. On example is the capability of acquisition of data with unprecedented size that cannot be fit into a single machine, which calls for the development of distributed estimation and inferential approaches. Another example is the transition from old quote-driven markets to order-driven markets with high frequency data. In this dissertation we address several challenges in distributed statistics and limit order modeling in high frequency trading.Despite a vast literature on support vector machine (SVM), much less is known about the inferential properties of SVM, especially in a distributed setting. We propose a multi-round distributed linear-type (MDL) estimator for conducting inference for linear SVM. The proposed estimator is computationally efficient. In particular, it only requires an initial SVM estimator and then successively refines the estimator by solving simple weighted least squares problem. Theoretically, we establish the Bahadur representation of the estimator. Based on the representation, the asymptotic normality is further derived, which shows that the MDL estimator achieves the optimal statistical efficiency, i.e., the same efficiency as the classical linear SVM applying to the entire data set in a single machine setup. Moreover, our asymptotic result avoids the condition on the number of machines or data batches, which is commonly assumed in distributed estimation literature, and allows the case of diverging dimension. We provide simulation studies to demonstrate the performance of the proposed MDL estimator.The estimation and support recovery for high-dimensional linear regression model with heavy-tailed noise is a challenge problem, especially in a distributed setting. To deal with heavy-tailed noise whose variance can be infinite, we adopt the quantile regression loss function instead of the commonly used squared loss. However, the non-smooth quantile loss poses new challenges to high-dimensional distributed estimation in both computation and theoretical development. To address the challenge, we transform the response variable and establish a new connection between quantile regression and ordinary linear regression. Then, we provide a distributed estimator that is both computationally and communicationally efficient, where only the gradient information is communicated at each iteration. Theoretically, we show that, after a constant number of iterations, the proposed estimator achieves a near-oracle convergence rate without any restriction on the number of machines. Moreover, we establish the theoretical guarantee for the support recovery. The simulation analysis is provided to demonstrate the effectiveness of our method. With the help of limit order book and high frequency data, all agents who want to buy or sell equity can post their offers at whatever prices and quantities they choose. The main challenge is to tractably model the complex micro-structure and evolution of the limit order book. We model the order book as two coupled measure-valued stochastic processes where the limit and market orders arrive at the book according to independent Poisson processes. We assume that the price at which the limit orders are placed follows a distribution that depends on the current best price on both sides. We consider a high frequency regime where the rates of the incoming orders are large and the limit orders are placed close to the current best price, and study the asymptotic behavior of the limit order book in this setting. We provide both the price and measure processes in the asymptotic setting as solution to stochastic differential equations.
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