HKU Scholars Hubhttp://hub.hku.hkThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Thu, 19 Sep 2024 21:01:14 GMT2024-09-19T21:01:14Z50131Integrating Domain Knowledge in AI-Assisted Criminal Sentencing of Drug Trafficking Caseshttp://hdl.handle.net/10722/304342Title: Integrating Domain Knowledge in AI-Assisted Criminal Sentencing of Drug Trafficking Cases
Authors: Wu, TH; Kao, CM; Cheung, ASY; Cheung, MK; Wang, C; Chen, YC; Yuan, G; Cheng, CKR
Abstract: Judgment prediction is the task of predicting various outcomes of legal cases of which sentencing prediction is one of the most important yet difficult challenges. We study the applicability of machine learning (ML) techniques in predicting prison terms of drug trafficking cases. In particular, we study how legal domain knowledge can be integrated with ML models to construct highly accurate predictors. We illustrate how our criminal sentence predictors can be applied to address four important issues in legal knowledge management, which include (1) discovery of model drifts in legal rules, (2) identification of critical features in legal judgments, (3) fairness in machine predictions, and (4) explainability of machine predictions.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10722/3043422020-01-01T00:00:00ZAI-Assisted Criminal Sentencing of Drug Trafﬁcking Cases: A Model for Combining Human and Algorithmic Legal Decision-Makinghttp://hdl.handle.net/10722/304343Title: AI-Assisted Criminal Sentencing of Drug Trafﬁcking Cases: A Model for Combining Human and Algorithmic Legal Decision-Making
Authors: Chen, YC; Cheung, MK; Cheung, ASY; WU, TH; Kao, CM; Wang, C; YUAN, G; Cheng, CKR
Description: Encoding Law and Justice II
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10722/3043432021-01-01T00:00:00ZSpectral distribution of the sample covariance of high-dimensional time series with unit rootshttp://hdl.handle.net/10722/284857Title: Spectral distribution of the sample covariance of high-dimensional time series with unit roots
Authors: Onatski, A; Wang, C
Abstract: We study the empirical spectral distributions of two sample-covariance-type matrices associated with high-dimensional time series with unit roots. The first matrix is S = XX' /T, where X is an n × T data with rows represented by n i.i.d. copies of T consecutive observations of a difference-stationary process. The second matrix is W = n ∫<font size=-1><sub>0</sub></font><font size=-1><sup>1</sup></font> W<font size=-1><sub>n</sub></font> (t)W<font size=-1><sub>n</sub></font> (t)' dt, where W<font size=-1><sub>n</sub></font> (t) is an n-dimensional vector with i.i.d. Brownian motion components. We show that, as n and T diverge to infinity proportionally, the two distributions weakly converge to nonrandom limits. The limit corresponding to S has a density ϕ(x) that decays as x<font size=-1><sup>−3/2</sup></font> when x → ∞. The limit corresponding to W is a Feller-Pareto distribution.
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/10722/2848572022-01-01T00:00:00ZSpurious Factor Analysishttp://hdl.handle.net/10722/285066Title: Spurious Factor Analysis
Authors: Onatski, A; Wang, C
Abstract: This paper draws parallels between the principal components analysis of factorless high‐dimensional nonstationary data and the classical spurious regression. We show that a few of the principal components of such data absorb nearly all the data variation. The corresponding scree plot suggests that the data contain a few factors, which is corroborated by the standard panel information criteria. Furthermore, the Dickey–Fuller tests of the unit root hypothesis applied to the estimated “idiosyncratic terms” often reject, creating an impression that a few factors are responsible for most of the nonstationarity in the data. We warn empirical researchers of these peculiar effects and suggest to always compare the analysis in levels with that in differences.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10722/2850662021-01-01T00:00:00ZMulti-sample test for high-dimensional covariance matriceshttp://hdl.handle.net/10722/261160Title: Multi-sample test for high-dimensional covariance matrices
Authors: Zhang, C; Bai, Z; Hu, J; Wang, C
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10722/2611602018-01-01T00:00:00ZAlternative Asymptotics For Cointegration Tests In Large Varshttp://hdl.handle.net/10722/259494Title: Alternative Asymptotics For Cointegration Tests In Large Vars
Authors: Onatski, A; Wang, C
Abstract: Johansen's (1988,1991) likelihood ratio test for cointegration rank of a vector autoregression (VAR) depends only on the squared sample canonical correlations between current changes and past levels of a simple transformation of the data. We study the asymptotic behavior of the empirical distribution of those squared canonical correlations when the number of observations and the dimensionality of the VAR diverge to infinity simultaneously and proportionally. We find that the distribution weakly converges to the so‐called Wachter distribution. This finding provides a theoretical explanation for the observed tendency of Johansen's test to find “spurious cointegration.”
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10722/2594942018-01-01T00:00:00ZAlternative Asymptotics for Cointegration Tests in Large VARshttp://hdl.handle.net/10722/296460Title: Alternative Asymptotics for Cointegration Tests in Large VARs
Authors: Wang, C
Description: Parallel Invited Session A1: Recent Development in Time Series; Organizers: The Asian Regional Section of the International Association for Statistical Computing (IASC-ARS) & Chinese Association for Statistical Computing (CASC)
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10722/2964602018-01-01T00:00:00ZSome new results on random matrix theory with application to analysis of dynamic factor modelshttp://hdl.handle.net/10722/296462Title: Some new results on random matrix theory with application to analysis of dynamic factor models
Authors: Wang, C
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10722/2964622018-01-01T00:00:00ZSpectral distribution of the sample covariance of high-dimensional time series with unit rootshttp://hdl.handle.net/10722/296463Title: Spectral distribution of the sample covariance of high-dimensional time series with unit roots
Authors: Wang, C
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10722/2964632019-01-01T00:00:00ZSpectral distribution of the sample covariance of high-dimensional time series with unit rootshttp://hdl.handle.net/10722/296464Title: Spectral distribution of the sample covariance of high-dimensional time series with unit roots
Authors: Wang, C; Onatski, A
Abstract: The aim is to study the empirical spectral distributions of two sample-covariance-type matrices associated with high-dimensional time series with unit roots. The first matrix is $S = XX'/T$; where $X$ is an $n imes T$ data matrix with rows represented by $n$ i.i.d. copies of $T$ consecutive observations of a difference-stationary process. The second matrix is $W = nint_0^1 B_n (t)B_n (t)' dt$; where $B_n(t)$ is an $n$-dimensional vector with i.i.d. Brownian motion components. We show that, as $n$ and $T$ diverge to infinity proportionally, the two distributions weakly converge to non-random limits. The limit corresponding to $S$ has a density $f(x)$ that decays as $x^{-3/2}$ when $x oinfty$. The limit corresponding to $W$ is a Feller-Pareto distribution.
Description: Session EO019: New developments in time series analysis - no. E0300 / A0300; This Conference is co-organized by the Working Group on Computational and Methodological Statistics (CMStatistics), the network of Computational and Financial Econometrics (CFENetwork), the Department of Applied Mathematics and the Institute of Statistics of the National Chung Hsing University.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10722/2964642019-01-01T00:00:00ZExtreme Canonical Correlations And High-dimensional Cointegration Analysishttp://hdl.handle.net/10722/272343Title: Extreme Canonical Correlations And High-dimensional Cointegration Analysis
Authors: Onatski, A; Wang, C
Abstract: We prove that the extreme squared sample canonical correlations between a random walk and its own innovations almost surely converge to the upper and lower boundaries of the support of the Wachter distribution when the sample size and the dimensionality go to infinity proportionally. This result is used to derive previously unknown analytic expressions for the Bartlett-type correction coefficients for Johansen’s trace and maximum eigenvalue tests in a high-dimensional VAR(1). An analysis of cointegration among a large number of log exchange rates illustrates the usefulness of our theoretical results.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10722/2723432019-01-01T00:00:00ZTest On The Linear Combinations Of Covariance Matrices In High-dimensional Datahttp://hdl.handle.net/10722/272344Title: Test On The Linear Combinations Of Covariance Matrices In High-dimensional Data
Authors: Bai, Z; Hu, J; Wang, C; Zhang, C
Abstract: In this paper, we propose a new test on the linear combinations of covariance matrices in high-dimensional data. Our statistic can be applied to many hypothesis tests on covariance matrices. In particular, the test proposed by Li and Chen (Ann Stat 40:908–940, 2012) on the homogeneity of two population covariance matrices is a special case of our test. The results are illustrated by an empirical example in financial portfolio allocation.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10722/2723442021-01-01T00:00:00ZOn singular values of data matrices with general independent columnshttp://hdl.handle.net/10722/342100Title: On singular values of data matrices with general independent columns
Authors: Mei, T; Wang, C; Yao, J
Abstract: We analyze the singular values of a large p × n data matrix Xn = (xn1,...,xnn), where the columns {xnj} are independent p-dimensional vectors, possibly with different distributions. Assuming that the covariance matrices Σnj = Cov(xnj) of the column vectors can be asymptotically simultaneously diagonalized, with appropriately converging spectra, we establish a limiting spectral distribution (LSD) for the singular values of Xn when both dimensions p and n grow to infinity in comparable magnitudes. Our matrix model goes beyond and includes many different types of sample covariance matrices in existing work, such as weighted sample covariance matrices, Gram matrices, and sample covariance matrices of a linear time series model. Furthermore, three applications of our general approach are developed. First, we obtain the existence and uniqueness of the LSD for realized covariance matrices of a multi-dimensional diffusion process with anisotropic time-varying co-volatility. Second, we derive the LSD for singular values of data matrices from a recent matrix-valued auto-regressive model. Finally, we also obtain the LSD for singular values of data matrices from a generalized finite mixture model.
Sat, 01 Apr 2023 00:00:00 GMThttp://hdl.handle.net/10722/3421002023-04-01T00:00:00Z