wanyu/IteraTeR_full_sent huggingface dataset:
Original:  As a by-product, the paper also sets a risk-based capital standard to ensure the capital requirement of can cover the total given risk, and the effect of the risk level on optimal retention ratio, dividend payout level and optimal control policy are also presented.
Revised:  As a by-product, the paper also sets a risk-based capital standard to ensure the capital requirement of can cover the total given risk, and the effect of the risk level on optimal retention ratio, dividend payout level and optimal control strategy are also presented.
Edit intent: clarity
Original:  The estimators considered in this paper cover maximum likelihood estimators, skipped maximum likelihood estimators, Cram\'er-von-Mises Minimum Distance estimators, and , as a special case of quantile-based estimators, Pickands Estimator. We further consider an estimator matching the population median and an asymmetric, robust estimator of scale (kMAD) to the empirical ones (kMedMAD), which may be tuned to an expected FSBP of 34\%. These estimators are compared to one-step estimators distinguished as optimal in the shrinking neighborhood setting, i.e.;
Revised:  The estimators we primarily focus on, MBRE and OMSE, are one-step estimators distinguished as optimal in the shrinking neighborhood setting, i.e.;
Edit intent: clarity
Original:  the most bias-robust estimator minimizing the maximal (asymptotic) bias and the estimatorminimizing the maximal (asymptotic) MSE. For each of these  estimators, we determine the finite sample breakdown point, the influence function, as well as  statistical accuracy measured by asymptotic bias, variance, and mean squared error - all evaluated uniformly on shrinking convex contamination neighborhoods.
Revised:  they minimize the maximal bias, respectively, on a specific such neighborhood, the maximal mean squared error. For their initialization, we propose a particular Location-Dispersion (LD) estimator, kMedMAD, which matches the population median and kMAD (an asymmetric variant of the median of absolute deviations) against the empirical counterparts. These optimally-robust estimators are compared to maximum likelihood, skipped maximum likelihood, Cramer-von-Mises minimum distance, method of median, and Pickands estimators. To quantify their deviation from robust optimality, for each of these estimators, we determine the finite sample breakdown point, the influence function, as well as statistical accuracy measured by asymptotic bias, variance, and mean squared error - all evaluated uniformly on shrinking convex contamination neighborhoods.
Edit intent: meaning-changed
Original:  the most bias-robust estimator minimizing the maximal (asymptotic) bias and the estimatorminimizing the maximal (asymptotic) MSE. For each of these  estimators, we determine the finite sample breakdown point, the influence function, as well as  statistical accuracy measured by asymptotic bias, variance, and mean squared error - all evaluated uniformly on shrinking convex contamination neighborhoods.
Revised:  the most bias-robust estimator minimizing the maximal (asymptotic) bias and the estimatorminimizing the maximal (asymptotic) MSE. For each of these suboptimal estimators, we determine the finite sample breakdown point, the influence function, as well as statistical accuracy measured by asymptotic bias, variance, and mean squared error - all evaluated uniformly on shrinking convex contamination neighborhoods.
Edit intent: clarity
Original:  the most bias-robust estimator minimizing the maximal (asymptotic) bias and the estimatorminimizing the maximal (asymptotic) MSE. For each of these  estimators, we determine the finite sample breakdown point, the influence function, as well as  statistical accuracy measured by asymptotic bias, variance, and mean squared error - all evaluated uniformly on shrinking convex contamination neighborhoods.
Revised:  the most bias-robust estimator minimizing the maximal (asymptotic) bias and the estimatorminimizing the maximal (asymptotic) MSE. For each of these estimators, we determine the finite sample breakdown point, the influence function, as well as the statistical accuracy measured by asymptotic bias, variance, and mean squared error - all evaluated uniformly on shrinking convex contamination neighborhoods.
Edit intent: fluency
Original:  the most bias-robust estimator minimizing the maximal (asymptotic) bias and the estimatorminimizing the maximal (asymptotic) MSE. For each of these  estimators, we determine the finite sample breakdown point, the influence function, as well as  statistical accuracy measured by asymptotic bias, variance, and mean squared error - all evaluated uniformly on shrinking convex contamination neighborhoods.
Revised:  the most bias-robust estimator minimizing the maximal (asymptotic) bias and the estimatorminimizing the maximal (asymptotic) MSE. For each of these estimators, we determine the finite sample breakdown point, the influence function, as well as statistical accuracy measured by asymptotic bias, variance, and MSE - all evaluated uniformly on shrinking convex contamination neighborhoods.
Edit intent: clarity
Original:  the most bias-robust estimator minimizing the maximal (asymptotic) bias and the estimatorminimizing the maximal (asymptotic) MSE. For each of these  estimators, we determine the finite sample breakdown point, the influence function, as well as  statistical accuracy measured by asymptotic bias, variance, and mean squared error - all evaluated uniformly on shrinking convex contamination neighborhoods. Finally, we check these asymptotic theoretical findings against finite sample behavior by an extensive simulation study  .
Revised:  the most bias-robust estimator minimizing the maximal (asymptotic) bias and the estimatorminimizing the maximal (asymptotic) MSE. For each of these estimators, we determine the finite sample breakdown point, the influence function, as well as statistical accuracy measured by asymptotic bias, variance, and mean squared error - all evaluated uniformly on shrinking neighborhoods. These asymptotic findings are complemented by an extensive simulation study .
Edit intent: clarity
Original: We study robustness properties of several procedures for joint estimation of shape and scale in a generalized Pareto model. The estimators we primarily focus on, MBRE and OMSE, are one-step estimators distinguished as optimally-robust in the shrinking neighborhood setting, i. e.; they minimize the maximal bias, respectively, on a specific such neighborhood, the maximal mean squared error. For their initialization, we propose a particular Location-Dispersion (LD) estimator, kMedMAD, which matches the population median and kMAD (an asymmetric variant of the median of absolute deviations ) against the empirical counterparts. These optimally-robust estimators are compared to maximum likelihood, skipped maximum likelihood, Cramer-von-Mises minimum distance, method of median, and Pickands estimators.
Revised: This paper deals with optimally-robust estimators are compared to maximum likelihood, skipped maximum likelihood, Cramer-von-Mises minimum distance, method of median, and Pickands estimators.
Edit intent: coherence
Original:  These optimally-robust estimators are compared to maximum likelihood, skipped maximum likelihood, Cramer-von-Mises minimum distance, method of median, and Pickands estimators. To quantify their deviation from robust optimality, for each of these suboptimal estimators, we determine the finite sample breakdown point, the influence function, as well as the statistical accuracy measured by asymptotic bias, variance, and MSE - all evaluated uniformly on shrinking neighborhoods. These asymptotic findings are complemented by an extensive simulation study to assess their finite sample behavior .
Revised:  These optimally-robust parameter estimation in generalized Pareto distributions (GPDs). These arise naturally in many situations where one is interested in the behavior of extreme events as motivated by the Pickands-Balkema-de Haan extreme value theorem (PBHT). The application we have in mind is calculation of the regulatory capital required by Basel II for a bank to cover operational risk. In this context the tail behavior of the underlying distribution is crucial. This is where extreme value theory enters, suggesting to estimate these high quantiles parameterically using, e.g. GPDs. Robust statistics in this context offers procedures bounding the influence of single observations, so provides reliable inference in the presence of moderate deviations from the distributional model assumptions, respectively from the mechanisms underlying the PBHT .
Edit intent: meaning-changed
Original:  We start by studying the most commonly used estimator, the realized covariance matrix {\it  (RCV)  . We show that in the high dimensional case when the dimension p and the observation frequency n grow in the same rate, the limiting empirical spectral distribution of RCV depends on the covolatility processes not only through the underlying integrated covariance matrixSigma , but also on how the covolatility processes vary in time.
Revised:  We start by studying the most commonly used estimator, the {\it (RCV) . We show that in the high dimensional case when the dimension p and the observation frequency n grow in the same rate, the limiting empirical spectral distribution of RCV depends on the covolatility processes not only through the underlying integrated covariance matrixSigma , but also on how the covolatility processes vary in time.
Edit intent: clarity
Original:  We start by studying the most commonly used estimator, the realized covariance matrix {\it  (RCV)  . We show that in the high dimensional case when the dimension p and the observation frequency n grow in the same rate, the limiting empirical spectral distribution of RCV depends on the covolatility processes not only through the underlying integrated covariance matrixSigma , but also on how the covolatility processes vary in time.
Revised:  We start by studying the most commonly used estimator, the realized covariance matrix {\it realized covariance (RCV) . We show that in the high dimensional case when the dimension p and the observation frequency n grow in the same rate, the limiting empirical spectral distribution of RCV depends on the covolatility processes not only through the underlying integrated covariance matrixSigma , but also on how the covolatility processes vary in time.
Edit intent: meaning-changed
Original:  We start by studying the most commonly used estimator, the realized covariance matrix {\it  (RCV)  . We show that in the high dimensional case when the dimension p and the observation frequency n grow in the same rate, the limiting empirical spectral distribution of RCV depends on the covolatility processes not only through the underlying integrated covariance matrixSigma , but also on how the covolatility processes vary in time.
Revised:  We start by studying the most commonly used estimator, the realized covariance matrix {\it (RCV) matrix . We show that in the high dimensional case when the dimension p and the observation frequency n grow in the same rate, the limiting empirical spectral distribution of RCV depends on the covolatility processes not only through the underlying integrated covariance matrixSigma , but also on how the covolatility processes vary in time.
Edit intent: fluency
Original:  We start by studying the most commonly used estimator, the realized covariance matrix {\it  (RCV)  . We show that in the high dimensional case when the dimension p and the observation frequency n grow in the same rate, the limiting empirical spectral distribution of RCV depends on the covolatility processes not only through the underlying integrated covariance matrixSigma , but also on how the covolatility processes vary in time.
Revised:  We start by studying the most commonly used estimator, the realized covariance matrix {\it (RCV) . We show that in the high dimensional case when the dimension p and the observation frequency n grow in the same rate, the limiting spectral distribution (LSD) of the RCV matrix depends on the covolatility processes not only through the underlying integrated covariance matrixSigma , but also on how the covolatility processes vary in time.
Edit intent: clarity
Original:  We start by studying the most commonly used estimator, the realized covariance matrix {\it  (RCV)  . We show that in the high dimensional case when the dimension p and the observation frequency n grow in the same rate, the limiting empirical spectral distribution of RCV depends on the covolatility processes not only through the underlying integrated covariance matrixSigma , but also on how the covolatility processes vary in time.
Revised:  We start by studying the most commonly used estimator, the realized covariance matrix {\it (RCV) . We show that in the high dimensional case when the dimension p and the observation frequency n grow in the same rate, the limiting empirical spectral distribution of RCV depends on the covolatility process not only through the underlying integrated covariance matrixSigma , but also on how the covolatility processes vary in time.
Edit intent: fluency
Original:  We start by studying the most commonly used estimator, the realized covariance matrix {\it  (RCV)  . We show that in the high dimensional case when the dimension p and the observation frequency n grow in the same rate, the limiting empirical spectral distribution of RCV depends on the covolatility processes not only through the underlying integrated covariance matrixSigma , but also on how the covolatility processes vary in time.
Revised:  We start by studying the most commonly used estimator, the realized covariance matrix {\it (RCV) . We show that in the high dimensional case when the dimension p and the observation frequency n grow in the same rate, the limiting empirical spectral distribution of RCV depends on the covolatility processes not only through the targeting ICV matrix , but also on how the covolatility processes vary in time.
Edit intent: meaning-changed
Original:  We start by studying the most commonly used estimator, the realized covariance matrix {\it  (RCV)  . We show that in the high dimensional case when the dimension p and the observation frequency n grow in the same rate, the limiting empirical spectral distribution of RCV depends on the covolatility processes not only through the underlying integrated covariance matrixSigma , but also on how the covolatility processes vary in time.
Revised:  We start by studying the most commonly used estimator, the realized covariance matrix {\it (RCV) . We show that in the high dimensional case when the dimension p and the observation frequency n grow in the same rate, the limiting empirical spectral distribution of RCV depends on the covolatility processes not only through the underlying integrated covariance matrixSigma , but also on how the covolatility process varies in time.
Edit intent: fluency
Original:  In particular, for two high dimensional diffusion processes with the same integrated covariance matrix, the empirical spectral distributions of their RCVs can be very different. Hence in terms of making inference about the spectrum of the integrated covariance matrix, the RCV is in generalnot a good proxy to rely on in the high dimensional caseenko-Pastur type theorem for weighted sample covariance matrices, based on which we further establish a Mar\v{c}enko-Pastur type theorem for RCV matrices for a class \mathcal{C} of diffusion processes.
Revised:  not a good proxy to rely on in the high dimensional caseenko-Pastur type theorem for weighted sample covariance matrices, based on which we further establish a Mar\v{c}enko-Pastur type theorem for RCV matrices for a class \mathcal{C} of diffusion processes.
Edit intent: coherence
Original:  Hence in terms of making inference about the spectrum of the integrated covariance matrix, the RCV is in generalnot a good proxy to rely on in the high dimensional caseenko-Pastur type theorem for weighted sample covariance matrices, based on which we further establish a Mar\v{c}enko-Pastur type theorem for RCV matrices for a class \mathcal{C} of diffusion processes.
Revised:  Hence in terms of making inference about the spectrum of the integrated covariance matrix, the RCV is in general a good proxy to rely on in the high dimensional caseenko-Pastur type theorem for weighted sample covariance matrices, based on which we further establish a Mar\v{c}enko-Pastur type theorem for RCV matrices for a class \mathcal{C} of diffusion processes.
Edit intent: fluency
Original:  Hence in terms of making inference about the spectrum of the integrated covariance matrix, the RCV is in generalnot a good proxy to rely on in the high dimensional caseenko-Pastur type theorem for weighted sample covariance matrices, based on which we further establish a Mar\v{c}enko-Pastur type theorem for RCV matrices for a class \mathcal{C} of diffusion processes.
Revised:  Hence in terms of making inference about the spectrum of the integrated covariance matrix, the RCV is in generalnot We establish a Mar\v{cenko-Pastur type theorem for weighted sample covariance matrices, based on which we further establish a Mar\v{c}enko-Pastur type theorem for RCV matrices for a class \mathcal{C} of diffusion processes.
Edit intent: clarity
Original:  We show that the limiting empirical spectral distribution of our proposed estimator TVARCV does depend solely on that of Sigma through a Marcenko-Pastur equation, and hence the TVARCV can be used to recover the empirical spectral distribution of Sigma by inverting the Marcenko-Pastur equation, which can then be applied to further applications such as portfolio allocation, risk management, etc. .
Revised:  We show that for diffusion processes in class \mathcal{C solely on that of Sigma through a Marcenko-Pastur equation, and hence the TVARCV can be used to recover the empirical spectral distribution of Sigma by inverting the Marcenko-Pastur equation, which can then be applied to further applications such as portfolio allocation, risk management, etc. .
Edit intent: meaning-changed
Original:  We show that the limiting empirical spectral distribution of our proposed estimator TVARCV does depend solely on that of Sigma through a Marcenko-Pastur equation, and hence the TVARCV can be used to recover the empirical spectral distribution of Sigma by inverting the Marcenko-Pastur equation, which can then be applied to further applications such as portfolio allocation, risk management, etc. .
Revised:  We show that the limiting empirical spectral distribution of our proposed estimator TVARCV does depend solely on that of the targeting ICV matrix through a Mar\v{c .
Edit intent: meaning-changed
Original:  We show that in the high dimensional case when the dimension p and the observation frequency n grow in the same rate, the limiting spectral distribution (LSD) of RCV depends on the covolatility process not only through the targeting ICV ,but also on how the covolatility process varies in time .
Revised:  We show that in the high dimensional case when the dimension p and the observation frequency n grow in the same rate, the limiting spectral distribution (LSD) of RCV depends on the covolatility process ,but also on how the covolatility process varies in time .
Edit intent: clarity
Original:  We show that in the high dimensional case when the dimension p and the observation frequency n grow in the same rate, the limiting spectral distribution (LSD) of RCV depends on the covolatility process not only through the targeting ICV ,but also on how the covolatility process varies in time .
Revised:  We show that in the high dimensional case when the dimension p and the observation frequency n grow in the same rate, the limiting spectral distribution (LSD) of RCV depends on the covolatility process not only through the targeting ICV but also on how the covolatility process varies in time .
Edit intent: fluency
Original:  We show that in the high dimensional case when the dimension p and the observation frequency n grow in the same rate, the limiting spectral distribution (LSD) of RCV depends on the covolatility process not only through the targeting ICV ,but also on how the covolatility process varies in time .
Revised:  We show that in the high dimensional case when the dimension p and the observation frequency n grow in the same rate, the limiting spectral distribution (LSD) of RCV depends on the covolatility process not only through the targeting ICV ,not only through the targeting ICV, but also on how the covolatility process varies in time .
Edit intent: fluency
Original:  We establish a Marc enko-Pastur type theorem for weighted sample covariance matrices, based on which we obtain a Marc enko-Pastur type theorem for RCV for a class %DIFDELCMD < \sC %%%  of diffusion processes.
Revised:  We establish a Marc enko--Pastur type theorem for weighted sample covariance matrices, based on which we obtain a Marc enko-Pastur type theorem for RCV for a class %DIFDELCMD < \sC %%% of diffusion processes.
Edit intent: fluency
Original:  We establish a Marc enko-Pastur type theorem for weighted sample covariance matrices, based on which we obtain a Marc enko-Pastur type theorem for RCV for a class %DIFDELCMD < \sC %%%  of diffusion processes.
Revised:  We establish a Marc enko-Pastur type theorem for weighted sample covariance matrices, based on which we obtain a Marc enko--Pastur type theorem for RCV for a class %DIFDELCMD < \sC %%% of diffusion processes.
Edit intent: clarity
Original:  We establish a Marc enko-Pastur type theorem for weighted sample covariance matrices, based on which we obtain a Marc enko-Pastur type theorem for RCV for a class %DIFDELCMD < \sC %%%  of diffusion processes.
Revised:  We establish a Marc enko-Pastur type theorem for weighted sample covariance matrices, based on which we obtain a Marc enko-Pastur type theorem for RCV for a class %DIFDELCMD < \sC %%% \mathcal{C of diffusion processes.
Edit intent: meaning-changed
Original:  We show that for processes in class %DIFDELCMD < \sC%%%   , the TVARCV possesses the desirable property that its LSD depends solely on that of the targeting ICV through the Marc enko-Pastur equation, and hence, in particular, the TVARCV can be used to recover the empirical spectral distribution of the ICV by using existing algorithms.
Revised:  We show that for processes in class %DIFDELCMD < \sC%%% \mathcal , the TVARCV possesses the desirable property that its LSD depends solely on that of the targeting ICV through the Marc enko-Pastur equation, and hence, in particular, the TVARCV can be used to recover the empirical spectral distribution of the ICV by using existing algorithms.
Edit intent: meaning-changed
Original:  We show that for processes in class %DIFDELCMD < \sC%%%   , the TVARCV possesses the desirable property that its LSD depends solely on that of the targeting ICV through the Marc enko-Pastur equation, and hence, in particular, the TVARCV can be used to recover the empirical spectral distribution of the ICV by using existing algorithms.
Revised:  We show that for processes in class %DIFDELCMD < \sC%%% C , the TVARCV possesses the desirable property that its LSD depends solely on that of the targeting ICV through the Marc enko-Pastur equation, and hence, in particular, the TVARCV can be used to recover the empirical spectral distribution of the ICV by using existing algorithms.
Edit intent: meaning-changed
Original:  We show that for processes in class %DIFDELCMD < \sC%%%   , the TVARCV possesses the desirable property that its LSD depends solely on that of the targeting ICV through the Marc enko-Pastur equation, and hence, in particular, the TVARCV can be used to recover the empirical spectral distribution of the ICV by using existing algorithms.
Revised:  We show that for processes in class %DIFDELCMD < \sC%%% , the TVARCV possesses the desirable property that its LSD depends solely on that of the targeting ICV through the Marc enko--Pastur equation, and hence, in particular, the TVARCV can be used to recover the empirical spectral distribution of the ICV by using existing algorithms.
Edit intent: fluency