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Related Concept Videos

Variance01:15

Variance

The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative deviation occurs when the data value is less than the mean. If the deviations are added, the sum is always zero. So one cannot simply add the deviations to get the data spread. By squaring the deviations, the numbers are made positive; thus, their sum will also be positive.The standard deviation measures the spread in the same units as the data.
Determination of Expected Frequency01:08

Determination of Expected Frequency

Suppose one wants to test independence between the two variables of a contingency table. The values in the table constitute the observed frequencies of the dataset. But how does one determine the expected frequency of the dataset? One of the important assumptions is that the two variables are independent, which means the variables do not influence each other. For independent variables, the statistical probability of any event involving both variables is calculated by multiplying the individual...
Standard Deviation01:10

Standard Deviation

The most commonly used measure of variation is the standard deviation. It is a numerical value measuring how far data values are from their mean. The standard deviation value is small when the data are concentrated close to the mean, exhibiting slight variation or spread. The standard deviation value is never negative, it is either positive or zero. The standard deviation is larger when the data values are more spread out from the mean, which means the data values are exhibiting more...
Noncompartmental Analysis: Statistical Moment Theory00:56

Noncompartmental Analysis: Statistical Moment Theory

Noncompartmental analyses leverage statistical moment theory to examine time-related changes in macroscopic events, encapsulating the collective outcomes stemming from the constituent elements in play. Statistical moment theory is a mathematical approach used to describe the time course of drug concentration in the body without assuming a specific compartmental model. SMT provides insights into drug absorption, distribution, metabolism, and elimination by treating drug concentration versus time...
Empirical Method to Interpret Standard Deviation01:09

Empirical Method to Interpret Standard Deviation

The empirical rule, also known as the three-sigma rule, allows a statistician to interpret the standard deviation in a normally distributed dataset. The rule states that 68% of the data lies within one standard deviation from the mean, 95% lies within two standard deviations from the mean, and 99.7% lies within three standard deviations from the mean. Additionally, this rule is also called the 68-95-99.7 rule.
This rule is used widely in statistics to calculate the proportion of data values...
Quantitative Analysis01:12

Quantitative Analysis

Quantitative analysis is a technique for measuring the amount of specific constituents in a sample. When the sample's composition is unknown, qualitative analysis is performed first to identify its components, which ensures that the correct substances are measured during the quantitative phase.
In quantitative analysis, two key measurements are made: the sample quantity and a property proportional to the amount of the analyte (the substance being analyzed). This forms the basis of the method...

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A Multimodal Wide-Field Fourier-Transform Raman Microscope
06:48

A Multimodal Wide-Field Fourier-Transform Raman Microscope

Published on: December 30, 2025

Vast Volatility Matrix Estimation using High Frequency Data for Portfolio Selection.

Jianqing Fan1, Yingying Li, Ke Yu

  • 1Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ 08544, ( jqfan@princeton.edu ).

Journal of the American Statistical Association
|December 25, 2012
PubMed
Summary
This summary is machine-generated.

High-frequency data improves portfolio allocation by accurately estimating volatility matrices. New "refresh time" methods enhance portfolio selection efficiency and stability with gross-exposure constraints.

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Last Updated: May 15, 2026

A Multimodal Wide-Field Fourier-Transform Raman Microscope
06:48

A Multimodal Wide-Field Fourier-Transform Raman Microscope

Published on: December 30, 2025

Area of Science:

  • Quantitative Finance
  • Financial Econometrics

Background:

  • Portfolio allocation benefits from gross-exposure constraints for enhanced efficiency and stability.
  • High-frequency financial data offers a larger sample size for estimating high-dimensional volatility matrices.

Purpose of the Study:

  • To investigate volatility matrix estimation using high-dimensional, high-frequency data for portfolio selection.
  • To propose and compare novel "refresh time"-based methods for covariance matrix estimation.

Main Methods:

  • Utilizing "pairwise-refresh time" and "all-refresh time" methods based on Barndorff-Nielsen et al. (2008).
  • Establishing concentration inequalities for the estimated volatility matrix.
  • Conducting extensive simulations with 50 simulated assets and 30 Dow Jones Industrial Average stocks.

Main Results:

  • The proposed methods accurately capture time-varying volatility and correlations.
  • High-frequency data-based estimates provide more precise guidance for future portfolio allocation compared to low-frequency methods.
  • Demonstrated significant advantages of high-frequency data in simulation and empirical studies.

Conclusions:

  • "Refresh time" methods provide a robust framework for volatility matrix estimation with high-frequency data.
  • The approach enhances portfolio selection accuracy and stability, especially under gross-exposure constraints.
  • High-frequency data analysis is crucial for modern portfolio management in dynamic markets.