Environmetrika

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    • Complex Sample Surveys
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Environmetrika

EnvironmetrikaEnvironmetrikaEnvironmetrika
  • Home
  • Complex Sample Surveys
  • Contact Us
  • Applications
  • Accuracy Assessments
  • NFI
  • Global Forest Monitoring
Forest health monitoring

What we do

Environmetrika develops multivariate time-series estimators for complex sample surveys that monitor large environmental and ecological systems. These statistical methods are relevant to complex sample surveys for extensive biological, physical, and social systems; and accuracy assessments of remotely sensed data. Statistical methods are closely related to the Kalman filter, which supports applications such as navigation and control systems, robotics and artificial intelligence. 

Applications and the Challenges

Applications and the Challenges

Applications and the Challenges

Environmetrika primarily supports sample surveys that use repeated measurements of population elements over time, where those elements are selected with probability sampling. These supply time-series of population estimates for "study variables" that serve an analyst’s objectives. 


Population statistics use

  • Linear estimators for means and t

Environmetrika primarily supports sample surveys that use repeated measurements of population elements over time, where those elements are selected with probability sampling. These supply time-series of population estimates for "study variables" that serve an analyst’s objectives. 


Population statistics use

  • Linear estimators for means and totals;
  • Synthetic estimators, such as additive margins in statistical tables;
  • Pseudo estimators, such as rates of change and other nonlinear functions of primary population statistics. 


In the special case of monitoring terrestrial systems, measurements are field observations or very high resolution remotely sensed data for a probability sample of monitoring sites. 


However, population estimates for study variables might not be sufficiently accurate for the analyst’s objectives.  

Solution

Applications and the Challenges

Applications and the Challenges

Environmetrika develops and applies statistical estimators that improve sample survey estimates for study variables with correlated estimates for "auxiliary variables." 


Measurements of auxiliary variables use relatively inexpensive technologies. Examples include low- and medium-resolution remote sensing, full-coverage predictions with geo

Environmetrika develops and applies statistical estimators that improve sample survey estimates for study variables with correlated estimates for "auxiliary variables." 


Measurements of auxiliary variables use relatively inexpensive technologies. Examples include low- and medium-resolution remote sensing, full-coverage predictions with geospatial models, deterministic ecosystem models that predict expected changes over time, administrative records, independent surveys from other sources, and others. Therefore, population estimates for auxiliary variables can be more precise than those for study variables. However, auxiliary variables are imperfectly correlated with study variables, and therefore, they do not directly satisfy the the analyst's objectives. 


Environmetrika develops statistical estimators that use population estimates for auxiliary variables to improve population estimates for study variables, which do directly satisfy the the analyst's objectives. 


These methods replace model-assisted regression estimators with linear transformations of estimators for stochastic systems, where probability sampling is the stochastic process.


 

Support for Complex Designs

Support for Complex Designs

Support for Complex Designs

  • Multi-phase and multi-stage sampling; 
  • Pre-stratification and post-stratification; 
  • Finite and infinite population models; 
  • Equal and unequal inclusion probabilities; 
  • Interpenetrating panels, with or without overlap; 
  • Multiple independent surveys; 
  • Data missing at random; 
  • Small domains and small areas; 
  • Detection of anomalous prediction residua

  • Multi-phase and multi-stage sampling; 
  • Pre-stratification and post-stratification; 
  • Finite and infinite population models; 
  • Equal and unequal inclusion probabilities; 
  • Interpenetrating panels, with or without overlap; 
  • Multiple independent surveys; 
  • Data missing at random; 
  • Small domains and small areas; 
  • Detection of anomalous prediction residuals; 
  • Probability samples of QA/QC data;
  • Hypothesis testing and outlier detection; 
  • Model-based estimation with diagnostics; 
  • Linear and nonlinear estimators; 
  • Synthetic and pseudo estimators; 
  • Equality and inequality constraints;
  • Accuracy assessment for remotely sensed data; and 
  • Forecasting
  • Robust numerics with numerous variables

Expertise

Support for Complex Designs

Support for Complex Designs

Environmetrika develops statistical methods that use a multivariate difference estimator, which is the foundation for model-assisted regression estimators in sample surveys. These methods employ mature numerical methods, such as those developed by system engineers for digital signal processing. 


Environmetrika supports multivariate sample 

Environmetrika develops statistical methods that use a multivariate difference estimator, which is the foundation for model-assisted regression estimators in sample surveys. These methods employ mature numerical methods, such as those developed by system engineers for digital signal processing. 


Environmetrika supports multivariate sample survey estimates for thousands of study variables with thousands of auxiliary variables, including very large covariance matrices. Those estimators are robust, numerically stable and computationally efficient. A step-wise approach accommodates covariance matrices that are ill-conditioned or rank deficient.


This combination of the sample survey and system engineering disciplines produces relatively simple solutions to large and complex analyses.  

Raymond L. Czaplewski, Ph.D.

Founder, Environmetrika


Curriculum vitae


 Scientist Emeritus, USDA Forest Service 


Wikipedia


ORCID iD  0000-0001-5259-5593 


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Complex Sample Surveys

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Global Forest Monitoring

National Forest Inventory (NFI)

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