Statistical techniques

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All (207)

All (207) (0 to 10 of 207 results)

1. Analytical Studies: Methods and References
Journals and periodicals: 11-633-X
Description: Papers in this series provide background discussions of the methods used to develop data for economic, health, and social analytical studies at Statistics Canada. They are intended to provide readers with information on the statistical methods, standards and definitions used to develop databases for research purposes. All papers in this series have undergone peer and institutional review to ensure that they conform to Statistics Canada's mandate and adhere to generally accepted standards of good professional practice.
Release date: 2026-04-24
2. Effects of model misspecification on small area estimators
Articles and reports: 12-001-X202500200001
Description: Nested error regression models are commonly used to incorporate unit specific auxiliary variables to improve small area estimates. When the mean structure of the model is misspecified, the design-based mean squared prediction error (MSPE) of Empirical Best Linear Unbiased Predictors (EBLUP) generally increases. The Observed Best Prediction (OBP) method has been proposed with the intent to improve on the design-based MSPE over EBLUP. In this paper, we conduct a Monte Carlo simulation experiments to understand the effect of misspsecification of mean structures on different small area estimators. Our findings suggest that the OBP using unit-level auxiliary variables does not outperform the EBLUP in terms of design-based MSPE, unless the number of small areas m is extremely large. Conversely, the performance of OBP significantly improves when area-level auxiliary variables are employed. This paper includes both analytical and numerical evidence to demonstrate these observations, providing practical insights for addressing model misspecification in small area estimation (SAE).
Release date: 2025-12-23
3. Integrating probability and non-probability samples through deep learning-based mass imputation
Articles and reports: 12-001-X202500200007
Description: Although probability samples have been regarded as the gold standard to collect information for population-based study, non-probability samples have been used frequently in practice due to low cost, convenience, and the lack of the sampling frame for the survey. Naïve estimates based on non-probability samples without any adjustments may be misleading due to selection bias. Recently, a valid data integration approach that includes mass imputation, propensity score weighting, and calibration has been used to improve the representativeness of non-probability samples. The effectiveness of the mass imputation approach depends on the underlying model assumptions. In this paper, we propose using deep learning for the mass imputation in the combining of probability and non-probability samples and compare it with several modern machine learning-based mass imputation approaches, including generalized additive modeling, regression tree, random forest, and XG-boosting. In the simulation study, deep learning-based approaches have been shown to be more robust and effective than other mass imputation approaches against the failure of underlying model assumptions under non-linearity scenarios.
Release date: 2025-12-23
4. Generalized regression estimation under misspecified sample design
Articles and reports: 12-001-X202500200008
Description: Classical design-based survey estimation relies on a properly specified sampling design for valid inference. We consider the properties of regression estimation under a misspecified sample design, in which the nominal and true inclusion probabilities do not necessarily match. This general misspecified sample design setting encompasses many challenges in the modern survey environment. Under this setting, an asymptotic analysis of the regression estimator, an expression of the bias, and an expression of the variance are presented. Further, a consistent variance estimator is derived and an expression which estimates the bias in-part or in-whole is discussed. This later expression may be used as an indicator of the presence of bias due to misspecification by a practitioner. A simulation study is conducted to support the presented theory.
Release date: 2025-12-23
5. Mapping location and co-location of industries at the neighborhood level: A spatial kernel density approach
Articles and reports: 18-001-X2025001
Description: This paper brings the analysis of business cluster to a more granular geographic scale by developing a methodology for identifying business clusters at the neighborhood level. The proposed method identifies clusters of businesses at the DB level, which is one of the most granular spatial units of analysis defined by Statistics Canada. The method is developed with an application to four census metropolitan areas (CMAs) of different sizes and for different industry cluster specifications, including simple 2-digit North American Industry Classification System (NAICS) groups as well as industry clusters resulting from groupings of NAICS codes, as defined by Delgado et al. (2014).
Release date: 2025-10-10
6. Efficient Record Linkage for Large Datasets by Business Names Archived
Articles and reports: 11-522-X202500100019
Description: Accurate and efficient record linkage is crucial for maintaining a comprehensive and current Statistical Business Register (SBR) at Statistics Canada. Linking external business lists to the SBR by name presents computational and methodological challenges, especially as data volumes grow. This paper describes a scalable methodology that employs blocking techniques to constrain the computational search space and integrates multiple similarity measures—from edit distances and n-gram overlaps to embedding-based methods using Sentence-BERT (SBERT)—to identify likely matches. By combining simple character-level comparisons with more advanced semantic embedding methods, the approach can adapt to various naming conventions and complexities. While it does not guarantee superior accuracy in all circumstances, it offers a pragmatic balance between computational feasibility and linkage quality.
Release date: 2025-09-08
7. Evaluating the Accuracy when Linking Records in Waves Archived
Articles and reports: 11-522-X202500100020
Description: At Statistics Canada, many data sets are linked with quasi-identifiers such as the first name, last name, or address. In such cases, linkage errors are a potential concern and must be measured. In that regard, previous studies have shown that the evaluation may be based on modeling the number of links from a given record while accounting for all the interactions among the linkage variables and dispensing with clerical reviews, so long as the decision to link two records does not involve other records. In this communication, the methodology is adapted for a class of practical strategies, which violate this constraint by linking the records in consecutive waves, where a given wave links a subset of the records that are not linked in previous waves. In particular, the linkage may be based on a deterministic wave followed by a probabilistic one.
Release date: 2025-09-08
8. Model-Based Threshold Selection for Agricultural Linkages Archived
Articles and reports: 11-522-X202500100021
Description: Optimal threshold selection is a critical challenge in probabilistic linkage, with significant implications for the accuracy and reliability of linked datasets. This paper analyzes the performance of the neighbour model, a recently proposed error model which models linkage errors by the number of links from each record. Three threshold selection algorithms utilizing the neighbour model were assessed, highlighting the strengths and limitations of each. Their performance was assessed through simulation studies, which demonstrated that methods using the neighbour model achieved lower relative bias compared to two established methods for threshold selection. Additionally, the practical utility was validated through goodness-of-fit tests conducted on four agricultural datasets, showing the potential of the model for use in real-world applications.
Release date: 2025-09-08
9. T1 Redesign: T1 Partnership Identification Process Archived
Articles and reports: 11-522-X202500100022
Description: In Canada, T1 Tax forms are used to report personal income, whether earned as an employee or through self-employment. Income from self-employment, or "T1 Business Income" is reported by sole proprietorships or partnerships. A T1 partnership involves two or more legal entities jointly filing for a shared business. T1 business data is received as individual filings, meaning partnerships are received separately for each partner. Internal record linkage within the T1 business database is performed to identify partnerships and prevent overcoverage within the final population of T1 businesses. This new T1 partnership identification process takes advantage of newer algorithms, such as DBSCAN numerical clustering fuzzy matching, to identify internal linkages. Graph theory is used to construct the list of partnerships from the row-pairs identified in the linkage process.
Release date: 2025-09-08
10. Development of Linkage-Adjusted Weights Accounting for Gender for the 2021 Canadian Census Health and Environment Cohort Archived
Articles and reports: 11-522-X202500100023
Description: The latest Canadian Census Health and Environment Cohort (CanCHEC) continues a series of population-based microdata linkages focused on population health research by demographic, social and economic characteristics. The 2021 CanCHEC consists of 95.5% of the 2021 Census long-form sample survey records. The records of survey respondents that could not be linked to the Derived Record Depository and those presumed to be duplicates account for the remaining 4.5%. Linkage-adjusted main and replicate weights allow researchers to estimate and evaluate the variance of summary measures about population health in the presence of missed linked pairs to better understand the experiences of diverse population groups.
Release date: 2025-09-08

Data (1)

Data (1) ((1 result))

1. Income divergence index (D-index) by census tract
Table: 11-10-0074-01
Geography: Census tract
Frequency: Occasional
Description:
The divergence index (D-index) describes the degree that families with different income levels are mixing together in neighbourhoods. It compares neighbourhood (census tract, CT) discrete income distributions to a base distribution, which is the income quintiles of the neighbourhood’s census metropolitan area (CMA).

Release date: 2020-06-22

Analysis (199)

Analysis (199) (10 to 20 of 199 results)

11. One-Stop-Shop for Artificial Intelligence and Machine Learning for Official Statistics Archived
Articles and reports: 11-522-X202500100027
Description: Several challenges encountered when constructing U.S. administrative record-based (AR-based) population estimates for 2020 are identified. They include locational accuracy, person coverage and its consistency over time, filtering out non-residents and people not alive on the reference date, uncovering missing links across person and address records, and predicting demographic characteristics. Several ways to address these issues are discussed. Regression results illustrate how the challenges and solutions affect the AR-based county population estimates.
Release date: 2025-09-08
12. Imputation of nonignorable missing data in surveys using auxiliary margins via hot deck and sequential imputation
Articles and reports: 12-001-X202500100004
Description: Survey data collection often is plagued by unit and item nonresponse. To reduce reliance on strong assumptions about the missingness mechanisms, statisticians can use information about population marginal distributions known, for example, from censuses or administrative databases. One approach that does so is the Missing Data with Auxiliary Margins, or MD-AM, framework, which uses multiple imputation for both unit and item nonresponse so that survey-weighted estimates accord with the known marginal distributions. However, this framework relies on specifying and estimating a joint distribution for the survey data and nonresponse indicators, which can be computationally and practically daunting in data with many variables of mixed types. We propose two adaptations to the MD-AM framework to simplify the imputation task. First, rather than specifying a joint model for unit respondents’ data, we use random hot deck imputation while still leveraging the known marginal distributions. Second, instead of sampling from conditional distributions implied by the joint model for the missing data due to item nonresponse, we apply multiple imputation by chained equations for item nonresponse before imputation for unit nonresponse. Using simulation studies with nonignorable missingness mechanisms, we demonstrate that the proposed approach can provide more accurate point and interval estimates than models that do not leverage the auxiliary information. We illustrate the approach using data on voter turnout from the U.S. Current Population Survey.
Release date: 2025-06-30
13. Comments by David Haziza on “Trends and directions in sample survey theory and methods”
Articles and reports: 12-001-X202500100013
Description: This discussion of the paper by Rao and Lohr focuses on the use of machine learning procedures for estimating finite population parameters. While there is growing interest in these methods within national statistical offices, several areas remain largely unexplored and warrant significant attention in the coming years. In this discussion, I highlight potential topics for future research and development in this rapidly evolving field.
Release date: 2025-06-30
14. Exploring a skewness conjecture: Expanding Cochran’s rule to a proportion estimated from a complex sample
Articles and reports: 12-001-X202400200001
Description: Cochran’s rule states that a standard (Wald) two-sided 95% confidence interval around a sample mean drawn from a population with positive skewness is reasonable when the sample size is greater than 25 times the square of the skewness coefficient of the population. We investigate whether a variant of this crude rule applies for a proportion estimated from a stratified simple random sample.
Release date: 2024-12-20
15. Models of linkage error for capture-recapture estimation without clerical reviews
Articles and reports: 12-001-X202400200007
Description: The capture-recapture method can be applied to measure the coverage of administrative and big data sources, in official statistics. In its basic form, it involves the linkage of two sources while assuming a perfect linkage and other standard assumptions. In practice, linkage errors arise and are a potential source of bias, where the linkage is based on quasi-identifiers. These errors include false positives and false negatives, where the former arise when linking a pair of records from different units, and the latter arise when not linking a pair of records from the same unit. So far, the existing solutions have resorted to costly clerical reviews, or they have made the restrictive conditional independence assumption. In this work, these requirements are relaxed by modeling the number of links from a record instead. The same approach may be taken to estimate the linkage accuracy without clerical reviews, when linking two sources that each have some undercoverage.
Release date: 2024-12-20
16. Design-based estimation of small and empty domains in survey data analysis using order constraints
Articles and reports: 12-001-X202400200010
Description: Recent work in survey domain estimation has shown that incorporating a priori assumptions about orderings of population domain means reduces the variance of the estimators and provides smaller confidence intervals with good coverage. Here we show how partial ordering assumptions allow design-based estimation of sample means in domains for which the sample size is zero, with conservative variance estimates and confidence intervals. Order restrictions can also substantially improve estimation and inference in small-size domains. Examples with well-known survey data sets demonstrate the utility of the methods. Code to implement the examples using the R package csurvey is given in the appendix.
Release date: 2024-12-20
17. Adaptive cluster sampling, a quasi Bayesian approach
Articles and reports: 12-001-X202400200014
Description: Adaptive cluster sampling designs were proposed as a method that could be used when sampling rare populations whose units tend to appear in clusters. The resulting estimator is not based on any model assumptions and is design unbiased. It can have smaller variance than the standard estimator which does not incorporate the fact that one is dealing with a rare population. Here we will demonstrate that, when adaptive cluster sampling is appropriate, its estimator does not take into account all the available information in the design. We present a quasi Bayesian approach which incorporates the information which is now ignored. We will see that the resulting estimator is a significant improvement over the current methods.
Release date: 2024-12-20
18. Design consistent random forest models for data collected from a complex sample
Articles and reports: 12-001-X202400200015
Description: Random forest models, which are the result of averaging the estimated values from a large number of tree models, represent a useful and flexible tool for modeling the data nonparametrically to provide accurately predicted values. There are many potential applications for these types of models when dealing with survey data. However, survey data is usually collected using an informative sample design, so it is necessary to have an algorithm for creating random forest models that account for this design during model estimation. The tree models used in the forest are typically obtained by estimating tree models on bootstrapped samples of the original data. Since the models depend on the observed data and the values observed in the sample depend on the informative sample design, the usual method for estimation is likely to lead to a biased random forest model when applied to survey data. In this article, we provide an algorithm and a set of conditions that produce consistent random forest models under an informative sample design and compare this method to the usual random forest modeling method. We show that ignoring the design can lead to biased model estimates.
Release date: 2024-12-20
19. Interpreting population totals from the Labour Force Survey
Articles and reports: 75-005-M2024004
Description: This article provides information about population totals in the Labour Force Survey (LFS), including details on who is included in the survey target population, and a description of the methodology used to produce monthly population totals in the LFS. The note also provides guidance on how to interpret population statistics in the LFS, and discusses the extent to which the LFS can be used to examine disaggregated labour market indicators for new immigrants and non-permanent residents.
Release date: 2024-09-20
20. Reconstruction attack risk using Statistics Canada Census Data Archived
Articles and reports: 11-522-X202200100008
Description: The publication of more disaggregated data can increase transparency and provide important information on underrepresented groups. Developing more readily available access options increases the amount of information available to and produced by researchers. Increasing the breadth and depth of the information released allows for a better representation of the Canadian population, but also puts a greater responsibility on Statistics Canada to do this in a way that preserves confidentiality, and thus it is helpful to develop tools which allow Statistics Canada to quantify the risk from the additional data granularity. In an effort to evaluate the risk of a database reconstruction attack on Statistics Canada’s published Census data, this investigation follows the strategy of the US Census Bureau, who outlined a method to use a Boolean satisfiability (SAT) solver to reconstruct individual attributes of residents of a hypothetical US Census block, based just on a table of summary statistics. The technique is expanded to attempt to reconstruct a small fraction of Statistics Canada’s Census microdata. This paper will discuss the findings of the investigation, the challenges involved in mounting a reconstruction attack, and the effect of an existing confidentiality measure in mitigating these attacks. Furthermore, the existing strategy is compared to other potential methods used to protect data – in particular, releasing tabular data perturbed by some random mechanism, such as those suggested by differential privacy.
Release date: 2024-03-25

Reference (7)

Reference (7) ((7 results))

1. Methods for Constructing Life Tables for Canada, Provinces and Territories
Surveys and statistical programs – Documentation: 84-538-X
Geography: Canada
Description: This electronic publication presents the methodology underlying the production of the life tables for Canada, provinces and territories.
Release date: 2023-08-28
2. Canadian Cancer Registry System Guide, 2007 Edition Archived
Surveys and statistical programs – Documentation: 82-225-X200701010508
Description:
The Record Linkage Overview describes the process used in annual internal record linkage of the Canadian Cancer Registry. The steps include: preparation; pre-processing; record linkage; post-processing; analysis and resolution; resolution entry; and, resolution processing.
Release date: 2008-01-18
3. Using the postal code as merge key for independent data files: matching data from the Canadian Census and an administrative file of school test scores in Quebec Archived
Surveys and statistical programs – Documentation: 11-522-X20050019476
Description:
The paper will show how, using data published by Statistics Canada and available from member libraries of the CREPUQ, a linkage approach using postal codes makes it possible to link the data from the outcomes file to a set of contextual variables. These variables could then contribute to producing, on an exploratory basis, a better index to explain the varied outcomes of students from schools. In terms of the impact, the proposed index could show more effectively the limitations of ranking students and schools when this information is not given sufficient weight.
Release date: 2007-03-02
4. The Integrated Approach to Economic Surveys in Canada Archived
Surveys and statistical programs – Documentation: 68-514-X
Description:
Statistics Canada's approach to gathering and disseminating economic data has developed over several decades into a highly integrated system for collection and estimation that feeds the framework of the Canadian System of National Accounts.
The key to this approach was creation of the Unified Enterprise Survey, the goal of which was to improve the consistency, coherence, breadth and depth of business survey data.
The UES did so by bringing many of Statistics Canada's individual annual business surveys under a common framework. This framework included a single survey frame, a sample design framework, conceptual harmonization of survey content, means of using relevant administrative data, common data collection, processing and analysis tools, and a common data warehouse.
Release date: 2006-11-20
5. The Longitudinal Administrative Databank (LAD) and the Longitudinal Immigration Database (IMDB): Building the LAD_IMDB - A Technical Paper Archived
Surveys and statistical programs – Documentation: 89-612-X
Description:
This paper describes the structure and linkage of two databases: the Longitudinal Administrative Databank (LAD), and the Longitudinal Immigration Database (IMDB). The combined data associate landed immigrant taxfilers on the LAD with their key characteristics upon immigration. The paper highlights how the combined information, referred to here as the LAD_IMDB, enhances and complements the existing separate databases. The paper compares the full IMDB file with the sample of immigrants to assess the representativeness of the sample file.
Release date: 2004-01-05
6. Linking Provincial Student Assessments with National and International Assessments Archived
Surveys and statistical programs – Documentation: 81-595-M2003005
Geography: Canada
Description:
This paper develops technical procedures that may enable ministries of education to link provincial tests with national and international tests in order to compare standards and report results on a common scale.
Release date: 2003-05-29
7. An Overview of the Issues Related to the Use of Personal Identifiers Archived
Surveys and statistical programs – Documentation: 85-602-X
Description:
The purpose of this report is to provide an overview of existing methods and techniques making use of personal identifiers to support record linkage. Record linkage can be loosely defined as a methodology for manipulating and / or transforming personal identifiers from individual data records from one or more operational databases and subsequently attempting to match these personal identifiers to create a composite record about an individual. Record linkage is not intended to uniquely identify individuals for operational purposes; however, it does provide probabilistic matches of varying degrees of reliability for use in statistical reporting. Techniques employed in record linkage may also be of use for investigative purposes to help narrow the field of search against existing databases when some form of personal identification information exists.
Release date: 2000-12-05

Date modified:: 2026-05-15

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