Source Time Coverage Basis Definition of FTHB FTHB Reported Share Median Age of Buyer NAR Survey July 2024-June 2025 ~6,100 responses Member Survey Self-identified 21% 59 Ginnie Mae +GSE RMBS Loan-Level July 2024-June 2025 ~2.4 Million Actual lending data 3-year no-ownership rule 62% NA Primary Residence Primary Residence Home Purchase Loans Home Purchase HMDA LAR Loan-Level 2024 ~3.1 Million Actual lending data No clear definition - by age cohort 40% 65% 1-4 Primary Residence Under 35 Under 45 Home Purchase Loans American Community Survey 1YR PUMS Latest in CensusVision ~3.54 Million addresses Annual national survey - focus on movers who own No clear definition - by age Age-based share 43 CPS ASEC PUMS 2025 ~95,000 Annual national survey No clear definition - by age Age-based share 42 Households - focus on movers who own

The United States has two measures of economic output: gross domestic product (GDP) and gross domestic income (GDI). While these are conceptually equivalent, their initial estimates differ because these initial estimates are computed from different and incomplete data sources. I study the difference, or “statistical discrepancy,” between GDP and GDI in percent and document three features. First, its size does not materially shrink on average as more data become available. Second, the size of the initial discrepancy in absolute value does not predict the size of the discrepancy in absolute value after revisions. Third, the initial discrepancy has some predictive information about revisions to lagged GDP growth but no predictive information about revisions to lagged GDI growth.

This article describes a simple and fast algorithm for generating uniformly sampled correlation matrices (R) with a fixed mean absolute discrepancy (MAD) relative to a target (population) Rpop. The algorithm can be profitably used in many settings including model robustness studies and stress testing of investment portfolios, or in dynamic model-fit analyses to generate R matrices with a known degree of model-approximation error (as operationalized by the MAD). Using results from higher-dimensional geometry, I show that Rn×n matrices with a fixed MAD lie in the intersection of two sets that represent: (a) an elliptope and (b) the surface of a cross-polytope. When n = 3, these sets can be visualized as an elliptical tetrahedron and the surface of an octahedron. An online supplement includes R code for implementing the algorithm and for reproducing all of the results in the article.

Legally defined Regional District polygons were drawn from metes and bounds descriptions as written in Letters Patent for Regional Districts in the province of British Columbia. In the event of a discrepancy in the data, the metes and bounds description will prevail. Although the boundaries were drawn based on the legal metes and bounds descriptions, they may differ from how regional districts and their member municipalities and electoral areas currently view and/or manage their boundaries. Where discrepancies are noted, the Ministry of Municipal Affairs (the custodian) enters into discussion with the local governments whose boundaries are affected. In order to effect a change to the boundary, Cabinet approval is required. This is done through an Order in Council (OIC). While discrepancies to administrative boundaries are being resolved, boundaries may be adjusted on an ongoing basis until the requested changes are completed. The OIC_YEAR and OIC_NUMBER fields indicate the year that the boundary was passed under OIC and its associated number. The AFFECTED_ADMIN_AREA_ABRVN identifies the administrative areas that are affected by the OIC. Please note that the Northern Rockies Regional Municipality appears to be a gap in the Regional District layer, but it is a municipality and can be found in the Municipalities Layer. A polygon dataset that includes all of the administrative areas currently in the Administrative Boundaries Management System (ABMS) is available here. A complimentary point dataset that defines the administrative areas is also available available here. Other individual datasets are available from the following records: https://catalogue.data.gov.bc.ca/dataset/municipalities-legally-defined-administrative-areas-of-bc https://catalogue.data.gov.bc.ca/dataset/electoral-areas-legally-defined-administrative-areas-of-bc https://catalogue.data.gov.bc.ca/dataset/province-of-british-columbia-legally-defined-administrative-areas-of-bc https://catalogue.data.gov.bc.ca/dataset/islands-trust-legally-defined-administrative-areas-of-bc https://catalogue.data.gov.bc.ca/dataset/local-trust-areas-legally-defined-administrative-areas-of-bc

Legally defined Electoral Area polygons were drawn from metes and bounds descriptions as written in Letters Patent for Regional District Electoral Areas in the province of British Columbia. In the event of a discrepancy in the data, the metes and bounds description will prevail. Although the boundaries were drawn based on the legal metes and bounds descriptions, they may differ from how regional districts and their member municipalities and electoral areas currently view and/or manage their boundaries. Where discrepancies are noted, the Ministry of Municipal Affairs (the custodian) enters into discussion with the local governments whose boundaries are affected. In order to effect a change to the boundary, Cabinet approval is required. This is done through an Order in Council (OIC). While discrepancies to administrative boundaries are being resolved, boundaries may be adjusted on an ongoing basis until the requested changes are completed. The OIC_YEAR and OIC_NUMBER fields indicate the year that the boundary was passed under OIC and its associated number. The AFFECTED_ADMIN_AREA_ABRVN identifies the administrative areas that are affected by the OIC. A polygon dataset that includes all of the administrative areas currently in the Administrative Boundaries Management System (ABMS) is available here. A complimentary point dataset that defines the administrative areas is also available available here. Other individual datasets are available from the following records: https://catalogue.data.gov.bc.ca/dataset/municipalities-legally-defined-administrative-areas-of-bc https://catalogue.data.gov.bc.ca/dataset/regional-districts-legally-defined-administrative-areas-of-bc https://catalogue.data.gov.bc.ca/dataset/province-of-british-columbia-legally-defined-administrative-areas-of-bc https://catalogue.data.gov.bc.ca/dataset/islands-trust-legally-defined-administrative-areas-of-bc https://catalogue.data.gov.bc.ca/dataset/local-trust-areas-legally-defined-administrative-areas-of-bc

Legally defined Regional District polygons were drawn from metes and bounds descriptions as written in Letters Patent for Regional Districts in the province of British Columbia. In the event of a discrepancy in the data, the metes and bounds description will prevail. Although the boundaries were drawn based on the legal metes and bounds descriptions, they may differ from how regional districts and their member municipalities and electoral areas currently view and/or manage their boundaries. Where discrepancies are noted, the Ministry of Municipal Affairs (the custodian) enters into discussion with the local governments whose boundaries are affected. In order to effect a change to the boundary, Cabinet approval is required. This is done through an Order in Council (OIC). While discrepancies to administrative boundaries are being resolved, boundaries may be adjusted on an ongoing basis until the requested changes are completed. The OIC_YEAR and OIC_NUMBER fields indicate the year that the boundary was passed under OIC and its associated number. The AFFECTED_ADMIN_AREA_ABRVN identifies the administrative areas that are affected by the OIC. Please note that the Northern Rockies Regional Municipality appears to be a gap in the Regional District layer, but it is a municipality and can be found in the Municipalities Layer. A polygon dataset that includes all of the administrative areas currently in the Administrative Boundaries Management System (ABMS) is available here. A complimentary point dataset that defines the administrative areas is also available available here. Other individual datasets are available from the following records: https://catalogue.data.gov.bc.ca/dataset/municipalities-legally-defined-administrative-areas-of-bc https://catalogue.data.gov.bc.ca/dataset/electoral-areas-legally-defined-administrative-areas-of-bc https://catalogue.data.gov.bc.ca/dataset/province-of-british-columbia-legally-defined-administrative-areas-of-bc https://catalogue.data.gov.bc.ca/dataset/islands-trust-legally-defined-administrative-areas-of-bc https://catalogue.data.gov.bc.ca/dataset/local-trust-areas-legally-defined-administrative-areas-of-bc

Average mean difference under random subsets within dataset.

Legally defined Municipal polygons were drawn from metes and bounds descriptions as written in Letters Patent for Municipalities in the province of British Columbia. In the event of a discrepancy in the data, the metes and bounds description will prevail. Although the boundaries were drawn based on the legal metes and bounds descriptions, they may differ from how regional districts and their member municipalities and electoral areas currently view and/or manage their boundaries. Where discrepancies are noted, the Ministry of Municipal Affairs (the custodian) enters into discussion with the local governments whose boundaries are affected. In order to effect a change to the boundary, Cabinet approval is required. This is done through an Order in Council (OIC). While discrepancies to administrative boundaries are being resolved, boundaries may be adjusted on an ongoing basis until the requested changes are completed. The OIC_YEAR and OIC_NUMBER fields indicate the year that the boundary was passed under OIC and its associated number. The AFFECTED_ADMIN_AREA_ABRVN identifies the administrative areas that are affected by the OIC. See all of the administrative areas currently in the Administrative Boundaries Management System (ABMS). The complimentary point dataset that defines the administrative areas is also available. Other individual legally defined administrative area datasets are available from the following records: Regional Districts Electoral Areas Province of British Columbia Islands Trust Local Trust Areas

Average mean difference after mean and variance adjustments under random subsets within dataset.

NOTE: denotes a vector of length n, composed of random numbers from the uniform distribution that are independent from each other and from all the other random variables considered. denotes the cumulative distribution function of the standard normal distribution, and denotes the cumulative distribution function of the density of the model – or a randomized version of it when X is discrete:where is a small positive number so that remains bigger than the closest smaller discrete value to . Normalized data are defined as .We considered the following t functions: mean, variance, and only in the case of unnormalized data, and maximum (only for comparing with under the Poisson model), and only in the case of normalized data, skewness, kurtosis, andwhere denotes the ascending ordered version of . is obtained as , with the likelihood ratio statistic as and an adequate weight function [37]. Centered mean and variance are the empirical mean and variance minus the mean and variance expected with .

KL-Divergence and Maximum Mean Discrepancy between the distribution of real and synthetic data for each variable of the datasets.

Average mean discrepancies and fit indices for three competing models of the STARS.

This article deals with robust inference for parametric copula models. Estimation using canonical maximum likelihood might be unstable, especially in the presence of outliers. We propose to use a procedure based on the maximum mean discrepancy (MMD) principle. We derive nonasymptotic oracle inequalities, consistency and asymptotic normality of this new estimator. In particular, the oracle inequality holds without any assumption on the copula family, and can be applied in the presence of outliers or under misspecification. Moreover, in our MMD framework, the statistical inference of copula models for which there exists no density with respect to the Lebesgue measure on [0,1]d, as the Marshall-Olkin copula, becomes feasible. A simulation study shows the robustness of our new procedures, especially compared to pseudo-maximum likelihood estimation. An R package implementing the MMD estimator for copula models is available. Supplementary materials for this article are available online.

Mean discrepancy and accuracy of the predictions obtained by the Markov original (OM) and simplified models (SM1 and SM2).