Frank J. Massey

Bio: Frank J. Massey is an academic researcher from University of Oregon. The author has contributed to research in topics: Cumulative distribution function & Goodness of fit. The author has an hindex of 1, co-authored 1 publications receiving 4410 citations.

The Kolmogorov-Smirnov Test for Goodness of Fit

Abstract: The test is based on the maximum difference between an empirical and a hypothetical cumulative distribution. Percentage points are tabled, and a lower bound to the power function is charted. Confidence limits for a cumulative distribution are described. Examples are given. Indications that the test is superior to the chi-square test are cited.

On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown

Abstract: The standard tables used for the Kolmogorov-Smirnov test are valid when testing whether a set of observations are from a completely-specified continuous distribution. If one or more parameters must be estimated from the sample then the tables are no longer valid. A table is given in this note for use with the Kolmogorov-Smirnov statistic for testing whether a set of observations is from a normal population when the mean and variance are not specified but must be estimated from the sample. The table is obtained from a Monte Carlo calculation. A brief Monte Carlo investigation is made of the power of the test.

Global, regional, and national comparative risk assessment of 79 behavioural, environmental and occupational, and metabolic risks or clusters of risks, 1990–2015: A systematic analysis for the Global Burden of Disease Study 2015

Abstract: BACKGROUND The Global Burden of Diseases, Injuries, and Risk Factors Study 2015 provides an up-to-date synthesis of the evidence for risk factor exposure and the attributable burden of disease. By providing national and subnational assessments spanning the past 25 years, this study can inform debates on the importance of addressing risks in context. METHODS We used the comparative risk assessment framework developed for previous iterations of the Global Burden of Disease Study to estimate attributable deaths, disability-adjusted life-years (DALYs), and trends in exposure by age group, sex, year, and geography for 79 behavioural, environmental and occupational, and metabolic risks or clusters of risks from 1990 to 2015. This study included 388 risk-outcome pairs that met World Cancer Research Fund-defined criteria for convincing or probable evidence. We extracted relative risk and exposure estimates from randomised controlled trials, cohorts, pooled cohorts, household surveys, census data, satellite data, and other sources. We used statistical models to pool data, adjust for bias, and incorporate covariates. We developed a metric that allows comparisons of exposure across risk factors-the summary exposure value. Using the counterfactual scenario of theoretical minimum risk level, we estimated the portion of deaths and DALYs that could be attributed to a given risk. We decomposed trends in attributable burden into contributions from population growth, population age structure, risk exposure, and risk-deleted cause-specific DALY rates. We characterised risk exposure in relation to a Socio-demographic Index (SDI). FINDINGS Between 1990 and 2015, global exposure to unsafe sanitation, household air pollution, childhood underweight, childhood stunting, and smoking each decreased by more than 25%. Global exposure for several occupational risks, high body-mass index (BMI), and drug use increased by more than 25% over the same period. All risks jointly evaluated in 2015 accounted for 57·8% (95% CI 56·6-58·8) of global deaths and 41·2% (39·8-42·8) of DALYs. In 2015, the ten largest contributors to global DALYs among Level 3 risks were high systolic blood pressure (211·8 million [192·7 million to 231·1 million] global DALYs), smoking (148·6 million [134·2 million to 163·1 million]), high fasting plasma glucose (143·1 million [125·1 million to 163·5 million]), high BMI (120·1 million [83·8 million to 158·4 million]), childhood undernutrition (113·3 million [103·9 million to 123·4 million]), ambient particulate matter (103·1 million [90·8 million to 115·1 million]), high total cholesterol (88·7 million [74·6 million to 105·7 million]), household air pollution (85·6 million [66·7 million to 106·1 million]), alcohol use (85·0 million [77·2 million to 93·0 million]), and diets high in sodium (83·0 million [49·3 million to 127·5 million]). From 1990 to 2015, attributable DALYs declined for micronutrient deficiencies, childhood undernutrition, unsafe sanitation and water, and household air pollution; reductions in risk-deleted DALY rates rather than reductions in exposure drove these declines. Rising exposure contributed to notable increases in attributable DALYs from high BMI, high fasting plasma glucose, occupational carcinogens, and drug use. Environmental risks and childhood undernutrition declined steadily with SDI; low physical activity, high BMI, and high fasting plasma glucose increased with SDI. In 119 countries, metabolic risks, such as high BMI and fasting plasma glucose, contributed the most attributable DALYs in 2015. Regionally, smoking still ranked among the leading five risk factors for attributable DALYs in 109 countries; childhood underweight and unsafe sex remained primary drivers of early death and disability in much of sub-Saharan Africa. INTERPRETATION Declines in some key environmental risks have contributed to declines in critical infectious diseases. Some risks appear to be invariant to SDI. Increasing risks, including high BMI, high fasting plasma glucose, drug use, and some occupational exposures, contribute to rising burden from some conditions, but also provide opportunities for intervention. Some highly preventable risks, such as smoking, remain major causes of attributable DALYs, even as exposure is declining. Public policy makers need to pay attention to the risks that are increasingly major contributors to global burden. FUNDING Bill & Melinda Gates Foundation.

Tests for Specification Errors in Classical Linear Least-Squares Regression Analysis

Abstract: SUMMARY The effects on the distribution of least-squares residuals of a series of model mis-specifications are considered. It is shown that for a variety of specification errors the distributions of the least-squares residuals are normal, but with non-zero means. An alternative predictor of the disturbance vector is used in developing four procedures for testing for the presence of specification error. The specification errors considered are omitted variables, incorrect functional form, simultaneous equation problems and heteroskedasticity. THE objectives of this paper are two. The first is to derive the distributions of the classical linear least-squares residuals under a variety of specification errors. The errors considered are omitted variables, incorrect functional form, simultaneous equation problems and heteroskedasticity. It is assumed that the disturbance terms are independently and normally distributed. It will be shown that the effect of the specification errors considered above is, with the exception of the error of heteroskedasticity, to yield residuals which though normally distributed do not have zero means, so that the distribution of the squared residuals is non-central x2. The second objective is to derive procedures to test for the presence of the specification errors considered in the first part of the paper. The tests are developed by comparing the distribution of residuals under the hypothesis that the specification of the model is correct to the distribution of the residuals yielded under the alternative hypothesis that there is a specification error of one of the types considered in the first part of the paper. As a preliminary step to deriving the test procedures the classical least-squares residual vector is transformed to a sub-vector which has more desirable properties for testing the null hypothesis that the specification of the model is correct. Also, under certain assumptions, with respect to the alternative hypothesis, it is shown that the mean vector of the residuals can be approximated by a linear sum of vectors qj,

A technology-based global inventory of black and organic carbon emissions from combustion

Abstract: [1] We present a global tabulation of black carbon (BC) and primary organic carbon (OC) particles emitted from combustion. We include emissions from fossil fuels, biofuels, open biomass burning, and burning of urban waste. Previous ‘‘bottom-up’’ inventories of black and organic carbon have assigned emission factors on the basis of fuel type and economic sector alone. Because emission rates are highly dependent on combustion practice, we consider combinations of fuel, combustion type, and emission controls and their prevalence on a regional basis. Central estimates of global annual emissions are 8.0 Tg for black carbon and 33.9 Tg for organic carbon. These estimates are lower than previously published estimates by 25–35%. The present inventory is based on 1996 fuel-use data, updating previous estimates that have relied on consumption data from 1984. An offset between decreased emission factors and increased energy use since the base year of the previous inventory prevents the difference between this work and previous inventories from being greater. The contributions of fossil fuel, biofuel, and open burning are estimated as 38%, 20%, and 42%, respectively, for BC, and 7%, 19%, and 74%, respectively, for OC. We present a bottom-up estimate of uncertainties in source strength by combining uncertainties in particulate matter emission factors, emission characterization, and fuel use. The total uncertainties are about a factor of 2, with uncertainty ranges of 4.3–22 Tg/yr for BC and 17–77 Tg/yr for OC. Low-technology combustion contributes greatly to both the emissions and the uncertainties. Advances in emission characterization for small residential, industrial, and mobile sources and topdown analysis combining field measurements and transport modeling with iterative inventory development will be required to reduce the uncertainties further. INDEX TERMS: 0305 Atmospheric Composition and Structure: Aerosols and particles (0345, 4801); 0322 Atmospheric Composition and Structure: Constituent sources and sinks; 0345 Atmospheric Composition and Structure: Pollution—urban and regional (0305); 0360 Atmospheric Composition and Structure: Transmission and scattering of radiation; 0365 Atmospheric Composition and Structure: Troposphere—composition and chemistry; KEYWORDS: emission, black carbon, organic carbon, fossil fuel, biofuel, biomass burning