Evaluation of Simultaneous Equation Techniques in the Presence of Misspecification Error: A Monte Carlo Approach

One  of  the  assumptions  of  Classical  Linear  Regression  Model (CLRMA),  is  that  the  regression  model be  ‘correctly’   specified.  If  the  model  is  not  ‘correctly’  specified,  the  problem  of  model  misspecification  error arises. The objective of the study is to know the performances of the estimator and also the estimator that is greatly affected by misspecification error due to omission of relevant explanatory variable.  Four simultaneous equation techniques (OLS, 2SLS, 3SLS, LIML) were applied to a two-equation model and investigated on their performances when plagued with the problem of misspecification error. A Monte Carlo method simulation method was employed to investigate the effect of these estimators due to misspecification of the model. The findings revealed that the estimates obtained by 2SLS and 3SLS are similar and variances by all the estimates reduced consistently as the sample size increases. The study had revealed that 2 3 SLS performed best using average of parameter criterion while OLS generated the least variances. LIML is mostly affected by misspecification. Keywords: Monte Carlo, Misspecification error, Simultaneous equation

Estimation of Garch Models for Nigerian Exchange Rates Under Non-Gaussian Innovations

Financial series often displays evidence of leptokurticity and in that case, the empirical distribution often fails normality.  GARCH models were initially based on normality assumption but estimated model based on this assumption cannot capture all the degree of leptokurticity in the return series. In this paper, we applied variants of GARCH models under non-normal innovations-t-distribution and Generalized Error Distribution (GED) on selected Nigeria exchange rates. The Berndt, Hall, Hall, Hausman (BHHH) numerical derivatives applied in the estimation of models converged faster and the time varied significantly across models. Asymmetric GARCH model with t-distribution (GARCH-t) was selected in most of the cases whereas for Nigeria-US Dollar exchange rate, GARCH-GED was specified. Both distributions showed evidence of leptokurticity in Naira exchange rate return series. The result is of practical importance to practitioners. Key Words: GARCH, Exchange rate, Model specification, Non-Gaussian distribution.

On the Modification of M-out-of-N Bootstrap Method for Heavy-Tailed Distributions

This paper is on the modification of m-out-of-n bootstrap method for heavy-tailed distributions such as income distribution. The objective of this paper is to present a modified m-out-of-n bootstrap method (mmoon) and to compare its performance with m-out-of-n bootstrap method (moon). The distribution involved has finite variance. The simulated data sets used was drawn from Singh-Maddala distribution. The methodology involves decomposition of the empirical distribution and sampling only  times with replacement from a sample size , such that  and . The nature of the upper tail of a distribution is the major reason for the poor performance of classical bootstrap methods even in large samples. The ‘mmoon’ bootstrap method is proposed as an alternative method to ‘moon’ bootstrap method. Choosing an estimator of interest, the statistical precision of the bootstrap estimator is measured through bootstrap estimates of: standard error; absolute bias; coefficient of variation and root mean square error. The findings suggest that ‘mmoon’ performs better than moon in moderate and larger samples and it converges faste

Design and Implementation of An Improved Camera Mounted Remote Controlled Quadcopter

Aeronautics and other studies on the science of aircraft have advanced to the point where Unmanned Aerial Vehicles (UAVs) or drones are now being extensively designed. However, such aircrafts are large and not maneuverable in tight spots especially fixed wing aircraft, therefore, the design of multi-rotors are now being considered. It is inherent that small unmanned aircraft with optimal maneuverability and the ability to carry small payloads such as cameras should be designed for operations in places where a full-size aircraft are either too big or too expensive to be deployed. One of the types of Small Unmanned Aerial Vehicle (SUAV) is a Quadcopter, which can be implemented in different applications. Quadcopters are rapidly gaining interest due to their stability, low cost in building, handling capabilities and agility. Uses of such craft include aerial photography or surveillance, ground surveillance and mapping, package delivery, for rescue operations and as a research tool into ways of designing more advanced aircraft. This study therefore designed and implemented an improved industry-grade Small Unmanned Aerial Vehicle (SUAV) multi-rotor Quadcopter. Quadcopter structure model, basic components, hovering stability, dimensions, and description of basic principles of quadcopter were discussed. The study showed that SUAVs are useful across a broad range of applications. Keywords: Unmanned Aerial Vehicles, Aeronautics, Aircraft, Multi-rotors, Quadcopter, Surveillance, Aerial Photography, Small Unmanned Aerial Vehicle. DOI: 10.7176/CEIS/11-2-08 Publication date: April 30th 202

Kidney disease in hepatitis B surface antigen-positive children: experience from a centre in south-west Nigeria and a review of the Nigerian literature

Kidney disease is an important extra-hepatic manifestation of hepatitis B virus (HBV) infection. However, there is paucity of recent literature on kidney disease in children and adolescents with HBV infection from several parts of sub-Saharan Africa including Nigeria.To review the pattern of kidney disease in hepatitis B surface antigen (HBsAg)-positive children and adolescents seen at a tertiary hospital in south-west Nigeria.A retrospective study was undertaken of HBsAg-seropositive children with kidney disease managed at University College Hospital, Ibadan, from January 2004 to December 2015. Patients were identified from the paediatric nephrology unit admissions and the renal histology registers.24 children and adolescents were studied, 17 of whom were male (70.8%), and the median age was 10.0 years (range 3-15). Ten (41.7%) had nephrotic syndrome, five (20.8%) had non-nephrotic glomerulonephritis, five (20.8%) were in end-stage renal disease (ESRD), including a patient with posterior urethral valves, and four had acute kidney injury secondary to acute tubular necrosis. Renal histology was available for 10 patients: nine had nephrotic syndrome associated with minimal change disease in six, focal segmental glomerulosclerosis in two and one had membanoproliferative glomerulonephritis. The patient with non-nephrotic glomerulonephritis had diffuse global sclerosis.The pattern of kidney disease in HBV-positive children demonstrated a predominance of nephrotic syndrome, followed by non-nephrotic glomerulonephritis, ESRD and acute kidney injury. Better diagnostic facilities and treatment are required. Prevention of HBV infection by universal childhood immunisation is the ultimate goal

Global fertility in 204 countries and territories, 1950–2021, with forecasts to 2100:a comprehensive demographic analysis for the Global Burden of Disease Study 2021

BackgroundAccurate assessments of current and future fertility—including overall trends and changing population age structures across countries and regions—are essential to help plan for the profound social, economic, environmental, and geopolitical challenges that these changes will bring. Estimates and projections of fertility are necessary to inform policies involving resource and health-care needs, labour supply, education, gender equality, and family planning and support. The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2021 produced up-to-date and comprehensive demographic assessments of key fertility indicators at global, regional, and national levels from 1950 to 2021 and forecast fertility metrics to 2100 based on a reference scenario and key policy-dependent alternative scenarios.MethodsTo estimate fertility indicators from 1950 to 2021, mixed-effects regression models and spatiotemporal Gaussian process regression were used to synthesise data from 8709 country-years of vital and sample registrations, 1455 surveys and censuses, and 150 other sources, and to generate age-specific fertility rates (ASFRs) for 5-year age groups from age 10 years to 54 years. ASFRs were summed across age groups to produce estimates of total fertility rate (TFR). Livebirths were calculated by multiplying ASFR and age-specific female population, then summing across ages 10–54 years. To forecast future fertility up to 2100, our Institute for Health Metrics and Evaluation (IHME) forecasting model was based on projections of completed cohort fertility at age 50 years (CCF50; the average number of children born over time to females from a specified birth cohort), which yields more stable and accurate measures of fertility than directly modelling TFR. CCF50 was modelled using an ensemble approach in which three sub-models (with two, three, and four covariates variously consisting of female educational attainment, contraceptive met need, population density in habitable areas, and under-5 mortality) were given equal weights, and analyses were conducted utilising the MR-BRT (meta-regression—Bayesian, regularised, trimmed) tool. To capture time-series trends in CCF50 not explained by these covariates, we used a first-order autoregressive model on the residual term. CCF50 as a proportion of each 5-year ASFR was predicted using a linear mixed-effects model with fixed-effects covariates (female educational attainment and contraceptive met need) and random intercepts for geographical regions. Projected TFRs were then computed for each calendar year as the sum of single-year ASFRs across age groups. The reference forecast is our estimate of the most likely fertility future given the model, past fertility, forecasts of covariates, and historical relationships between covariates and fertility. We additionally produced forecasts for multiple alternative scenarios in each location: the UN Sustainable Development Goal (SDG) for education is achieved by 2030; the contraceptive met need SDG is achieved by 2030; pro-natal policies are enacted to create supportive environments for those who give birth; and the previous three scenarios combined. Uncertainty from past data inputs and model estimation was propagated throughout analyses by taking 1000 draws for past and present fertility estimates and 500 draws for future forecasts from the estimated distribution for each metric, with 95% uncertainty intervals (UIs) given as the 2·5 and 97·5 percentiles of the draws. To evaluate the forecasting performance of our model and others, we computed skill values—a metric assessing gain in forecasting accuracy—by comparing predicted versus observed ASFRs from the past 15 years (2007–21). A positive skill metric indicates that the model being evaluated performs better than the baseline model (here, a simplified model holding 2007 values constant in the future), and a negative metric indicates that the evaluated model performs worse than baseline.FindingsDuring the period from 1950 to 2021, global TFR more than halved, from 4·84 (95% UI 4·63–5·06) to 2·23 (2·09–2·38). Global annual livebirths peaked in 2016 at 142 million (95% UI 137–147), declining to 129 million (121–138) in 2021. Fertility rates declined in all countries and territories since 1950, with TFR remaining above 2·1—canonically considered replacement-level fertility—in 94 (46·1%) countries and territories in 2021. This included 44 of 46 countries in sub-Saharan Africa, which was the super-region with the largest share of livebirths in 2021 (29·2% [28·7–29·6]). 47 countries and territories in which lowest estimated fertility between 1950 and 2021 was below replacement experienced one or more subsequent years with higher fertility; only three of these locations rebounded above replacement levels. Future fertility rates were projected to continue to decline worldwide, reaching a global TFR of 1·83 (1·59–2·08) in 2050 and 1·59 (1·25–1·96) in 2100 under the reference scenario. The number of countries and territories with fertility rates remaining above replacement was forecast to be 49 (24·0%) in 2050 and only six (2·9%) in 2100, with three of these six countries included in the 2021 World Bank-defined low-income group, all located in the GBD super-region of sub-Saharan Africa. The proportion of livebirths occurring in sub-Saharan Africa was forecast to increase to more than half of the world's livebirths in 2100, to 41·3% (39·6–43·1) in 2050 and 54·3% (47·1–59·5) in 2100. The share of livebirths was projected to decline between 2021 and 2100 in most of the six other super-regions—decreasing, for example, in south Asia from 24·8% (23·7–25·8) in 2021 to 16·7% (14·3–19·1) in 2050 and 7·1% (4·4–10·1) in 2100—but was forecast to increase modestly in the north Africa and Middle East and high-income super-regions. Forecast estimates for the alternative combined scenario suggest that meeting SDG targets for education and contraceptive met need, as well as implementing pro-natal policies, would result in global TFRs of 1·65 (1·40–1·92) in 2050 and 1·62 (1·35–1·95) in 2100. The forecasting skill metric values for the IHME model were positive across all age groups, indicating that the model is better than the constant prediction.InterpretationFertility is declining globally, with rates in more than half of all countries and territories in 2021 below replacement level. Trends since 2000 show considerable heterogeneity in the steepness of declines, and only a small number of countries experienced even a slight fertility rebound after their lowest observed rate, with none reaching replacement level. Additionally, the distribution of livebirths across the globe is shifting, with a greater proportion occurring in the lowest-income countries. Future fertility rates will continue to decline worldwide and will remain low even under successful implementation of pro-natal policies. These changes will have far-reaching economic and societal consequences due to ageing populations and declining workforces in higher-income countries, combined with an increasing share of livebirths among the already poorest regions of the world.FundingBill & Melinda Gates Foundation

Global burden of 288 causes of death and life expectancy decomposition in 204 countries and territories and 811 subnational locations, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021

BACKGROUND Regular, detailed reporting on population health by underlying cause of death is fundamental for public health decision making. Cause-specific estimates of mortality and the subsequent effects on life expectancy worldwide are valuable metrics to gauge progress in reducing mortality rates. These estimates are particularly important following large-scale mortality spikes, such as the COVID-19 pandemic. When systematically analysed, mortality rates and life expectancy allow comparisons of the consequences of causes of death globally and over time, providing a nuanced understanding of the effect of these causes on global populations. METHODS The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2021 cause-of-death analysis estimated mortality and years of life lost (YLLs) from 288 causes of death by age-sex-location-year in 204 countries and territories and 811 subnational locations for each year from 1990 until 2021. The analysis used 56 604 data sources, including data from vital registration and verbal autopsy as well as surveys, censuses, surveillance systems, and cancer registries, among others. As with previous GBD rounds, cause-specific death rates for most causes were estimated using the Cause of Death Ensemble model-a modelling tool developed for GBD to assess the out-of-sample predictive validity of different statistical models and covariate permutations and combine those results to produce cause-specific mortality estimates-with alternative strategies adapted to model causes with insufficient data, substantial changes in reporting over the study period, or unusual epidemiology. YLLs were computed as the product of the number of deaths for each cause-age-sex-location-year and the standard life expectancy at each age. As part of the modelling process, uncertainty intervals (UIs) were generated using the 2·5th and 97·5th percentiles from a 1000-draw distribution for each metric. We decomposed life expectancy by cause of death, location, and year to show cause-specific effects on life expectancy from 1990 to 2021. We also used the coefficient of variation and the fraction of population affected by 90% of deaths to highlight concentrations of mortality. Findings are reported in counts and age-standardised rates. Methodological improvements for cause-of-death estimates in GBD 2021 include the expansion of under-5-years age group to include four new age groups, enhanced methods to account for stochastic variation of sparse data, and the inclusion of COVID-19 and other pandemic-related mortality-which includes excess mortality associated with the pandemic, excluding COVID-19, lower respiratory infections, measles, malaria, and pertussis. For this analysis, 199 new country-years of vital registration cause-of-death data, 5 country-years of surveillance data, 21 country-years of verbal autopsy data, and 94 country-years of other data types were added to those used in previous GBD rounds. FINDINGS The leading causes of age-standardised deaths globally were the same in 2019 as they were in 1990; in descending order, these were, ischaemic heart disease, stroke, chronic obstructive pulmonary disease, and lower respiratory infections. In 2021, however, COVID-19 replaced stroke as the second-leading age-standardised cause of death, with 94·0 deaths (95% UI 89·2-100·0) per 100 000 population. The COVID-19 pandemic shifted the rankings of the leading five causes, lowering stroke to the third-leading and chronic obstructive pulmonary disease to the fourth-leading position. In 2021, the highest age-standardised death rates from COVID-19 occurred in sub-Saharan Africa (271·0 deaths [250·1-290·7] per 100 000 population) and Latin America and the Caribbean (195·4 deaths [182·1-211·4] per 100 000 population). The lowest age-standardised death rates from COVID-19 were in the high-income super-region (48·1 deaths [47·4-48·8] per 100 000 population) and southeast Asia, east Asia, and Oceania (23·2 deaths [16·3-37·2] per 100 000 population). Globally, life expectancy steadily improved between 1990 and 2019 for 18 of the 22 investigated causes. Decomposition of global and regional life expectancy showed the positive effect that reductions in deaths from enteric infections, lower respiratory infections, stroke, and neonatal deaths, among others have contributed to improved survival over the study period. However, a net reduction of 1·6 years occurred in global life expectancy between 2019 and 2021, primarily due to increased death rates from COVID-19 and other pandemic-related mortality. Life expectancy was highly variable between super-regions over the study period, with southeast Asia, east Asia, and Oceania gaining 8·3 years (6·7-9·9) overall, while having the smallest reduction in life expectancy due to COVID-19 (0·4 years). The largest reduction in life expectancy due to COVID-19 occurred in Latin America and the Caribbean (3·6 years). Additionally, 53 of the 288 causes of death were highly concentrated in locations with less than 50% of the global population as of 2021, and these causes of death became progressively more concentrated since 1990, when only 44 causes showed this pattern. The concentration phenomenon is discussed heuristically with respect to enteric and lower respiratory infections, malaria, HIV/AIDS, neonatal disorders, tuberculosis, and measles. INTERPRETATION Long-standing gains in life expectancy and reductions in many of the leading causes of death have been disrupted by the COVID-19 pandemic, the adverse effects of which were spread unevenly among populations. Despite the pandemic, there has been continued progress in combatting several notable causes of death, leading to improved global life expectancy over the study period. Each of the seven GBD super-regions showed an overall improvement from 1990 and 2021, obscuring the negative effect in the years of the pandemic. Additionally, our findings regarding regional variation in causes of death driving increases in life expectancy hold clear policy utility. Analyses of shifting mortality trends reveal that several causes, once widespread globally, are now increasingly concentrated geographically. These changes in mortality concentration, alongside further investigation of changing risks, interventions, and relevant policy, present an important opportunity to deepen our understanding of mortality-reduction strategies. Examining patterns in mortality concentration might reveal areas where successful public health interventions have been implemented. Translating these successes to locations where certain causes of death remain entrenched can inform policies that work to improve life expectancy for people everywhere. FUNDING Bill & Melinda Gates Foundation

A comparative analysis of posterior simulation techniques in the estimation of bayesian regression model

In recent years, the development of several posterior simulation techniques has boosted the field of Bayesian econometrics especially in applied works. Prior distribution plays a dominant role in Bayesian analysis; priors are meant to reflect information the researcher has before seeing the data. This research examined the sensitivity of the Gibbs sampler (GS) and Monte Carlo Integration (MCI) methods to three different levels of correlation in prior covariance to know the effects of varying correlation on posterior simulation methods in estimating the parameters in a linear regression model. The three different levels of correlation are; Negative Correlation (NC), Positive Correlation (PC) and Zero correlation (ZC). The results showed that MCI outperformed the GS in most cases and the accuracy of MCI does not depend on the level of correlation either positive or negative while GS performed better when positive level of correlation was used as information in the prior covariance than using negative level of correlation. The use of MCI in Bayesian inference might be of practical importance to practitioners.En los últimos años, el desarrollo de varias técnicas de simulación posterior ha impulsado el campo de la econometría bayesiana, especialmente en trabajos aplicados. La distribución previa juega un papel dominante en el análisis bayesiano; los anteriores están destinados a reflejar la información que el investigador tiene antes de ver los datos. Esta investigación examinó la sensibilidad de los métodos de muestreo de Gibbs (GS) e Integración de Monte Carlo (MCI) a tres niveles diferentes de correlación en covarianza previa para conocer los efectos de la correlación variable en los métodos de simulación posterior al estimar los parámetros en un modelo de regresión lineal. Los tres niveles diferentes de correlación son: Correlación negativa (NC), correlación positiva (PC) y correlación cero (ZC). Los resultados mostraron que el MCI superó al GS en la mayoría de los casos y la precisión del MCI no depende del nivel de correlación, ya sea positivo o negativo, mientras que el GS se desempeñó mejor cuando se usó el nivel de correlación positivo como información en la covarianza previa que el uso de un nivel negativo de correlación. El uso de MCI en la inferencia bayesiana podría ser de importancia práctica para los profesionales

Dynamic linear regression by bayesian and bootstrapping techniques

Estimation of a dynamic linear regression is said to be of importance as events are measured on past events. However, estimation of dynamic models using the OLS is inefficient since it cannot produce the least variance and disregarding this problem would potentially lead to severe statistical problems. Therefore, the main objective of the study is to employ the bootstrap technique and Bayesian method in estimating the parameters of a dynamic regression model and compare their performances using standard deviation, absolute bias and mean square error of the estimates. The residual resampling technique is used for the bootstrap approach and the Normal-gamma model for the Bayesian approach. The results showed that the bootstrap technique outperformed the Bayesian method with lower standard error values. The bootstrap method also displayed an asymptotic propertySe dice que la estimación de una regresión lineal dinámica es importante a medida que los eventos se miden en eventos pasados. Sin embargo, la estimación de los modelos dinámicos que utilizan el MCO es ineficiente, ya que no puede producir la menor variación y el hecho de no tener en cuenta este problema podría conducir a problemas estadísticos graves. Por lo tanto, el objetivo principal del estudio es emplear la técnica bootstrap y el método bayesiano para estimar los parámetros de un modelo de regresión dinámica y comparar sus rendimientos utilizando desviación estándar, sesgo absoluto y error cuadrático medio de las estimaciones. La técnica de remuestreo residual se utiliza para el enfoque bootstrap y el modelo de gamma normal para el enfoque bayesiano. Los resultados mostraron que la técnica de arranque superó al método Bayesiano con valores de error estándar más bajos. El método de arranque también mostró una propiedad asintótica