Characterization of G -Semigroup by Intuitionistic N-Fuzzy Set (INFS) and its level set

Some characterizations of G -Semigroup by intuitionistic N-fuzzy sets have been given here. The concept of intuitionistic N-fuzzy set (INFS) and its level set has been applied to G -semigroup. The notions of intuitionistic N-fuzzy G -subsemigroup and intuitionistic N-fuzzy G - ideals (left, right, lateral, quasi, and bi) have been introduced and characterized by intuitionistic N-fuzzy sets

Some Nonlinear Exponential Smoothing Models are Unstable

This paper discusses the instability of eleven nonlinear state space models that underly exponential smoothing. Hyndman et al. (2002) proposed a framework of 24 state space models for exponential smoothing, including the well-known simple exponential smoothing, Holt's linear and Holt-Winters' additive and multiplicative methods. This was extended to 30 models with Taylor's (2003) damped multiplicative methods. We show that eleven of these 30 models are unstable, having infinite forecast variances. The eleven models are those with additive errors and either multiplicative trend or multiplicative seasonality, as well as the models with multiplicative errors, multiplicative trend and additive seasonality. The multiplicative Holt-Winters' model with additive errors is among the eleven unstable models. We conclude that: (1) a model with a multiplicative trend or a multiplicative seasonal component should also have a multiplicative error; and (2) a multiplicative trend should not be mixed with additive seasonality.Exponential smoothing, forecast variance, nonlinear models, prediction intervals, stability, state space models.

Public Provision of Education and Government Spending in Pakistan

The study has been carried out to measure the incidence of government spending on education in Pakistan at the provincial (both rural and urban) level, using the primary data of the Pakistan Social Standard Living Measures Survey (PSLM), 2004-2005, and by employing the three-step Benefit Incidence Approach methodology. The paper reviews the national policies emphasising provision of education in Pakistan, as well as the trend in coverage and public sector spending on education facilities in Pakistan. The study examines the inequalities in resource distribution and service provision in relation to the government education expenditure. The rural areas of Pakistan are the more disadvantaged in the provision of the education facilities. Overall, the expenditure on the education sector is progressive, both at the regional and the provincial levels. However, variation exists in the shares of different income groups benefit from the provision of educational facilities created by public expenditure.education, public expenditure, Public Policy, Gini Coefficient, Concentration Coefficient, Benefit Incidence Approach

Health Care Services and Government Spending in Pakistan

The study has been carried out to measure the incidence of government spending on health in Pakistan at provincial, both rural and urban level; using the primary data of the Pakistan Social Standard Living Measures Survey (PSLM), 2004-05, and by employing the three-step Benefit Incidence Approach (BIA) methodology. The paper reviews the national policies emphasising health services as well as the trend in access to and public sector spending on health care facilities in Pakistan. The study explores the inequalities in resource distribution and service provision against the government health expenditures. The rural areas of Pakistan are the more disadvantaged in the provision of the health care facilities. The expenditures in health sectors are overall regressive in rural Pakistan as well as at provincial and regional levels. Mother and Child subhead is regressive in Punjab and General Hospitals and Clinics are regressive in all provinces. Only the Preventive Measures and health facilities sub-sector is progressive in Pakistan. Public health expenditures are pro-rich in Pakistan.Health, Expenditure, Public Policy, Gini, Concentration Coefficient, Mother and Child, Preventive Measures, Hospital and Clinics

Invertibility Conditions for Exponential Smoothing Models

In this article we discuss invertibility conditions for some state space models, including the models that underly simple exponential smoothing, Holt's linear method, Holt-Winters' additive method and damped trend versions of Holt's and Holt-Winters' methods. The parameter space for which the model is invertible is compared to the usual parameter regions. We find that the usual parameter restrictions (requiring all smoothing parameters to lie between 0 and 1) do not always lead to invertible models. Conversely, some invertible models have parameters which lie outside the usual region. We also find that all seasonal exponential smoothing methods are non-invertible when the usual equations are used. However, this does not affect the forecast mean. Alternative models are presented which solve the problem while retaining the basic exponential smoothing ideas.exponential smoothing, invertibility, state space models.

A New Procedure For Multiple Testing Of Econometric Models

A significant role for hypothesis testing in econometrics involves diagnostic checking. When checking the adequacy of a chosen model, researchers typically employ a range of diagnostic tests, each of which is designed to detect a particular form of model inadequacy. A major problem is how best to control the overall probability of rejecting the model when it is true and multiple test statistics are used. This paper presents a new multiple testing procedure, which involves checking whether the calculated values of the diagnostic statistics are consistent with the postulated model being true. This is done through a combination of bootstrapping to obtain a multivariate kernel density estimator of the joint density of the test statistics under the null hypothesis and Monte Carlo simulations to obtain a p value using this kernel density. We prove that under some regularity conditions, the estimated p value of our test procedure is a consistent estimate of the true p value. The proposed testing procedure is applied to tests for autocorrelation in an observed time series, for normality, and for model misspecification through the information matrix. We find that our testing procedure has correct or nearly correct sizes and good powers, particular for more complicated testing problems. We believe it is the first good method for calculating the overall p value for a vector of test statistics based on simulation.Bootstrapping, consistency, information matrix test, Markov chain Monte Carlo simulation, multivariate kernel density, normality, serial correlation, test vector