Squares Method For Estimation Research Articles

Short-term forecasting of renewable energy consumption: Augmentation of a modified grey model with a Kalman filter

One of the important global trends in near future is to replace fossil-fuel energy with sustainable energy. The accurate predictions of the renewable energy consumption are seemingly crucial in both national and international levels. In the context of a limited number of historical data, grey prediction system of single variable is one of primary choices for such prediction. Nonetheless, this seems rather sceptical when the dynamics of a system relies on solely one variable. This paper presents a novel approach based on a modification of multivariable grey prediction model whereby the influences of exogenous variables are taken into account. Furthermore, instead of employing the least square method for parameter estimation, states and parameters in our proposed method are sequentially estimated by means of the traditional Kalman filtering. The genetic algorithm is additionally supplemented in the Kalman filter step in order to justify some unknown noise statistics. To validate the effectiveness of the proposed scheme, it is employed to estimate and predict the renewable energy consumption in Thailand along with its associated factors using the data from 1990 to 2015. Compared with the multivariable grey model using the least square method for estimation of model parameters, the results show that the hybrid approach provides a better estimation and prediction performance.

THE DYNAMIC CORRELATION BETWEEN FISCAL SPENDING ON EDUCATION, HEALTH, CONSUMPTION AND STANDARD OF LIVING IN NIGERIA

The fiscal spending of the government have always been a strong instrument towards achieving development and recovering economy from recession. This paper investigates the long run and short run impact of three component of government expenditure (education, health, and consumption expenditure) on standard of living in Nigeria with time series data from 1981 to 2017. The study employs ordinary least square method of estimation on a range of equation models: Vector Error Correction Model (VECM) and the Impulse Responses Function Model. The result shows that fiscal spending on education, health, and consumption have a long run relationship with standard of living in Nigeria and the speed of adjustment towards long –run equilibrium is 61.45%, moderately high. The short run coefficient results reveals that education expenditure in both lag 1 &2 have a positive and significant impact on standard of living while health and consumption expenditure have insignificant impact on standard of living in Nigeria. Using Impulse Response Function model, we found that none of our fiscal spending variables (education expenditure, health and consumer spending) were able to emit positive impulses/shocks on the standard of living in Nigeria. The study recommends that government should ensure that fiscal spending on education, health, and consumption should be well managed, accounted for and the method should be transparent to the populace.

Modelling Afghanistan’s Average Monthly Temperature from 1901 to 2015

The purpose of this investigation is to examine the variation of temperature in Afghanistan over the past 114 years. The historical dataset of the monthly average temperature from 1901 to 2015 were analyzed. The relationship between temperature and time during the four time intervals, i.e. (1901 -1930), (1931-1960), (1961-1990) and (1991-2015) is presented using a new analytical model based on the last –square method of estimation. We accurately fit a polynomial regression trend of degree 4 to the time series to describe the temperature variation. The results show the average difference of temperature between 2015 and 1901 increases about 1.03 °C. The average monthly difference between the maximum and minimum temperature was approximately 3.66 °C and the average monthly difference between the maximum and minimum temperature during these periods is approximately about 1.31 °C. This approach of modeling temperature using regression form significantly simplifies the data analysis. The information from data, namely the variation of the temperature, maybe be obtained from the extracted parameters such as slope, y-intercept, and the coefficients of polynomial function that are a function of time. More importantly, the parameters that describe the time variation temperature trends over 115 years obtained with a high R-squared do not vary significantly. This is in agreement with the Earth’s average temperature that has climbed to more 1 °C The evaluation of Afghanistan’s past climate data can be extremely important for understanding how climate has varied along with their possible predictable outcomes that come with increasing drought risk due to gradual increase of temperature. These results may be useful for environmental policy makers in comprehension of climate change in Afghanistan. The results can help develop appropriate strategies for the environment, and regulate resource use or pollution reduction to promote human welfare and/or nature protection.

On the Alpha Power Transformed Power Lindley Distribution

In this paper, we introduce a new generalization of the power Lindley distribution referred to asthe alpha power transformed power Lindley(APTPL). The APTPL model provides a better fit than the power Lindley distribution. It includes the alpha power transformed Lindley, power Lindley, Lindley, and gamma as special submodels. Various properties of the APTPL distribution including moments, incomplete moments, quantiles, entropy, and stochastic ordering are obtained. Maximum likelihood, maximum products of spacings, and ordinary and weighted least squares methods of estimation are utilized to obtain the estimators of the population parameters. Extensive numerical simulation is performed to examine and compare the performance of different estimates. Two important data sets are employed to show how the proposed model works in practice.

The Temperature of Japan Modelling Japan’s Average Monthly Temperature from 1901 to 2015

The purpose of this investigation is to examine the variation of temperature in Japan over the past 114 years. The historical dataset of the monthly average temperature from 1901 to 2015 were analyzed. The relationship between temperature and time during the four time intervals, i.e (1901 -1930), (1931-1960), (1961-1990) and (1991-2015) is described using a new analytical model based on the last –square method of estimation. We accurately fit a polynomial regression trend of degree 4 to the time series to describe the temperature variation. The results show the average difference of temperature between 2015 and 1901 increases about 0.97 °C. The average monthly difference between the maximum and minimum temperature was approximately 2.11 °C. This approach of modeling temperature using regression form significantly simplifies the data analysis. The information from data, namely the variation of the temperature, maybe be obtained from the extracted parameters such as slope, y-intercept, and the coefficients of polynomial function that are a function of time. More importantly, the parameters that describe the time variation temperature trends over 115 years obtained with a high R-squared do not vary significantly. This is in agreement with the Earth’s average temperature that has climbed to more 1 oC.

Technical Efficiency-Minimum Absolute Deviation and Corrected Least Squares Methods of Estimation

Technical Efficiency-Minimum Absolute Deviation and Corrected Least Squares Methods of Estimation

Do Social Responsibility and Social Media Dance together in Building Employer Reputation? Yes

This study theorizes that firms engaging in socially responsible activities are more likely to be perceived as a more attractive employer, and that this positive relationship may be amplified if firms have proficiency in leveraging social media platforms. This potential amplifier role may be explained through the greater social visibility enabled by social media. The proposed theory is tested using the structural equation modeling technique and the partial least squares method of estimation employing a secondary dataset on a sample composed of 100 large Spanish firms included in the Actualidad Economica’s Great Place to Work 2015. The empirical analysis supports our theory. This paper contributes to Information Systems research by theorizing and empirically demonstrating that social media capability creates business value by maximizing the positive impact of firm’s implementation of corporate social responsibility activities on the building of firm’s employer reputation.

Parameter estimation of partial linear model under monotonicity constraints with censored data

We propose a weighted least square method for estimation in the partial linear model with monotonicity constraints and right-censored data. This method uses the Kaplan–Meier weights to account for censoring and monotone B-splines to approximate the unknown monotone function. We show that the proposed estimator of regression coefficients is root-n consistent and asymptotically normal under appropriate assumptions. One advantage is that our method can be easily computed using existing software. A simulation study is conducted to evaluate the finite sample performance of the proposed method.

On the restricted r–k class estimator and the restricted r–d class estimator in linear regression

In this article, the restricted r–k class estimator and restricted r–d class estimator are introduced, which are general estimators of the r–k class estimator by Baye and Parker [Combining ridge and principal component regression: A money demand illustration, Commun. Stat. Theory Methods 13(2) (1984), pp. 197–205] and the r–d class estimator by Kaçıranlar and Sakallıoğlu [Combining the Liu estimator and the principal component regression estimator, Commun. Stat. Theory Methods 30(12) (2001), pp. 2699–2705], respectively. For the two cases when the restrictions are true and not true, the superiority of the restricted r–k class estimator and r–d class estimator over the restricted ridge regression estimator by Sarkar [A new estimator combining the ridge regression and the restricted least squares methods of estimation, Commun. Stat. Theory Methods 21 (1992), pp. 1987–2000] and the restricted Liu estimator by Kaçıranlar et al. [A new biased estimator in linear regression and a detailed analysis of the widely analysed dataset on Portland cement, Sankhya - Indian J. Stat. 61B(3) (1999), pp. 443–459] are discussed with respect to the mean squared error matrix criterion. Furthermore, a Monte Carlo evaluation of the estimators is given to illustrate some of the theoretical results.

Exchange Rate Depreciation and Government Policy in Nigeria: An Empirical Evidence (1980-2008)

This paper examines the Nigeria’s exchange rate depreciation and government policy in Nigeria. From the government policies point of view, we observed that, the understudied variables contributed significantly to exchange rate depreciation, and the timely control of these variables as recommended will to a great extent produce the desired appreciation of the naira exchange rate. However, this is only a microscopic aspect of whole lots of disturbances to the exchange rate. This paper adopts multiple regression analysis with Ordinary Least Squares method of estimation. The outcome of the results was enticing, indicating that, the expansionary monetary and fiscal policies pursued by the government and the constant interference of government in the market-driven economy resulted to dislocation and/or depreciation in the exchange rate. The ugly situation can only be corrected, when we look into the recommendations proffered in this paper.

Assessing Fit and Dimensionality in Least Squares Metric Multidimensional Scaling Using Akaike’s Information Criterion

Akaike’s information criterion is suggested as a tool for evaluating fit and dimensionality in metric multidimensional scaling that uses least squares methods of estimation. This criterion combines the least squares loss function with the number of estimated parameters. Numerical examples are presented. The results from analyses of both simulation data and real data demonstrate the utility of the Akaike’s information criterion in identifying the best approximating models in multidimensional scaling analyses.

Load Estimation in Balanced Radial Distribution System with Reduced Measurements

This article presents a technique for real-time load estimation in a balanced radial power distribution system in which the number of measurements required is significantly less than the number of load quantities to be estimated. As the number of measurements is lower than the number of quantities to be estimated, the weighted least square method of estimation cannot be used, and therefore, an artificial neural network-based methodology is used for estimating the loads. From extensive performance evaluation studies on different distribution systems, it was found that with the meters currently available in the market, an estimation error of approximately 1% can be obtained with the proposed methodology.

Government health care spending and the poor: evidence from Nigeria

PurposeThe purpose of this paper is to examine whether or not government health care spending reduces the poor‐rich differences in health status. Specifically, it aims to assess the health status of the poorvis‐à‐visgovernment health spending in Nigeria.Design/methodology/approachRegression analysis was carried out using the Ordinary Least Square method of estimation while secondary data was used.FindingsIt was found that despite the increase in most components of health care spending in Nigeria, the health status of the average Nigerian and the condition of health infrastructure has not improved appreciably. Also, the poor have significantly worse health status than the non‐poor and they (the poor) are more strongly affected by public spending on health care relative to the non‐poor. Thus, the difference in impact of spending between the poor and the non‐poor could be substantial.Originality/valueThis study provides information that will help reposition policies on government spending, especially on health care, so as to enhance and improve the heath status of the poor in Nigeria, thereby reducing the poor‐rich differences in health status.

Using vegetation health indices and partial least squares method for estimation of corn yield

In this paper the possibility of predicting corn yield by the use of real time acquired satellite data from the Advance Very High Resolution Radiometer (AVHRR) sensor and Partial Least Squares (PLS) method was investigated. To test the methodology in practice, 23 years (1982–2004) of AVHRR data together with official corn yield statistics of Haskell County, Kansas, USA, were used for model development and validation. The AVHRR reflectances in the visible and thermal bands, extracted from the National Oceanic and Atmospheric Administration (NOAA)/NESDIS archive, were transformed into Vegetation Health (VH) Indices (Vegetation Condition Index (VCI) and Temperature Condition Index (TCI)). The PLS method was used to construct a model relating corn yield anomaly with VH indices. Independent model verification showed that the error of corn yield prediction in Haskell County, Kansas, USA, was less than 6%. For several reasons this approach could have excellent potential as a commercial application: satellite data are inexpensive, easily available and yield estimates can be known two to three months before harvest has been completed.

A unifying theoretical and algorithmic framework for least squares methods of estimation in diffusion tensor imaging

A unifying theoretical and algorithmic framework for diffusion tensor estimation is presented. Theoretical connections among the least squares (LS) methods, (linear least squares (LLS), weighted linear least squares (WLLS), nonlinear least squares (NLS) and their constrained counterparts), are established through their respective objective functions, and higher order derivatives of these objective functions, i.e., Hessian matrices. These theoretical connections provide new insights in designing efficient algorithms for NLS and constrained NLS (CNLS) estimation. Here, we propose novel algorithms of full Newton-type for the NLS and CNLS estimations, which are evaluated with Monte Carlo simulations and compared with the commonly used Levenberg–Marquardt method. The proposed methods have a lower percent of relative error in estimating the trace and lower reduced χ 2 value than those of the Levenberg–Marquardt method. These results also demonstrate that the accuracy of an estimate, particularly in a nonlinear estimation problem, is greatly affected by the Hessian matrix. In other words, the accuracy of a nonlinear estimation is algorithm-dependent. Further, this study shows that the noise variance in diffusion weighted signals is orientation dependent when signal-to-noise ratio (SNR) is low (⩽5). A new experimental design is, therefore, proposed to properly account for the directional dependence in diffusion weighted signal variance.

A Note on the Estimation of Autocorrelation in Repeated Measurements

Maximum likelihood and the method of moments have been popular methods of estimation for analyzing repeated measurements with autocorrelation. They are used for normal and non-normal data respectively. An alternative is the quasi-least squares method of estimation. This method, based on the principle of generalized least squares, does not make any distributional assumptions and differs from the two popular methods in estimating the autocorrelation. In this paper we study large sample properties of the three methods of estimation for unbalanced data. Using asymptotic relative efficiency criterion, for normally distributed measurements we show that the quasi-least squares estimates are better than the moment estimates and are good competitors to the maximum likelihood estimates. Furthermore, using simulations we show that the quasi-least squares estimates are more efficient than the maximum likelihood and moment estimates on a wide range of the correlation parameter if the data is non-normal. Thus if normality is not tenable, the quasi-least squares estimates could be used as an alternative to the maximum likelihood and moment estimates.

Estimation of variance components based on bio-model of diallel crosses (balanced)

For a bio-model of dial lei crosses (Cockerham-Weir, 1977) with all four methods of Griffing's assumptions estimators of variance components are obtained by Quadratic Least Squares method of estimation outlined by Seely (1969, 1970, 1971), Seely-Zyskind (1971) and Yuan (1977), in the case of balanced data.

A GENERALIZED FRACTIONALLY INTEGRATED AUTOREGRESSIVE MOVING‐AVERAGE PROCESS

Abstract. This paper considers the long memory Gegenbauer autoregressive movingaverage (GARMA) process that generalizes the fractionally integrated ARMA (ARFIMA) process to allow for hyperbolic and sinusoidal decay in autocorrelations. We propose the conditional sum of squares method for estimation (which is asymptotically equivalent to the maximum likelihood estimation) and develop the asymptotic theory. Many results are in sharp contrast to those of the ARFIMA model. Simulations are conducted to assess the performance of the proposed estimators in small sample applications. Two applications to the sunspot data and the US inflation rates based on the wholesale price index are provided.

Adaptive least squares method for estimation of partial cloud coverage within a pixel

Abstract A study of the estimation of partial cloud cover within a pixel has been conducted in order to be able to use pixels partially contaminated with cloud in sea surface temperature determination. The existing estimation methods based on the least squares method with constraints of minimizing the mixing ratio and observation vector, are theoretically compared and then an adaptive least squares method is proposed. In a comparative study the estimation accuracies for the proposed and other existing methods, including the maximum likelihood method, are compared with simulated and real satellite image data of NOAA AVHRR and MOS-1 VTIR. The results with the simulation data show that the maximum likelihood method is best followed by the adaptive least squares method, the least squares method and the observation vector, while the results with the real VTIR data show that the proposed adaptive least squares method is best followed by the least squares method, the maximum likelihood method and the observation...

A New Method for Estimating Armax Models

If an ARMAX model has zeros in the MA part which are close to the unit circle, then the one step predictor can have large transients. In this case the standard least squares method for estimation of parameters is not suitable. A new method based on backforecasting is therefore developed. A simulation experiment shows that the new method is superior to standard least squares method for a ordinary third order system.