A robust MM estimates for the linear model is revisited. This estimates are defined by a three-stage procedures and posses the following properties: (i) they are highly efficient when the errors have a normal distribution and (ii) their breakdown-point is 0.5. A numerical examples are used to show that the MM estimates has a higher breakdown point and is more efficient than The RLS (Reweighted Least Squares Regression based on The Least Median Squares) estimates.
Suatu penganggar teguh dalam model linear dinamakan Penganggar MM diperkenalkan kembali. Penganggar ini ditakrifkan menerusi pendekatan 3 peringkat dan mempunyai sifat sifat seperti berikut: i) kecekpan yang tinggi sekiranya ralat tertabur secara normal dan ii) titik musnah bersamaan 0.5. Contoh berangka telah digunakan ulituk menunjukkan bahawa penganggar ini mempunyai titik musnah yang tinggi dan lebih cekap daripada penganggar KDTB (Penganggar Kuasadua Terkecil Berpemberat berdasarkan Kaedah Kuasadua Terkecil).
This paper proposes the use of bootstrap, robust and fuzzy multiple linear regressions method in
handling general insurance in order to get improved results. The main objective of bootstrapping is to
estimate the distribution of an estimator or test statistic by resampling one's data or a model estimated
from the data under conditions that hold in a wide variety of econometric applications. In addition,
bootstrap also provides approximations to distributions of statistics, coverage probabilities of confidence
intervals, and rejection probabilities of hypothesis tests that produce accurate results. In this paper, we
emphasize the combining and modelling using bootstrapping, robust and fuzzy regression methodology.
The results show that alternative methods produce better results than multiple linear regressions (MLR)
Replicated linear functional relationship model is often used to describe
relationships between two circular variables where both variables have error terms and
replicate observations are available. We derive the estimate of the rotation parameter
of the model using the maximum likelihood method. The performance of the proposed
method is studied through simulation, and it is found that the biasness of the estimates
is small, thus implying the suitability of the method. Practical application of the
method is illustrated by using a real data set.
Missing value problem is common when analysing quantitative data. With the rapid growth of computing capabilities, advanced methods in particular those based on maximum likelihood estimation has been suggested to best handle the missing values problem. In this paper, two modern imputing approaches namely expectation-maximization (EM) and expectation-maximization with bootstrapping (EMB) are proposed in this paper for two kinds of linear functional relationship (LFRM) models, namely LFRM1 for full model and LFRM2 for linear functional relationship model when slope parameter is estimated using a nonparametric approach. The performance of EM and EMB are measured using mean absolute error, root-mean-square error and estimated bias. The results of the simulation study suggested that both EM and EMB methods are applicable to the LFRM with EMB algorithm outperforms the standard EM algorithm. Illustration using a practical example and a real data set is provided.
Recently, there is strong interest on the subject of outlier problem in circular data. In this paper, we focus on detecting outliers in a circular regression model proposed by Down and Mardia. The basic properties of the model are available including the exact form of covariance matrix of the parameters. Hence, we intend to identify outliers in the model by looking at the effect of the outliers on the covariance matrix. The method resembles closely the COVRATIO statistic for the case of linear regression problem. The corresponding critical values and the performance of the outlier detection procedure are studied via simulations. For illustration, we apply the procedure on the wind data set.
Multiple imputation method is a widely used method in missing data analysis. The method consists of a three-stage
process including imputation, analyzing and pooling. The number of imputations to be selected in the imputation step
in the first stage is important. Hence, this study aimed to examine the performance of multiple imputation method at
different numbers of imputations. Monotone missing data pattern was created in the study by deleting approximately 24%
of the observations from the continuous result variable with complete data. At the first stage of the multiple imputation
method, monotone regression imputation at different numbers of imputations (m=3, 5, 10 and 50) was performed. In the
second stage, parameter estimations and their standard errors were obtained by applying general linear model to each
of the complete data sets obtained. In the final stage, the obtained results were pooled and the effect of the numbers of
imputations on parameter estimations and their standard errors were evaluated on the basis of these results. In conclusion,
efficiency of parameter estimations at the number of imputation m=50 was determined as about 99%. Hence, at the
determined missing observation rate, increase was determined in efficiency and performance of the multiple imputation
method as the number of imputations increased.
In high-dimensional quantitative structure-activity relationship (QSAR) modelling, penalization methods have been a popular choice to simultaneously address molecular descriptor selection and QSAR model estimation. In this study, a penalized linear regression model with L1/2-norm is proposed. Furthermore, the local linear approximation algorithm is utilized to avoid the non-convexity of the proposed method. The potential applicability of the proposed method is tested on several benchmark data sets. Compared with other commonly used penalized methods, the proposed method can not only obtain the best predictive ability, but also provide an easily interpretable QSAR model. In addition, it is noteworthy that the results obtained in terms of applicability domain and Y-randomization test provide an efficient and a robust QSAR model. It is evident from the results that the proposed method may possibly be a promising penalized method in the field of computational chemistry research, especially when the number of molecular descriptors exceeds the number of compounds.
Crude oil prices do play significant role in the global economy and are a key input into option pricing formulas, portfolio allocation, and risk measurement. In this paper, a hybrid model integrating wavelet and multiple linear regressions (MLR) is proposed for crude oil price forecasting. In this model, Mallat wavelet transform is first selected to decompose an original time series into several subseries with different scale. Then, the principal component analysis (PCA) is used in processing subseries data in MLR for crude oil price forecasting. The particle swarm optimization (PSO) is used to adopt the optimal parameters of the MLR model. To assess the effectiveness of this model, daily crude oil market, West Texas Intermediate (WTI), has been used as the case study. Time series prediction capability performance of the WMLR model is compared with the MLR, ARIMA, and GARCH models using various statistics measures. The experimental results show that the proposed model outperforms the individual models in forecasting of the crude oil prices series.
By using a linear operator, we obtain some new results for a normalized analytic function f defined by means of the Hadamard product of Hurwitz zeta function. A class related to this function will be introduced and the properties will be discussed.
Preliminary analysis of the short-term impact of a running headlights intervention revealed that there has been a significant drop in conspicuity-related motorcycle accidents in the pilot areas, Seremban and Shah Alam, Malaysia. This paper attempts to look in more detail at conspicuity-related accidents involving motorcycles. The aim of the analysis was to establish a statistical model to describe the relationship between the frequency of conspicuity-related motorcycle accidents and a range of explanatory variables so that new insights can be obtained into the effects of introducing a running headlight campaign and regulation. The exogenous variables in this analysis include the influence of time trends, changes in the recording and analysis system, the effect of fasting activities during Ramadhan and the "Balik Kampong" culture, a seasonal cultural-religious holiday activity unique to Malaysia. The model developed revealed that the running headlight intervention reduced the conspicuity-related motorcycle accidents by about 29%. It is concluded that the intervention has been successful in improving conspicuity-related motorcycle accidents in Malaysia.
The increase in car usage due to economic prosperity has led to increase in occupant injuries. One way to reduce the injuries encountered by road accident victims is by implementing the rear seatbelt (RSB) law. Rear seatbelt wearing has been proven to save lives. In Malaysia, the implementation of the restraint system for front occupant has started in the 70's. However, the rear seatbelt enforcement law only came in 2009, after six months of an advocacy program. Prior to the introduction of the rear seatbelt law, rear seatbelt wearing rate was rather low, started to increase gradually during the advocacy period and jumped to the highest level after two month of the enforcement. This paper attempts to assess the effectiveness of the rear seatbelt intervention in reducing injuries among passenger car occupants in Malaysia using the generalized linear model (GLM). In GLM procedure, the dependent variable is the number of people from passenger vehicles that sustained severe and slight injuries, for the study period. The study period selected covers six months before implementation, six months during advocacy program, and six months after the law is implemented. The independent variables considered are enforcement and balik kampung activities (both are dummy variables) and time effect. Our results suggest that RSB intervention (p-value= 0.0001) had significantly reduced the number of people sustained serious and slight injuries by about 20%. The implementation of change in the RSB law has benefited not only in reducing the number of injuries but also result to great impact to the health outcomes.
Lycopene and total phenolics of pink guava puree industry by-products (refiner, siever and decanter)
were evaluated after steam blanching at selected temperatures and times. Lycopene content was in the order of decanter > siever > refiner (7.3, 6.3 and 1.5 mg/100 g, respectively), and the content of total phenolics was in the order of refiner > siever > decanter (4434.1, 2881.3 and 1529.3 mg GAE/100 g, respectively). Regression coefficients for temperatures (x1) and times (x2) from multiple linear regression models of siever and decanter showed significant (p
Monthly data about oil production at several drilling wells is an example of
spatio-temporal data. The aim of this research is to propose nonlinear spatio-temporal
model, i.e. Feedforward Neural Network - VectorAutoregressive (FFNN-VAR) and FFNN
- Generalized Space-Time Autoregressive (FFNN-GSTAR), and compare their forecast
accuracy to linearspatio-temporal model, i.e. VAR and GSTAR. These spatio-temporal
models are proposed and applied for forecasting monthly oil production data at three
drilling wells in East Java, Indonesia. There are 60 observations that be divided to two
parts, i.e. the first 50 observations for training data and the last 10 observations for
testing data. The results show that FFNN-GSTAR(11) and FFNN-VAR(1) as nonlinear
spatio-temporal models tend to give more accurate forecast than VAR(1) and GSTAR(11)
as linear spatio-temporal models. Moreover, further research about nonlinear spatiotemporal
models based on neural networks and GSTAR is needed for developing new
hybrid models that could improve the forecast accuracy.
This paper investigates a novel offset-free control scheme based on a multiple model predictive controller (MMPC) and an adaptive integral action controller for nonlinear processes. Firstly, the multiple model description captures the essence of the nonlinear process, while keeping the MPC optimization linear. Multiple models also enable the controller to deal with the uncertainty associated with changing setpoint. Then, a min-max approach is utilized to counter the effect of parametric uncertainty between the linear models and the nonlinear process. Finally, to deal with other uncertainties, such as input and output disturbances, an adaptive integral action controller is run in parallel to the MMPC. Thus creating a novel offset-free approach for nonlinear systems that is more easily tuned than observer-based MPC. Simulation results for a pH-controller, which acts as an example of a nonlinear process, are presented to demonstrate the usefulness of the technique compared to using an observer-based MPC.
Forecasting a multiple seasonal data is differ from a usual seasonal data since it contains more than one cycle in a
data. Multiple linear regression (MLR) models have been used widely in load forecasting because of its usefulness in the
forecast a linear relationship with other factors but MLR has a disadvantage of having difficulties in modelling a nonlinear
relationship between the variables and influencing factors. Neural network (NN) model, on the other hand, is a good
model for modelling a nonlinear data. Therefore, in this study, a combination of MLR and NN models has proposed this
combination to overcome the problem. This hybrid model is then compared with MLR and NN models to see the performance
of the hybrid model. RMSE is used as a performance indicator and a proposed graphical error plot is introduce to see the
error graphically. From the result obtained this model gives a better forecast compare to the other two models.
Kajian yang dijalankan adalah berkaitan dengan penentuan model yang sesuai serta analisis data penyerapan logam berat oleh sayuran berdaun yang terpilih iaitu kangkung (Ipomea aquatica), sawi bunga (Brassica chinensis var parachinensis), bayam (Amaranthus oleraceus L) dan sawi putih (Brassica chinensis L.). Kajian ini bertujuan untuk menentukan dan membandingkan kandungan serta corak pengambilan logam berat yang diserap oleh sayuran dan juga bahagian-bahagiannya yang meliputi daun, batang dan akar. Penentuan model yang dibuat bertujuan bagi melihat corak penyerapan logam berat oleh sayuran atau bahagian sayuran tertentu. Logam berat yang dikaji terdiri daripada kadmium , kromium, kuprum, ferum , mangan, plumbum dan zink. Plot serakan digunakan bagi menentukan corak pengambilan logam berat dalam sayuran dan bahagian-bahagiannya. Selain itu ujian Kruskal-Wallis digunakan bagi membuat perbandingan median di antara logam berat yang diserap oleh sayuran yang dikaji. Nilai khi-kuasa dua dan juga nilai-p digunakan bagi menentukan sama ada sesuatu logam berat yang diserap itu berkait rapat dengan jenis sayuran secara signifikan. Secara umum bolehlah dikatakan bahawa logam Fe, Mn dan Zn adalah dominan dalam semua bahagian sayuran yang dikaji. Selain itu, melalui ujian Kruskal-Wallis didapati penyerapan kesemua logam berat pada setiap bahagian sayuran adalah berbeza secara signifikan. Penyuaian model regresi linear, kuadratik, kubik atau eksponen telah dilakukan terhadap data ini dan didapati kebanyakan data dapat disuaikan dengan baik oleh model kuadratik dan kubik berdasarkan nilai pekali penentuan (R2).
This paper gives a comprehensive discussion on complex regression model by extending the idea of regression model to circular variables. Various aspect have been considered such as the biasness of parameters, error assumptions and model checking. The advantage of this approach is that it allows the use of usual technique available in ordinary linear regression for the regression of circular variables. The quality of the estimates and the feasibility of the approach were illustrated via simulation. The model was then applied to the wave direction data.
Climate changes have become serious issues that have been widely discussed by researchers. One of the issues concerns with the study in changes of rainfall patterns. Changes in rainfall patterns affect the dryness and wetness conditions of a region. In this study, the three-dimensional loglinear model was used to fit the observed frequencies and to model the expected frequencies of wet class transition on eight rainfall stations in Peninsular Malaysia. The expected frequency values could be employed to determine the odds value of wet classes of each station. Further, the odds values were used to estimate the wet class of the following month if the wet class of the previous month and current month were identified. The wet classification based on SPI index (Standardized Precipitation Index). For station that was analyzed, there was no difference found were between estimated and observed wet classes. It was concluded that the loglinear models can be used to estimate the wetness classes through the estimates of odds values.
Estimation and forecast of groundwater recharge and capacity of aquifer are essential issues in water resources investigation. In the current research, groundwater recharge, recharge coefficient and effective rainfall were determined through a case study using empirical methods applicable to the tropical zones. The related climatological data between January 2000 and December 2010 were collected in Selangor, Malaysia. The results showed that groundwater recharge was326.39 mm per year, effective precipitation was 1807.97 mm per year and recharge coefficient was 18% for the study area. In summary, the precipitation converted to recharge, surface runoff and evapotranspiration are 12, 32 and 56% of rainfall, respectively. Correlation between climatic parameters and groundwater recharge showed positive and negative relationships. The highest correlation was found between precipitation and recharge. Linear multiple regressions between
recharge and measured climatologic data proved significant relationship between recharge and rainfall and wind speed. It was also proven that the proposed model provided an accurate estimation for similar projects.
This analysis demonstrates the application of a data duplication technique in linear regression with censored observations of the waiting time to third pregnancy ending in two outcome types, using data from Malaysia. The linear model not only confirmed the results obtained by the Cox proportional hazards model, but also identified two additional significant factors. The method provides a useful alternative when Cox proportionality assumption of the hazards is violated.