On the bias and mean square error of the least square estimator in a regression model with two inequality constraints and multivariate t error terms

1996 ◽  
Vol 25 (9) ◽  
pp. 2079-2091 ◽  
Author(s):  
Alan T.K. Wan
Keyword(s):  
Regression Model ◽  
Mean Square Error ◽  
Inequality Constraints ◽  
Least Square ◽  
Mean Square ◽  
Least Square Estimator ◽  
Error Terms ◽  
Multivariate T

scholarly journals Authentication of Patin Fish Oil (Pangasius micronemus) using FTIR Spectroscopy Combined with Chemometrics

2020 ◽  
pp. 23
Author(s):  
Anggita Rosiana Putri ◽  
Abdul Rohman ◽  
Sugeng Riyanto ◽  
Widiastuti Setyaningsih
Keyword(s):  
Root Mean Square Error ◽  
Fish Oil ◽  
Ftir Spectroscopy ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Partial Least Square ◽  
Least Square ◽  
Partial Least Square Regression ◽  
Coefficient Of Determination ◽  
Mean Square

Authentication of Patin fish oil (MIP) is essential to prevent adulteration practice, to ensure quality, nutritional value, and product safety. The purpose of this study is to apply the FTIR spectroscopy combined with chemometrics for MIP authentication. The chemometrics method consists of principal component regression (PCR) and partial least square regression (PLSR). PCR and PLSR were used for multivariate calibration, while for grouping the samples using discriminant analysis (DA) method. In this study, corn oil (MJ) was used as an adulterate. Twenty-one mixed samples of MIP and MJ were prepared with the adulterate concentration range of 0-50%. The best authentication model was obtained using the PLSR technique using the first derivative of FTIR spectra at a wavelength of 650-3432 cm-1. The coefficient of determination (R2) for calibration and validation was obtained 0.9995 and 1.0000, respectively. The value of root mean square error of calibration (RMSEC) and root mean square error of prediction (RMSEP) were 0.397 and 0.189. This study found that the DA method can group the samples with an accuracy of 99.92%.

scholarly journals A Comprehensive Review on Channel Estimation in OFDM System

2019 ◽  
Vol 5 (3) ◽  
pp. 6 ◽  
Author(s):  
Neha Dubey ◽  
Ankit Pandit
Keyword(s):  
Channel Estimation ◽  
Mean Square Error ◽  
Orthogonal Frequency Division Multiplexing ◽  
Transmission Rate ◽  
Minimum Mean Square Error ◽  
Estimation Method ◽  
Least Square ◽  
Estimation Methods ◽  
Mean Square ◽  
Mimo Ofdm

In wireless communication, orthogonal frequency division multiplexing (OFDM) plays a major role because of its high transmission rate. Channel estimation and tracking have many different techniques available in OFDM systems. Among them, the most important techniques are least square (LS) and minimum mean square error (MMSE). In least square channel estimation method, the process is simple but the major drawback is it has very high mean square error. Whereas, the performance of MMSE is superior to LS in low SNR, its main problem is it has high computational complexity. If the error is reduced to a very low value, then an exact signal will be received. In this paper an extensive review on different channel estimation methods used in MIMO-OFDM like pilot based, least square (LS) and minimum mean square error method (MMSE) and least minimum mean square error (LMMSE) methods and also other channel estimation methods used in MIMO-OFDM are discussed.

Multivariate analysis of three chemometric algorithms on rapid prediction of some important quality parameters of crude shea butter using Fourier transform-near infrared spectroscopy

2019 ◽  
Vol 27 (3) ◽  
pp. 220-231
Author(s):  
Emmanuel Amomba Seweh ◽  
Zou Xiaobo ◽  
Feng Tao ◽  
Shi Jiachen ◽  
Haroon Elrasheid Tahir ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Root Mean Square Error ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Cross Validation ◽  
Partial Least Square ◽  
Least Square ◽  
Mean Square ◽  
Saponification Value ◽  
Peroxide Values

A comparative study of three chemometric algorithms combined with NIR spectroscopy with the aim of determining the best performing algorithm for quantitative prediction of iodine value, saponification value, free fatty acids content, and peroxide values of unrefined shea butter. Multivariate calibrations were developed for each parameter using supervised partial least squares, interval partial least squares, and genetic-algorithm partial least square regression methods to establish a linear relationship between standard reference and the Fourier transformed-near infrared predicted. Results showed that genetic-algorithm partial least square models were superior in predicting iodine value and saponification value while partial least squares was excellent in predicting free fatty acids content and peroxide values. The nine-factor genetic-algorithm partial least square iodine value calibration model for predicting iodine value yielded excellent ( R2 cal = 0.97), ( R2 val = 0.97), low (root mean square error of cross-validation = 0.26), low (root mean square error of Prediction = 0.23), and (ratio of performance to deviation = 6.41); for saponification value, the nine-factor genetic-algorithm partial least square saponification value calibration model had excellent R2 cal (0.97), R2 val (0.99); low root mean square error of cross-validation (0.73), low root mean square error of Prediction (0.53), and (ratio of performance to deviation = 8.27); while for free fatty acids, the 11-factor partial least square free fatty acids produced very high R2 cal (0.97) and R2 val (0.97) with very low root mean square error of cross-validation (0.03), low root mean square error of Prediction (0.04) and (ratio of performance to deviation = 5.30) and finally for peroxide values, the 11-factor partial least square peroxide values calibration model obtained excellent R2 cal (0.96) and R2val (0.98) with low root mean square error of cross-validation (0.05), low root mean square error of Prediction (0.04), and (ratio of performance to deviation = 5.86). The built models were accurate and robust and can be reliably applied in developing a handheld quality detection device for screening, quality control checks, and prediction of shea butter quality on-site.

scholarly journals Estimasi Parameter Copula Plackett Untuk Data Bivariat Melalui Metode Generalized Linear Model Pada Regresi Mediannya

d'CARTESIAN ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 105
Author(s):  
Egidius Saut Poltak Situmorang ◽  
Bambang Susanto ◽  
Leopoldus Ricky Sasongko
Keyword(s):  
Linear Model ◽  
Mean Square Error ◽  
Generalized Linear Model ◽  
Parametric Bootstrap ◽  
Least Square ◽  
Mean Square

Hubungan antardua peubah acak dapat dilakukan melalui pendekatan regresi linier. Namun keterbatasan regresi linier dalam pemenuhan asumsi klasik sering menjadi kendala analisis. Keterbatasan ini dapat diatasi dengan melibatkan model distribusi bivariat yang disebut copula pada analisis regresi. Copula memiliki keunggulan salah satunya adalah mampu menunjukkan keterhubungan yang tidak linier. Generalized Linear Model (GLM) adalah bentuk perluasan regresi linier. Diketahui bahwa regresi kuantil pada Copula Plackett merupakan suatu bentuk GLM dengan suatu fungsi invers link . Penelitian ini bertujuan untuk menganalisis keterhubungan dua peubah melalui parameter Copula Plackett yang diestimasi melalui pendekatan Generalized Linier Model pada regresi mediannya dengan metode Least Square. Validasi parameter Copula Plackett dilakukan dengan metode simulasi parametric bootstrap melalui pengulangan metode bagi dua. Regresi median terbaik dipilih melalui nilai Mean Square Error terkecil. Perolehan parameter Copula Plackett diterapkan pada data penelitian, yaitu return IHSG dan return kurs beli JPY-IDR untuk menganalisis keterhubungan keduanya. Hasil penelitian menunjukkan bahwa keterhubungan return IHSG dan return kurs beli JPY-IDR dinyatakan  ada namun tidak dapat dikatakan saling bebas.

scholarly journals Pendekatan Generalized Linear Model Pada Regresi Kuantil Copula Normal Untuk Keterhubungan IHSG dan Kurs EUR-IDR

d'CARTESIAN ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 97
Author(s):  
Laurentia Nindya Sari Prameswara ◽  
Bambang Susanto ◽  
Leopoldus Ricky Sasongko
Keyword(s):  
Linear Model ◽  
Mean Square Error ◽  
Generalized Linear Model ◽  
Parametric Bootstrap ◽  
Least Square ◽  
Mean Square

Penelitian ini bertujuan untuk memperoleh estimasi parameter dan regresi kuantil pada suatu model distribusi bivariat yang disebut Copula sebagai alternatif regresi linier klasik dalam menganalisis keterhubungan dua peubah acak. Copula adalah model distribusi bivariat yang memiliki keunggulan selain karena tidak kaku terhadap asumsi distribusi tertentu, juga dapat menyatakan keterhubungan nonlinier. Copula yang dianalisis pada penelitian ini adalah Copula Normal. Sedangkan Generalized Linear Model (GLM) adalah perluasan dari model regresi linier klasik, yang salah satu komponen utamanya adalah fungsi link. Didapati bahwa regresi kuantil pada copula Normal merupakan suatu bentuk GLM dengan fungsi invers link yaitu . Regresi kuantil dan parameter copula Normal  diestimasi dengan pendekatan GLM menggunakan metode Least Square. Estimasi regresi kuantil terbaik dilakukan dengan menghitung Mean Square Error (MSE). Validasi parameter copula dilakukan melalui simulasi dengan parametric bootstrap. Data yang digunakan dalam penelitian ini adalah data return IHSG sebagai peubah tak bebas dan data return kurs beli EUR-IDR sebagai peubah bebas. Hasil penelitian menunjukkan bahwa keterhubungan IHSG dan kurs beli EUR-IDR lemah dan tidak linier.

scholarly journals Proving the Efficiency of Alternative Linear Regression Model Based on Mean Square Error (MSE) and Average Width using Aquaculture Data

2019 ◽  
Vol 8 (2S3) ◽  
pp. 377-381
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Mean Square Error ◽  
Linear Regression Model ◽  
Regression Method ◽  
Alternative Methods ◽  
Linear Regression Method ◽  
Mean Square ◽  
Average Width ◽  
Alternative Method

Multiple linear regressions (MLR) model is an important tool for investigating relationships between several response variables and some predictor variables. This method is very powerful and commonly used in finance, economic, medical, agriculture and many more. The main objective of this paper is to compare mean square error (MSE) and the average width between alternative linear regression models and linear regression model. The alternative method in this study is a combination of four methods, namely multiple linear regression method, the bootstrap method, a robust regression method and fuzzy regression through the construction of algorithms by using SAS software. Typically, the alternative method optimized by minimizing the mean square error (MSE) and average width. The results of the study showed a positive improvement for the estimation of parameters generated through these alternative methods

scholarly journals Attenuated Total Reflectance-FTIR Spectra Combined with Multivariate Calibration and Discrimination Analysis for Analysis of Patchouli Oil Adulteration

2019 ◽  
Vol 20 (1) ◽  
pp. 1
Author(s):  
Zaki Fahmi ◽  
Mudasir Mudasir ◽  
Abdul Rohman
Keyword(s):  
Root Mean Square Error ◽  
Ftir Spectroscopy ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Multivariate Calibration ◽  
Ftir Spectra ◽  
Partial Least Square ◽  
Least Square ◽  
Calibration Model ◽  
Mean Square

The adulteration of high priced oils such as patchouli oil with lower price ones is motivated to gain the economical profits. The aim of this study was to use FTIR spectroscopy combined with chemometrics for the authentication of patchouli oil (PaO) in the mixtures with Castor Oil (CO) and Palm Oil (PO). The FTIR spectra of PaO and various vegetable oils were scanned at mid infrared region (4000–650 cm–1), and were subjected to principal component analysis (PCA). Quantitative analysis of PaO adulterated with CO and PO were carried out with multivariate calibration of Partial Least Square (PLS) regression. Based on PCA, PaO has the close similarity to CO and PO. From the optimization results, FTIR normal spectra in the combined wavenumbers of 1200–1000 and 3100–2900 cm–1 were chosen to quantify PaO in PO with coefficient of determination (R2) value of 0.9856 and root mean square error of calibration (RMSEC) of 4.57% in calibration model. In addition, R2 and root mean square error of prediction (RMSEP) values of 0.9984 and 1.79% were obtained during validation, respectively. The normal spectra in the wavenumbers region of 1200–1000 cm–1 were preferred to quantify PaO in CO with R2 value of 0.9816 and RMSEC of 6.89% in calibration, while in validation model, the R2 value of 0.9974 and RMSEP of 2.57% were obtained. Discriminant analysis was also successfully used for classification of PaO and PaO adulterated with PO and CO without misclassification observed. The combination of FTIR spectroscopy and chemometrics provided an appropriate model for authentication study of PaO adulterated with PO and CO.

scholarly journals EFEKTIVITAS REGRESI KUANTIL DALAM MENGATASI PENCILAN PONTENSIAL

2020 ◽  
Vol 14 (2) ◽  
pp. 305-312
Author(s):  
Netti Herawati
Keyword(s):  
Quantile Regression ◽  
Mean Square Error ◽  
Akaike Information Criterion ◽  
Robust Regression ◽  
Information Criterion ◽  
Regression Method ◽  
Least Square ◽  
Mean Square ◽  
The Impact ◽  
Quantile Regression Method

Abstrak Regresi kuantil sebagai metode regresi yang robust dapat digunakan untuk mengatasi dampak kasus yang tidak biasa pada estimasi regresi. Tujuan dari penelitian ini adalah untuk mengevaluasi efektivitas regresi kuantil untuk menangani pencilan potensial dalam regresi linear berganda dibandingkan dengan metode kuadrat terkecil (MKT). Penelitian ini menggunakan data simulasi dengan p=3; n = 20, 40, 60, 100, 200 and   and  diulang 1000 kali. Efektivitas metode regresi kuantil dan MKT dalam pendugaan parameter β diukur dengan Mean square error (MSE) dan Akaike Information Criterion (AIC). Hasil penelitian menunjukkan bahwa regresi kuantil mampu menangani pencilan potensial dan memberikan penaksir yang lebih baik dibandingkan dengan MKT berdasarkan nilai MSE dan AIC. Kata kunci: AIC, MSE, pencilan, regresi kuantil Abstract Quantitative regression as a robust regression method can be used to overcome the impact of unusual cases on regression estimation. The purpose of this study is to evaluate the effectiveness of quantile regression to deal with potential outliers in multiple linear regression compared to the least squares methodordinary least square (OLS).   This study uses simulation data with p=3; n = 20, 40, 60, 100, 200 and   and  repeated 1000 times. The effectiveness of the quantile regression method and OLS in estimating β   parameters was measured by Mean square error (MSE) and Akaike Information Criterion (AIC). The results showed that quantile regression was able to handle potential outliers and provide better predictors compared to MKT based on MSE and AIC values. Keywords: AIC, MSE, outliers, quantile regression

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