Parametric Regression Approach Research Articles

Pointwise Nonparametric Estimation of Odds Ratio Curves with R: Introducing the flexOR Package

The analysis of odds ratio curves is a valuable tool in understanding the relationship between continuous predictors and binary outcomes. Traditional parametric regression approaches often assume specific functional forms, limiting their flexibility and applicability to complex data. To address this limitation and introduce more flexibility, several smoothing methods may be applied, and approaches based on splines are the most frequently considered in this context. To better understand the effects that each continuous covariate has on the outcome, results can be expressed in terms of splines-based odds ratio (OR) curves, taking a specific covariate value as reference. In this paper, we introduce an R package, flexOR, which provides a comprehensive framework for pointwise nonparametric estimation of odds ratio curves for continuous predictors. The package can be used to estimate odds ratio curves without imposing rigid assumptions about their underlying functional form while considering a reference value for the continuous covariate. The package offers various options for automatically choosing the degrees of freedom in multivariable models. It also includes visualization functions to aid in the interpretation and presentation of the estimated odds ratio curves. flexOR offers a user-friendly interface, making it accessible to researchers and practitioners without extensive statistical backgrounds.

Analyzing the machine Learning methods to predict Bitcoin Pricing

A cryptocurrency is a form of digital money that uses the blockchain technology and cryptography to protect the information about transactions and exchange made on the digital market. A cryptocurrency like Bitcoin consists of a big network that has many peers working on it and every peer has a record of the whole history that contains all the transactions that ever happened. Bitcoin is the most popular cryptocurrency. Bitcoin has attracted a lot of attention from individual and institutional investors. The purpose of this paper is to analyse the machine learning methods to predict Bitcoin pricing. Machine learning and its associated fields have made notable advances in recent years. Machine learning techniques is used in different areas of science particularly cryptocurrency price forecasting. Using this machine learning model, we can predict the price direction of Bitcoin. Machine learning methods have been demonstrated to be effective in predicting bitcoin prices. Few machine learning models to predict the Bitcoin price are Linear Regression, Logistic Regression, Bayesian Regression, Support Vendor Machine, Random Forest, Neural Network were discussed. Every method of machine learning has its own advantages and disadvantages, however from the literature analysis it is understood that the Artificial Neural Network and Support Vendor Machine have the highest effectiveness rate. Machine learning methods have higher prediction accuracy than parametric regression approaches.

Consistency and Asymptotic Normality of Estimator for Parameters in Multiresponse Multipredictor Semiparametric Regression Model

A multiresponse multipredictor semiparametric regression (MMSR) model is a combination of parametric and nonparametric regressions models with more than one predictor and response variables where there is correlation between responses. Due to this correlation we need to construct a symmetric weight matrix. This is one of the things that distinguishes it from the classical method, which uses a parametric regression approach. In this study, we theoretically developed a method of determining a confidence interval for parameters in a MMSR model based on a truncated spline, and investigating asymptotic properties of estimator for parameters in a MMSR model, especially consistency and asymptotic normality. The weighted least squares method was used to estimate the MMSR model. Next, we applied a pivotal quantity method, a Cramer–Wold theorem, and a Slutsky theorem to determine the confidence interval, investigate consistency, and asymptotic normality properties of estimator for parameters in a MMSR model. The obtained results were that the estimated regression function is linear to observation. We also obtained a 1001−α% confidence interval for parameters in the MMSR model, and the estimator for parameters in MMSR model was consistent and asymptotically normally distributed. In the future, these obtained results can be used as a theoretical basis in designing a standard toddlers growth chart to assess nutritional status.

Parametric Regression Approach for Gompertz Survival Times with Competing Risks

Parametric Regression Approach for Gompertz Survival Times with Competing Risks

ESTIMASI MODEL REGRESI SEMIPARAMETRIK SPLINE TRUNCATED MENGGUNAKAN METODE MAXIMUM LIKELIHOOD ESTIMATION (MLE)

Regression modeling with a semiparametric approach is a combination of two approaches, namely the parametric regression approach and the nonparametric regression approach. The semiparametric regression model can be used if the response variable has a known relationship pattern with one or more of the predictor variables used, but with the other predictor variables the relationship pattern cannot be known with certainty. The purpose of this research is to examine the estimation form of the semiparametric spline truncated regression model. Suppose that random error is assumed to be independent, identical, and normally distributed with zero mean and variance , then using this assumption, we can estimate the semiparametric spline truncated regression model using the Maximum Likelihood Estimation (MLE) method. Based on the results, the estimation results of the semiparametric spline truncated regression model were obtained p=(inv(M'M)) M'y

A physics-based parametric regression approach for feedwater pump system diagnosis

In this paper, we assessed the performance of a model-based approach for fault diagnosis of a nuclear power plant feedwater pump system. Physics-based models were constructed to monitor the performance of the system components. Plant data were used for the calibration of the models and subsequently in the diagnosis of abnormal events. We considered two real-time events representing scenarios of a pump fault and component performance degradation. The two events were correctly diagnosed, and the results demonstrated the high detection sensitivity of the physics-based models. Various sensor fault scenarios were simulated to show the capability of the approach to detect and uniquely identify sensor faults. Results for a scenario in which the plant operated in flexible power mode also showed that the diagnostic approach is insensitive to changes of operating conditions, which is one of the advantages of the model-based approach using physics-based models over purely data-driven approach.

Increased Household Income Improves Nutrient Consumption in Pakistan: A Cross-Sectional Study.

The provision of high-quality food is a primary factor in ensuring adequate nourishment and preventing malnourishment-related diseases in Pakistan. This study, therefore, aimed to quantify the impact of income on nutrient consumption in Pakistan, with the hypothesis that income has a primary role in reducing malnourishment in the developing world. To do this, we estimated nutrient–income elasticity—defined as the proportion of change in nutrient consumption in response to a change in income—for total calories, macronutrients, and micronutrients, using the nationally representative Household Integrated Economic Survey data (2010–2011) for Pakistan. Nutrient–income elasticity values were derived using several parametric regression approaches. We also assessed the non-linearity and endogeneity of the relationship. Calorie–income elasticity was found to be significantly different from zero, irrespective of the estimation technique used. Income elasticity for macronutrients and micronutrients was also found to be significantly different from zero, ranging from 0.29 to 0.65. This study, therefore, supports the hypothesis that increased household income likely improves nutrient consumption.

Analyzing The Effect of BI 7-Days Repo Rate on The Jakarta Composite Index Using Nonparametric Regression Approaches Based on Least Square Spline Estimator

During the Covid-19 pandemic, the Indonesia stock market was under great pressure, so that the value of the Jakarta Composite Index (JCI) fluctuated greatly. To maintain economic stability, Bank Indonesia has regulated monetary policy such as setting the BI 7-Days Repo Rate. Analysis of this effect is important to formulate the right policy. This study aims to design the best model in describing the relationship between JCI value and BI 7-Days Repo Rate. The analysis was carried out by using parametric regression approach based on the ordinary least square method and nonparametric regression approach based on least square spline estimator. The results showed that the parametric regression models failed to meet the classical assumptions. Meanwhile, nonparametric regression can produce an optimal model with high accurate prediction, with an overall mean absolute percentage error value of 3.16%. Furthermore, mean square error, coefficient of determination, and mean absolute deviation also show good results. Thus, the effect of the BI 7-Days Repo Rate on the JCI value forms a quadratic pattern, in which a positive relationship is formed when the BI 7-Days Repo Rate is set at more than 4.25% and vice versa for a negative relationship.

Spline estimation method in nonparametric regression using truncated spline approach

A parametric regression approach is used when the shape of the regression curve is known, and the nonparametric approach is used when the shape of the regression curve is unknown, the parametric regression model is still forced as a model of data patterns, it will cause inaccurate conclusions if the form of the function is not known. The truncated spline approach can be used to estimate curves in nonparametric regression models using a knot basis. The curve estimation method used is Weighted Least Square (WLS) for the truncated spline approach. In this study, the nonparametric regression model was implemented on fertilizer subsidy data in East Java. This study aims to examine comprehensively the factors that influence the satisfaction of the farming community. The response variable used in this study is the Courage of Field Extension Officers (Y), while the predictor variables include: Farmers National Culture (X1), Financial Reward for Field Extension Officers (X2), and Leadership Role (X3). The novelty of this research is trying to do regression modeling in which the whole relationship between the response variable and the predictor variable is non-linear. The results of the linearity assumption test show that all predictor variables show a non-linear relationship to the response variable, so it needs to be solved by nonparametric regression. The coefficient of determination shows that the variability of Courage of Field Extension Officers can be explained by 87,65% in the model, while the remaining 12,35% is explained by factors that are not included in the model.

Data imputation and machine learning improve association analysis and genomic prediction for resistance to fish photobacteriosis in the gilthead sea bream

Disease resistance represents a key trait for breeding programs in aquaculture species. Here we re-analysed 2bRAD sequence data from two experimental challenges of gilthead sea bream with Photobacterium damsealae piscicida. Using a high quality reference genome, we carried out variant calling and data imputation with Beagle to obtain a large set of SNPs (80,744). This allowed the identification of eight novel QTLs for resistance to photobacteriosis across different chromosomes and revealed a highly polygenic genetic architecture.Bayesian regression approaches and machine learning methods (support vector machines and linear bagging) were compared to evaluate relative performance to classify susceptible-resistant individuals. Both data sets showed higher Matthew Correlation Coefficient (MCC) and accuracy values for machine learning methods, particularly linear bagging, with 20–70 % increase in prediction performance. Overall, machine learning methods should be explored in parallel with parametric regression approaches to increase the chances of highly effective genomic prediction.

Mixture Model Nonparametric Regression and Its Application

Regression analysis is a statistical analysis used to determine the pattern of relationships between predictor variables and response variables. There are two models of estimation approaches in regression analysis, namely parametric regression, and nonparametric regression. The parametric regression approach is used in the shape of the regression curve is known. In cases with unknown relationship patterns, the development is done using nonparametric regression. Nonparametric regression is a model estimation method which is based on an approach that is not bound by certain assumptions of the regression curve shape. Nonparametric regression varies greatly with variable curves that are different between one predictor variable with another predictor variable. In nonparametric regression, there are several types of the recommended kernel, spline, and Fourier series. In many cases, however, these conservative nonparametric regression methods cannot handle more complex problems. Mixture methods by combining several methods such as a mixture of spline and Fourier series, kernel and Fourier series, and so on, give a better result. This study aims to obtain estimates of a mixture of a truncated spline, kernel, and Fourier series by using the Ordinary Least Square (OLS) method and obtain methods for selecting knots, bandwidth, and optimal oscillation parameters with the smallest GCV. The results of this study are the formulation of a mixed estimation model of the truncated spline, kernel, and Fourier series and the smallest GCV formula to obtain the optimum location and number of points of knots, bandwidth, and oscillations.

Modelling Scholastic Aptitude Test of State Islamic Colleges in Indonesia using Least Square Spline Estimator in Longitudinal Semiparametric Regression

Scholastic aptitude test is one of tests used to select student candidates who want to enroll to the state Islamic colleges (SIC) in Indonesia. This test is affected by some factors for instances percentage of student candidates who pass to enroll in that enrolment year (t), and place of these colleges (SIC) where the student candidates enroll (X). Association between t and scholastic aptitude test score (Y) have no certain pattern (as nonparametric component). One of estimator in nonparametric regression is least square spline that include knots which can accommodate locally properties and give good flexibility. Place of SIC is dummy variable, so we can use parametric regression approach. To investigate Y from year to year we can use longitudinal data. Therefore, in this research model Y affected by t (as nonparametric component) and X (as parametric component) use longitudinal semiparametric regression based on least square spline estimator. The results give an estimated order one semiparametric regression model of scholastic aptitude test scores with three knots of 70.64; 80.32, and 90.67, and minimum generalized cross validation value of 204.42. Also, the results show that average of Y in western Indonesia is greater than in eastern Indonesia with difference of 20.45.

Estimation of Matrix Variance-Covariance on Nonparametric Regression Spline Truncated for Longitudinal Data

Regression analysis is a statistical analysis used to determine the pattern of relationships between predictor variables and response variables. There are two models estimation approaches in regression analysis, namely parametric regression and nonparametric regression. The parametric regression approach is used if the shape of the regression curve is known. In cases with unknown relationship patterns, the development is done using nonparametric regression. Nonparametric regression is a model estimation method which is based on an approach that is not bound by certain assumptions of the regression curve shape. One of the most commonly used nonparametric regression curve estimates is the spline approach. Spline is one of the nonparametric approaches that is often used and has a very good ability to handle data characters that are smooth as well as data whose behavior changes at certain sub-intervals. Theoretically, the spline approach is not only able to estimate nonparametric regression curves for cross section data, but can also be developed for longitudinal data. Longitudinal data is a combination of cross section data and time series data where the longitudinal data between subjects are mutually independent, but between observations are dependent. This study aims to find the estimation curves of spline truncated multivariable nonparametric regression for longitudinal data using the Weighted Least Square (WLS) method and to find the estimation of variance-covariance matrix using the Maximum Likelihood Estimate (MLE) method.

Bayesian Calibration of p‐Values from Fisher's Exact Test

Summaryp‐Values are commonly transformed to lower bounds on Bayes factors, so‐called minimum Bayes factors. For the linear model, a sample‐size adjusted minimum Bayes factor over the class of g‐priors on the regression coefficients has recently been proposed (Held & Ott, The American Statistician 70(4), 335–341, 2016). Here, we extend this methodology to a logistic regression to obtain a sample‐size adjusted minimum Bayes factor for 2 × 2 contingency tables. We then study the relationship between this minimum Bayes factor and two‐sided p‐values from Fisher's exact test, as well as less conservative alternatives, with a novel parametric regression approach. It turns out that for all p‐values considered, the maximal evidence against the point null hypothesis is inversely related to the sample size. The same qualitative relationship is observed for minimum Bayes factors over the more general class of symmetric prior distributions. For the p‐values from Fisher's exact test, the minimum Bayes factors do on average not tend to the large‐sample bound as the sample size becomes large, but for the less conservative alternatives, the large‐sample behaviour is as expected.

Valuing portfolios of interdependent real options using influence diagrams and simulation-and-regression: A multi-stage stochastic integer programming approach

Although real options generally occur within portfolios, most valuation approaches based on either option pricing or decision analysis alone focus on single well-defined options. In this paper we present a new approach for modelling and approximating the value of portfolios of interdependent real options using both influence diagrams and simulation-and-regression. The key feature of this approach is that it translates the interdependencies between real options into a set of constraints and then directly models the dynamics of all underlying uncertainties using (Markovian) stochastic processes. These are then integrated in a portfolio optimisation problem which is formulated as a multi-stage stochastic integer program. Applying a simulation and parametric regression approach to approximate the value of this optimisation problem, we present a transparent valuation algorithm that explicitly takes into account vector-valued exercise decisions and the state variable’s multidimensional resource component. The approach is therefore applicable to a wide range of complex investment projects with both inherent interdependent flexibilities and many underlying uncertainties. The approach is illustrated by evaluating a complex natural resource investment that features both a large portfolio of interdependent real options and four stochastic factors. We analyse the way in which the approximated value of the portfolio and its individual options are affected by the initial copper price as well as by the degrees of production cost and copper price uncertainty.

Implied volatility surfaces during the period of global financial crisis

This paper adopts a parametric regression approach to model and calibrate implied volatility surface during the period of the global financial crisis. Due to its relatively low computational cost, it facilitates comparison across a great number of different competing models. The proposed regression models are backtested against historical S&P 500 prices during both volatile and non-volatile periods as proxied by the VIX index around the same time period, and the fits of the models are assessed. Furthermore both an equally weighted scheme and an alternative scheme based on observed implied volatilities as the weight are deployed and the results produced by these two schemes are contrasted and compared. Finally the concept of promptness, instead of the more traditional concept of time to maturity, is introduced as a covariate in the regression models to better capture the shape of the volatility surface during the period characterized by a prolonged low interest-rate environment.

Efficiency Comparisons of Different Estimators for Panel Data Models with Serially Correlated Errors: A Stochastic Parameter Regression Approach

This paper considers panel data models when the errors are first-order serially correlated as well as with stochastic regression parameters. The generalized least squares (GLS) estimators for these models have been derived and examined in this paper. Moreover, an alternative estimator for GLS estimators in small samples has been proposed, this estimator is called simple mean group (SMG). The efficiency comparisons for GLS and SMG estimators have been carried out. The Monte Carlo studies indicate that SMG estimator is more reliable in most situations than the GLS estimators, especially when the model includes one or more non-stochastic parameter.

PERBANDINGAN METODE CROSS VALIDATION DAN GENERALIZED CROSS VALIDATION DALAM REGRESI NONPARAMETRIK BIRESPON SPLINE

AbstrakAnalisis regresi merupakan salah satu metode yang sangat populer dalam statistika untuk menjelaskan hubungan sebab akibat antara satu/beberapa variabel prediktor terhadap satu variabel respon. Pada umumnya, pemodelan yang dapat dilakukan dengan menggunakan analisis regresi. Kurva regresi dapat diduga dengan pendekatan regresi parametrik dan pendekatan regresi nonparametrik. Namun, tidak semua data yang diperoleh mengikuti pola tertentu sehingga jenis data ini menggunakan pendekatan regresi nonparametrik. Pendekatan regresi nonparametrik tidak terkait dengan asumsi bentuk kurva regresi seperti halnya pada regresi parametrik, dan lebih fleksibel. Ada beberapa teknik yang dilakukan untuk estimasi dalam regresi nonparametrik yaitu Spline. Beberapa kasus dalam analisis regresi banyak dijumpai permasalahan yang tidak dapat diselesaikan dengan analisis regresi sederhana satu respon karena jika menggunakan dua variabel respon pada penelitian, maka harus dilihat nilai korelasi antar variabel. Akibatnya, persoalan regresi harus diselesaikan dengan model regresi birespon. Penelitian ini bertujuan untuk mendeskripsikan AKB dan status gizi buruk balita dan mendapatkan model Spline dalam regresi nonparametrik birespon terbaik melalui hubungan antara variabel yang diduga berpengaruh dengan menggunakan metode Cross Validation (CV) dan Generalized Cross Validation (GCV). Hasil yang didapat yaitu model terbaik yang sesuai untuk derajat kesehatan di Indonesia pada tahun 2015 yaitu dengan menggunakan metode CV dengan nilai CV minimum yang terletak pada model Spline linier satu knot yakni sebesar 77.37831 dengan MSE sebesar 76.75449.

Short-term flood forecasting with an amended semi-parametric regression ensemble model

Flood forecasting is very important research topic in disaster prevention and reduction. The characteristics of flood involve a rather complex systematic dynamic under the influence of different meteorological factors including linear and non-linear patterns. Recently there are many novel forecasting methods of improving the forecasting accuracy. This paper explores the potential and effect of the semiparametric regression to modelize flood water-level and to forecast the inundation of Mekong Delta in Vietnam. The semi-parametric regression technique is a combination of a parametric regression approach and a non-parametric regression concept. In the process of model building, three altered linear regression models are applied for the parametric component. They are stepwise multiple linear regression, partial least squares solution and multirecursive regression method. They are used to capture flood’s linear characteristics. The nonparametric part is solved by a modified estimation of a smooth function. Furthermore, some justified nonlinear regression models based on artificial neural network are also able to obtain flood’s non-linear characteristics. They help us to smooth the model's non-parametric constituent easily and quickly. The last element is the model's error. Then the semiparametric regression is used for ensemble model based on the principle component analysis technique. Flood water-level forecasting, with a lead time of one and more days, has been made by using a selected sequence of past water-level values and some relevant factors observed at a specific location. Time-series analytical method is utilized to build the model. Obtained empirical results indicate that the prediction by using the amended semi-parametric regression ensemble model is generally better than those obtained by using the other models presented in this study in terms of the same evaluation measurements. Our findings reveal that the estimation power of the modern statistical model is reliable and auspicious. The proposed model here can be used as a promising alternative forecasting tool for flood to achieve better forecasting accuracy and to optimize prediction quality further.

Assessing Euro crises from a time varying international CAPM approach

Abstract This paper initially reviews the current empirical literature on the euro exchange rate. We consider the relationship between the euro and other floating currencies in terms of excess returns on bond markets and also the relationship between the euro–dollar and the US and European equity markets. One novelty in the paper is to consider the variation in the euro–dollar rate from an international capital asset pricing model (CAPM) perspective. The second new innovation is to use a kernel weighted time varying parameter regression approach which allows structural parameters and risk premium terms to evolve over time. We find evidence that the euro–dollar rate is substantially influenced by equity markets in the US and in the Eurozone.