Stochastic Regression Model Research Articles

Compressed Least Squares Algorithm of Continuous-Time Linear Stochastic Regression Model Using Sampling Data

Compressed Least Squares Algorithm of Continuous-Time Linear Stochastic Regression Model Using Sampling Data

Distributed Least Squares Algorithm of Continuous-Time Stochastic Regression Model Based on Sampled Data

Distributed Least Squares Algorithm of Continuous-Time Stochastic Regression Model Based on Sampled Data

CNN-Based Stochastic Regression for IDDQ Outlier Identification

To reduce DPPM (defect parts per million) on IC products, IDDQ testing can be exploited for identifying the outliers which are potentially defective but not detected by sign-off functional and parametric tests. Conventional IDDQ testing paradigms depending on a simple statistical 6σ rule or engineers’ experience are usually too conservative to effectively identify non-trivial outliers, especially when spatial correlations are of great concern/influence. In the paper, an improved CNN-based method can be proposed for IDDQ outlier identification. In the proposed method, the mean and the standard deviation on the IDDQ value inside a die under test (DUT) can be predicted by employing a stochastic regression model. According to the predicted mean and standard deviation, we derive an expected IDDQ interval and identify the DUT as an outlier if its actual measured IDDQ value is beyond the expected interval. From the observation of the experimental results, the improved data pre-processing and the improved CNN-based stochastic regression can be contained to enhance the prediction accuracy of the expected IDDQ intervals. In the improved method, the spatial correlations of the neighboring dice inside a window can be considered by training a CNN-based stochastic regression model with a large volume of industrial data on 28nm and 65nm products. The trained model is highly-accurate prediction in the R (0.973) and RMSE (0.626 mA) of the expected IDDQ values on 28nm product and the R (0.942) and RMSE (2.155 uA) of the expected IDDQ values on 65nm product. Furthermore, the experimental results show that the trained model can capture the potential defective dice by identifying efficient IDDQ outliers.

Marginal and Conditional both Extreme Value Distributions: A Case of Stochastic Regression Model

A mathematical model is a mathematical connection that describes some real-life scenario. To handle real-world problems securely and effectively, simulation modelling is required. In this article, the author investigates the stochastic regression model scenario in which the dependent and independent variables in a linear regression model follow a distribution. We assume that the dependent and independent variables both exhibit Type I Extreme Value Distribution. The estimators are then derived using the Modified Maximum Likelihood (MML) estimation method. In accordance with this, a hypothesis testing technique is developed.

Moment estimation for uncertain regression model with application to factors analysis of grain yield

Uncertain regression analysis is a powerful analytical tool to model the relationships between explanatory variables and the response variable by uncertainty theory. One of the core problems in uncertain regression analysis is to estimate the unknown parameters of an uncertain regression model and the uncertain disturbance term. In this paper, the moment estimation of uncertain regression model is proposed, which can determine both the uncertain regression model and the disturbance term at one time. After that, the uncertain hypothesis test is used to test whether the estimated uncertain regression model is appropriate. Furthermore, a real-world example of factors analysis of grain yield is provided to illustrate the moment estimation. Finally, as a byproduct, this paper also indicates that the stochastic regression model cannot model the agriculture data.

Identification and adaptation with binary-valued observations under non-persistent excitation condition

Dynamical systems with binary-valued observations are widely used in information industry, technology of biological pharmacy and other fields. Though there have been much efforts devoted to the identification of such systems, most of the previous investigations are based on first-order gradient algorithm which usually has much slower convergence rate than the Quasi-Newton algorithm. Moreover, persistence of excitation (PE) conditions are usually required to guarantee consistent parameter estimates in the existing literature, which are hard to be verified or guaranteed for feedback control systems. In this paper, we propose an online projected Quasi-Newton type algorithm for parameter estimation of stochastic regression models with binary-valued observations and varying thresholds. By using both the stochastic Lyapunov function and martingale estimation methods, we establish the strong consistency of the estimation algorithm and provide the convergence rate, under a signal condition which is considerably weaker than the traditional PE condition and coincides with the weakest possible excitation known for the classical least square algorithm of stochastic regression models. Convergence of adaptive predictors and their applications in adaptive control are also discussed.

Stochastic Regression Model with Marginal Extreme Value Distribution and Conditional Normal Distribution

In various circumstances of stochastic regression analysis, one deals with a random vector (X, Y), where Y is an outcome of X but not vice-versa. In such situations, X has a non-normal distribution while the conditional distribution of (Y|X=x) may or may not be normal. In this paper, the distribution of X is assumed to be Extreme value distribution (Type I) and the conditional distribution of Y to be normal. Then Modified Maximum Likelihood (MML) estimators are derived. Hypothesis testing procedure is also developed.

Vehicle Road Accident Prediction Model Along Federal Road FT050 Kluang-A/Hitam-B/Pahat Route Using Excess Zero Data


 
 
 Traffic accidents have become a major socio-economic problem in Malaysia and are considered the primary cause of mortality. Over 60 percent of these fatal accidents occurred on rural roads. Nearly half of all fatalities took place on federal roads and over a quarter happened on state roads. It is also estimated that about 2 percent of the country's Gross Domestic Product (GDP), or approximately RM 9 billion, is lost through road accidents. Several models therefore have been developed for modelling the occurrence of accidents, but most of these models have plenty of deficiencies. The following study focuses on stochastic regression models, such as Poisson, Negative Binomial, Zero- Inflated Poisson and Zero-Inflated Negative Binomial with excess zero outcomes on the response variables. Furthermore, R-statistical programming is used to specify the regression relationship with a sophisticated result. The method used consider as updating approach in predicting potential road accidents, which can also produce an accuracy probability of hazardous locations. Based on road accident data collected over a five-year period from 2010 to 2014 at Federal Road F0050: Kluang- A/Hitam-B/Pahat in Johor, Malaysia, results of this study show that Zero Inflated model performed better, in terms of the comparative criteria based on the AIC value.
 
 

Knowledge-driven stochastic reliable modeling for steel bridge deck condition rating prediction

ABSTRACT The structurally deficient bridges increased from 6.2% to 7% of total bridges in California state. With this percentage, 7%; California state occupies one of the top states for bridges in “poor„ condition. Steel bridges represent about 11% of its bridge networks, so determining the condition rating objectively instead of subjectively is crucial. This paper aims to help significantly optimize the maintenance process by providing a rational basis for making decisions. This paper has integrated knowledge, stochastic analysis, Regression technique, and modeling to help the highway agencies to make a more reliable decision for future maintenance based on predicted conditions. Stochastic Regression models have been built using a training dataset extracted from the National Bridge Inventory (NBI) database for California State steel bridges, considering structural and operational parameters. A validation test has been performed using a new real dataset to measure observed data's correspondence to the predicted values. The results of Average Validity Percentage (85.6%) and Coefficient of Determination (R2 = 91.5%) show that the models' accuracy, the power, and scalability of integrating the knowledge-driven models are acceptable. The integrated developed models provide the infrastructure authority with actionable insights for smarter planning and maintenance decisions as better future outcomes.

LEAST SQUARES AND IVX LIMIT THEORY IN SYSTEMS OF PREDICTIVE REGRESSIONS WITH GARCH INNOVATIONS

The paper examines the effect of conditional heteroskedasticity on least squares inference in stochastic regression models of unknown integration order and proposes an inference procedure that is robust to models within the (near) I(0)–(near) I(1) range with GARCH innovations. We show that a regressor signal of exact order$O_{p}\left ( n\kappa _{n}\right ) $for arbitrary$\,\kappa _{n}\rightarrow \infty $is sufficient to eliminate stationary GARCH effects from the limit distributions of least squares based estimators and self-normalized test statistics. The above order dominates the$O_{p}\left ( n\right ) $signal of stationary regressors but may be dominated by the$O_{p}\left ( n^{2}\right ) $signal of I(1) regressors, thereby showing that least squares invariance to GARCH effects is not an exclusively I(1) phenomenon but extends to processes with persistence degree arbitrarily close to stationarity. The theory validates standard inference for self normalized test statistics based on the ordinary least squares estimator when$\kappa _{n}\rightarrow \infty $and$\kappa _{n}/n\rightarrow 0$and the IVX estimator (Phillips and Magdalinos (2009a), Econometric Inference in the Vicinity of Unity. Working paper, Singapore Management University; Kostakis, Magdalinos, and Stamatogiannis, 2015a,Review of Financial Studies28(5), 1506–1553.) when$\kappa _{n}\rightarrow \infty $and the innovation sequence of the system is a covariance stationary vec-GARCH process. An adjusted version of the IVX–Wald test is shown to also accommodate GARCH effects in purely stationary regressors, thereby extending the procedure’s validity over the entire (near) I(0)–(near) I(1) range of regressors under conditional heteroskedasticity in the innovations. It is hoped that the wide range of applicability of this adjusted IVX–Wald test, established in Theorem 4.4, presents an advantage for the procedure’s suitability as a tool for applied research.

Vehicle Road Accident Prediction Model along Federal Road FT050 Kluang-A/Hitam-B/Pahat Route Using Excess Zero Data

Traffic accidents have become a major socio-economic problem in Malaysia as it is the primary cause of mortality. Over 60 percent of these fatal accidents occurred on rural roads. Nearly half of all fatalities took place on federal roads and over a quarter happened on state roads. It is also estimated that about 2 percent of the country’s Gross Domestic Product (GDP), or approximately RM 9 billion, is lost through road accidents. Previous studies managed to develop several models for modelling the occurrence of accidents, but most of these models have plenty of deficiencies. The following study focuses on stochastic regression models, such as Poisson, Negative Binomial, Zero-Inflated Poisson and Zero-Inflated Negative Binomial with excess zero outcomes on the response variables. Furthermore, in order to specify the regression relationship with a sophisticated result, R-statistical programming is used. The method used is also the updating approach in predicting potential road accidents, which can also produce an accuracy probability of hazardous locations. Based on road accident data collected over a five-year period from 2010 to 2014 at Federal Road F0050: Kluang-A/Hitam- B/Pahat in Johor, Malaysia, results of this study show that Zero Inflated model performed better, in terms of the comparative criteria based on the AIC value.

Elements of Randomized Forecasting and Its Application to Daily Electrical Load Prediction in a Regional Power System

A randomized forecasting method based on the generation of ensembles of entropy-optimal forecasting trajectories is developed. The latter are generated by randomized dynamic regression models containing random parameters, measurement noises, and a random input. The probability density functions of random parameters and measurement noises are estimated using real data within the randomized machine learning procedure. The ensembles of forecasting trajectories are generated by the sampling of the entropy-optimal probability distributions. This procedure is used for the randomized prediction of the daily electrical load of a regional power system. A stochastic oscillatory dynamic regression model is designed. One-, two-, and three-day forecasts of the electrical load are constructed, and their errors are analyzed.

Online sparse identification for regression models

In this paper, we propose an online alternating minimization (OAM) algorithm to estimate the sparse coefficients of stochastic regression models from time-series data. We apply the alternating minimization (AM) directly to the penalty function of the variant of the least absolute shrinkage and selection operator (Lasso), which leads to convex subproblems, and thereby can be solved efficiently. Moreover, under certain mild assumptions, we derive a convergence analysis framework and establish the strong consistency for the OAM estimator. Numerical experiments demonstrate the effectiveness of the proposed algorithm.

A stochastic frontier regression model with dynamic frontier

We consider a stochastic frontier regression model with a time dependent efficiency process, which is assumed to follow an exponential autoregressive sequence. The likelihood for the model is derived in the context of a bivariate exponential distribution. Bayesian method is suggested for the estimation of parameters. We apply the model and the estimation procedure to a panel of US airlines data and show empirically that the model is dynamic in the sense that it reveals improvement in the efficiency or reduction in the inefficiency over time.

Real-time estimation for functional stochastic regression models

ABSTRACTIn this paper, a heteroscedastic functional regression model with martingale difference errors is considered. We are interested in real-time estimation of the regression as well as the conditional variance operators when the response is a real-valued random variable and the covariate belongs to an infinite-dimensional space. A Robbins–Monro-type estimator of the conditional variance is introduced when a sample is collected from an underlying stationary and ergodic process. First, a local uniform -consistency (for ) rate of the recursive estimator of the regression operator is established. Then, a pointwise mean-square consistency rate of the conditional variance is given when the regression function is supposed to be known and when it is estimated recursively. Simulation studies are conducted to assess the proposed estimator's performance, in terms of reducing the computational time without affecting significantly the accuracy, compared to its natural competitor. An application to real environmental data is also carried out to illustrate the real-time on day ahead prediction of the maximum ozone concentration in Mexico city as well as its volatility.

Determinants of Technical Efficiency in Wheat Production in Ethiopia

Ethiopia is the second largest wheat producing countries in Sub-Saharan Africa and most people rely on rain fed agriculture for their livelihoods. Wheat production has increased from 2,176,603 tons in 2005 to 4,219,257 tons in 2016 with 51.6% production volume increment. However, this production cannot meet the consumption demand and obliged to import wheat because of rapid population growth. This study intended to determine the technical efficiency of smallholder wheat farmers in Ethiopia. The main objective of study was to examine the effect of demographic, socioeconomic and institutional factors on technical efficiency of small holder wheat farmers in Ethiopia. The study used household level cross sectional data collected in 2015/16 cropping season from 1611 sample farmers selected by multistage sampling technique. A stochastic production frontier and two-limit Tobit regression models were used to estimate level of technical efficiency and identify factors affecting technical efficiency respectively. The study indicated that the average technical efficiency level of wheat producing farmers was 62% implying that there was technical efficiency variation among smallholder farmers in the study area. The result implied that there is an opportunity for wheat producers to increase output at existing levels of inputs with present technologies. By shifting the average farmer to the production frontier, the average yield would increase by 0.5 tons per hectare. The two-limit Tobit regression model results showed that experience of growing wheat, family size, own farm labor, livestock size, extension contact and training had positive and significant effect on technical efficiency. However, distant wheat plot have a negative and significance effect on technical efficiency level of the farmers. This suggests attention to productivity gains arising from efficient use of existing technologies is necessary. Therefore, the study suggested, policies and strategies should be directed towards increasing productivity through improving efficiency of the production process.

Negative Moment Bounds for Stochastic Regression Models with Deterministic Trends and Their Applications to Prediction Problems

Negative Moment Bounds for Stochastic Regression Models with Deterministic Trends and Their Applications to Prediction Problems

A new version of unbiased ridge regression estimator under the stochastic restricted linear regression model

Crouse et al. (Commun Stat Theory Methods 24:2341–2354, 1995) proposed the unbiased ridge regression estimator for the multicollinear regression model. Jibo Wu (The Scientific World Journal; Volume 2014, Article ID 206943, 1–8) introduced an unbiased two-parameter estimator based on prior information and two-parameter estimator proposed by Özkale and Kacıranlar, 2007. A new version of unbiased two-parameter estimator for the stochastic restricted linear regression model is proposed in this paper. The properties and the performance of the proposed estimator compared to other common estimators using the mean squares error criterion for the goodness of fit have been studied. Finally; A numerical example and a simulation study has been given to illustrate the performance of the proposed estimator.

Threshold Based Stochastic Regression Model with Gabor Filter for Segmentation and Random Forest Classification of Lung Cancer

Threshold Based Stochastic Regression Model with Gabor Filter for Segmentation and Random Forest Classification of Lung Cancer

Estimated potential impacts of soil and water conservation terraces on potato yields under different climate conditions

Terracing is a commonly used soil and water conservation beneficial management practice (BMP) designed to reduce soil water erosion in hilly areas. Former studies indicated that potato (Solanum tuberosum L.) yields in terraced fields appeared to be higher than nonterraced fields, even though the effective cultivation area was smaller due to berm construction in terraced fields. People hypothesized that the observed increase of potato yields was due to increased soil moisture retention caused by terracing. However, testing of this hypothesis is difficult due to lack of long-term complete records of soil moisture data together with potato yield information. The objective of this study is to assess the potato yields of terraced and nonterraced fields under different climate conditions with the assistance of a hydrological model to fill the data gaps. The historical soil moisture contents in fields with or without terraces were estimated by the Soil and Water Assessment Tool (SWAT). Then a stochastic regression model was constructed to assess the impact of soil moisture on potato yields based on 20 years of historical potato yields, estimated soil moisture content, and other biophysical data as inputs. Results showed that terracing could increase potato yields under dry and normal conditions, while nonterraced fields achieved higher yields under wet conditions. Soil moistures on terraced fields were significantly higher than on nonterraced fields. The mean annual potato yields in both terraced and nonterraced fields increased with the Soil Moisture Index (SMI) to an optimum at −1.1, then significantly decreased as SMI increased to above −0.8 or decreased to below −1.4. Statistical analysis confirmed that the optimum SMI for potato productions is around −1.1. In addition, the potato yields within each SMI group do not have significant differences for fields with or without terraces. These results indicated that as a soil and water conservation BMP, terracing could also help to improve potato productivity by improving soil water availability during the growing seasons of dry and normal years. However, the excessively high soil moisture trapped by terraces could lead to potato yield reduction during wet years. The results of this study could provide critical information for potato yield predictions and soil and water conservation BMP cost-benefit analysis under different climate conditions.