GM Estimates Research Articles

Harnessing photosynthetic C18O16O discrimination dynamics under leaf water nonsteady state to estimate mesophyll conductance: a new, regression-based method.

Mesophyll conductance (gm) is a crucial plant trait that can significantly limit photosynthesis. Measurement of photosynthetic C18O16O discrimination (Δ18O) has proved to be the only viable means of resolving gm in both C3 and C4 plants. However, the currently available methods to exploit Δ18O for gm estimation are error prone due to their inadequacy in constraining the degree of oxygen isotope exchange (θ) during mesophyll CO2 hydration. Here, we capitalized on experimental manipulation of leaf water isotopic dynamics to establish a novel, nonsteady state, regression-based approach for simultaneous determination of gm and θ from online Δ18O measurements. We demonstrated the methodological and theoretical robustness of this new Δ18O-gm estimation approach and showed through measurements on several C3 and C4 species that thisapproach can serve as a benchmark method against which to identify previously-unrecognized biases of the existing Δ18O-gm methods. Our results highlight the unique value of this nonsteady state-based approach for contributing to ongoing efforts toward quantitative understanding of mesophyll conductance for crop yield improvement and carbon cycle modeling.

Variational Bayesian and generalized maximum-likelihood based adaptive robust nonlinear filtering framework

An adaptive robust nonlinear filtering framework is proposed based on the variational Bayesian (VB) method and generalized maximum likelihood estimation (GM estimation) to simultaneously handle the outliers and uncertain measurement noise covariance matrix (MNCM) for state estimation. This framework utilizes the cubature criterion to solve nonlinear integration problems. By embedding GM estimation in the VB method, the uncertain MNCM is modified while robust estimation is performed. The modified MNCM also provides more accurate model parameters for GM estimation, achieving the unity of adaptability and robustness. The VBCEECKF algorithm was obtained by applying the strong robust centered error entropy criterion to the adaptive robust nonlinear filtering framework. The simulation results of target tracking under different noise conditions verify the superiority of the adaptive robust filter compared to existing methods.

Exploring the potential of Δ17O in CO2 for determining mesophyll conductance.

Mesophyll conductance to CO2 from the intercellular air space to the CO2-H2O exchange site has been estimated using δ18O measurements (gm18). However, the gm18 estimates are affected by the uncertainties in the δ18O of leaf water where the CO2-H2O exchange takes place and the degree of equilibration between CO2 and H2O. We show that measurements of Δ17O (i.e.Δ17O=δ17O-0.528×δ18O) can provide independent constraints on gm (gmΔ17) and that these gm estimates are less affected by fractionation processes during gas exchange. The gm calculations are applied to combined measurements of δ18O and Δ17O, and gas exchange in two C3 species, sunflower (Helianthus annuus L. cv. 'sunny') and ivy (Hedera hibernica L.), and the C4 species maize (Zea mays). The gm18 and gmΔ17 estimates agree within the combined errors (P-value, 0.876). Both approaches are associated with large errors when the isotopic composition in the intercellular air space becomes close to the CO2-H2O exchange site. Although variations in Δ17O are low, it can be measured with much higher precision compared with δ18O. Measuring gmΔ17 has a few advantages compared with gm18: (i) it is less sensitive to uncertainty in the isotopic composition of leaf water at the isotope exchange site and (ii) the relative change in the gm due to an assumed error in the equilibration fraction θeq is lower for gmΔ17 compared with gm18. Thus, using Δ17O can complement and improve the gm estimates in settings where the δ18O of leaf water varies strongly, affecting the δ18O (CO2) difference between the intercellular air space and the CO2-H2O exchange site.

Quantitative expression of mesophyll conductance temperature response in the FvCB model and impacts on plant gas exchange estimations

The way of quantitatively expressing mesophyll conductance (gm) in the Farquhar-von Caemmerer-Berry (FvCB) photosynthesis model and its impacts on plant gas exchange estimations have not been well explored, primarily due to huge uncertainties in gm parameterization. Here, a peaked Arrhenius function to depict gm temperature response was introduced into the FvCB model and parameterized through evaluating four different gm estimation methods in 19 C3 species at 31 experimental treatments. Results indicated that the FvCB model without explicitly considering gm cannot perform well in eight species/treatments, while the model that considers gm estimated by the chlorophyll fluorescence–gas exchange method and biochemical parameters estimated by the Bayesian retrieval algorithm was superior. Overall modeling accuracy was not further ameliorated when taking anatomy-based gm into consideration. The increasing Arrhenius function without considering the suboptimal stage of gm temperature response caused significant overestimations in photosynthesis under high leaf temperatures by 2–3 folds. The gm explicit expression had equally important effects on photosynthesis and transpiration estimations, which disagreed with “the asymmetric effects on photosynthesis and transpiration estimations” hypothesis proposed by Knauer et al. (2020). Literature survey plus our data indicated that observed variations of photosynthesis optimal temperature (ToptA) were primarily explained by the gm optimal temperature (Topt_gm) (58%) rather than biochemical limitations, which disagreed with “the JVr biochemical limitations” hypothesis proposed by Kumarathunge et al. (2019).

Advanced Proportional-Integral-Derivative Control Compensation Based on a Grey Estimated Model in Dynamic Balance of Single-Wheeled Robot

This paper aims to design a one-wheeled robot as regards its pitch freedom and balance control on the one hand and to assess the application feasibility of the GM (1,1) swing estimation controller on the other. System control focuses mainly on one-wheeled robot stability, body swings in position, and speed control. Mathematical modeling and GM (1,1) prediction control are under investigation. The mathematical modeling is firstly conducted through referencing to the Newtonian mechanics and the Lagrange equation, from which the robot transfer function and state-space differential equation are derived. Next, the linear quadratic regulator is applied as the control rule at the balance point. Applying GM (1,1) to assess the robot gyro signal at a dynamic state is a discussion. Next, model reference estimation control is processed, and a mathematical model of the balance control method is completed. Finally, a simulation is conducted to verify the feasibility of the GM (1,1) estimation reference model. The linear quadratic regulator, which is credited with tenacity, can provide pitch swing and balance control of the one-wheeled robot.

CRITIC Method and Grey System Theory in the Study of Global Electric Cars

Science and technology development is a crucial for the elimination of air pollutants. The electric car industry, for example, contributes to minimizing emissions and climate change. The purpose of this study is to present an overview of electric car sales and its market share in 14 countries, from past to future, by integrating important criteria through the inter-criteria correlation (CRITIC) method in multi-criteria decision-making (MCDM), grey model first-order one variables (GM(1,1)), and grey relation analysis (GRA) method in grey system theory. First, the GM(1,1) estimates future terms based on historical time-series. Second, the objective weights of each variable, in every year, are determined by the CRITIC method. Finally, the research uses the GRA method for computing grades and ranks. The empirical result then reveals the performance and rank of electric car sales during the time period of 2016–2023. The analysis results thus reveal market share picture and direction of growth in the electric car industry.

Whole-tree mesophyll conductance reconciles isotopic and gas-exchange estimates of water-use efficiency.

Photosynthetic water-use efficiency (WUE) describes the link between terrestrial carbon (C) and water cycles. Estimates of intrinsic WUE (iWUE) from gas exchange and C isotopic composition (δ13 C) differ due to an internal conductance in the leaf mesophyll (gm ) that is variable and seldom computed. We present the first direct estimates of whole-tree gm , together with iWUE from whole-tree gas exchange and δ13 C of the phloem (δ13 Cph ). We measured gas exchange, online 13 C-discrimination, and δ13 Cph monthly throughout spring, summer, and autumn in Eucalyptus tereticornis grown in large whole-tree chambers. Six trees were grown at ambient temperatures and six at a 3°C warmer air temperature; a late-summer drought was also imposed. Drought reduced whole-tree gm . Warming had few direct effects, but amplified drought-induced reductions in whole-tree gm . Whole-tree gm was similar to leaf gm for these same trees. iWUE estimates from δ13 Cph agreed with iWUE from gas exchange, but only after incorporating gm . δ13 Cph was also correlated with whole-tree 13 C-discrimination, but offset by -2.5±0.7‰, presumably due to post-photosynthetic fractionations. We conclude that δ13 Cph is a good proxy for whole-tree iWUE, with the caveats that post-photosynthetic fractionations and intrinsic variability of gm should be incorporated to provide reliable estimates of this trait in response to abiotic stress.

Reliability assessment of tissue classification algorithms for multi-center and multi-scanner data

BackgroundGray and white matter volume difference and change are important imaging markers of pathology and disease progression in neurology and psychiatry. Such measures are usually estimated from tissue segmentation maps produced by publicly available image processing pipelines. However, the reliability of the produced segmentations when using multi-center and multi-scanner data remains understudied. Here, we assess the robustness of six publicly available tissue classification pipelines across images acquired from different MR scanners and sites. MethodsWe used 90 T1-weighted images of a single individual, scanned in 73 sessions across 27 different sites to assess the robustness of the tissue classification tools. Variability in Dice similarity index values and tissue volumes was assessed for Atropos, BISON, Classify_Clean, FAST, FreeSurfer, and SPM12. ResultsBISON had the highest overall Dice coefficient for GM, followed by SPM12 and Atropos; while Atropos had the highest overall Dice coefficient for WM, followed by BISON and SPM12. BISON had the lowest overall variability in its volumetric estimates, followed by FreeSurfer, and SPM12. All methods also had significant differences between some of their estimates across different scanner manufacturers (e.g. BISON had significantly higher GM estimates and correspondingly lower WM estimates for GE scans compared to Philips and Siemens), and different signal-to-noise ratio (SNR) levels (e.g. FAST and FreeSurfer had significantly higher WM volume estimates for high versus medium and low SNR tertiles as well as correspondingly lower GM volume estimates). ConclusionsOur comparisons provide a benchmark on the reliability of the publicly used tissue classification techniques and the amount of variability that can be expected when using large multi-center and multi-scanner databases.

Modeling grey matter atrophy as a function of time, aging or cognitive decline show different anatomical patterns in Alzheimer's disease.

BackgroundGrey matter (GM) atrophy in Alzheimer's disease (AD) is most commonly modeled as a function of time. However, this approach does not take into account inter-individual differences in initial disease severity or changes due to aging. Here, we modeled GM atrophy within individuals across the AD clinical spectrum as a function of time, aging and MMSE, as a proxy for disease severity, and investigated how these models influence estimates of GM atrophy.MethodsWe selected 523 individuals from ADNI (100 preclinical AD, 288 prodromal AD, 135 AD dementia) with abnormal baseline amyloid PET/CSF and ≥1 year of MRI follow-up. We calculated total and 90 regional GM volumes for 2281 MRI scans (median [IQR]; 4 [3–5] scans per individual over 2 [1.6–4] years) and used linear mixed models to investigate atrophy as a function of time, aging and decline on MMSE. Analyses included clinical stage as interaction with the predictor and were corrected for baseline age, sex, education, field strength and total intracranial volume. We repeated analyses for a sample of participants with normal amyloid (n = 387) to assess whether associations were specific for amyloid pathology.ResultsUsing time or aging as predictors, amyloid abnormal participants annually declined −1.29 ± 0.08 points and − 0.28 ± 0.03 points respectively on the MMSE and −12.23 ± 0.47 cm3 and −8.87 ± 0.34 respectively in total GM volume (p < .001). For the time and age models atrophy was widespread and preclinical and prodromal AD showed similar atrophy patterns. Comparing prodromal AD to AD dementia, AD dementia showed faster atrophy mostly in temporal lobes as modeled with time, while prodromal AD showed faster atrophy in mostly frontoparietal areas as modeled with age (pFDR < 0.05). Modeling change in GM volume as a function of decline on MMSE, slopes were less steep compared to those based on time and aging (−4.1 ± 0.25 cm3 per MMSE point decline; p < .001) and showed steeper atrophy for prodromal AD compared to preclinical AD in the right inferior temporal gyrus (p < .05) and compared to AD dementia mostly in temporal areas (pFDR < 0.05). Associations with time, aging and MMSE remained when accounting for these effects in the other models, suggesting that all measures explain part of the variance in GM atrophy. Repeating analyses in amyloid normal individuals, effects for time and aging showed similar widespread anatomical patterns, while associations with MMSE were largely reduced.ConclusionEffects of time, aging and MMSE all explained variance in GM atrophy slopes within individuals. Associations with MMSE were weaker than those for time or age, but specific for amyloid pathology. This suggests that at least some of the atrophy observed in time or age models may not be specific to AD.

Uncertainties and limitations of using carbon-13 and oxygen-18 leaf isotope exchange to estimate the temperature response of mesophyll CO2 conductance in C3 plants.

The internal CO2 gradient imposed by mesophyll conductance (gm ) reduces substrate availability for C3 photosynthesis. With several assumptions, estimates of gm can be made from coupled leaf gas exchange with isoflux analysis of carbon ∆13 C-gm and oxygen in CO2 , coupled with transpired water (H2 O) ∆18 O-gm to partition gm into its biochemical and anatomical components. However, these assumptions require validation under changing leaf temperatures. To test these assumptions, we measured and modeled the temperature response (15-40°C) of ∆13 C-gm and ∆18 O-gm along with leaf biochemistry in the C3 grass Panicum bisulcatum, which has naturally low carbonic anhydrase activity. Our study suggests that assumptions regarding the extent of isotopic equilibrium (θ) between CO2 and H2 O at the site of exchange, and that the isotopic composition of the H2 O at the sites of evaporation ( ) and at the site of exchange ( ) are similar, may lead to errors in estimating the ∆18 O-gm temperature response. The input parameters for ∆13 C-gm appear to be less sensitive to temperature. However, this needs to be tested in species with diverse carbonic anhydrase activity. Additional information on the temperature dependency of cytosolic and chloroplastic pH may clarify uncertainties used for ∆18 O-gm under changing leaf temperatures.

Variation in photosynthetic characteristics with growth form in a water-limited scenario: Implications for assimilation rates and water use efficiency in crops

Photosynthesis is a complex process that is intrinsically determined by two main components: the CO2 diffusion from the atmosphere to the chloroplast and the biochemistry. Among CO2 diffusion, mesophyll conductance within the leaf (gm) has been receiving attention in the recent years as a key player determining photosynthesis both across species and in response to the environment; furthermore, gm estimation allows for disentangling the complete set of photosynthesis underlying mechanisms. In a water-limited scenario where crop productivity and efficiency need to be increased, the analysis of available data from photosynthesis among vascular plants and its response to water stress results helpful for a better understanding of crop management and improvement. Here, photosynthesis data are compiled to elucidate if crop and wild species from different growth forms present different photosynthesis limitations under optimum and water stress conditions. From the available data, a double process of apparent photosynthesis selection is revealed: higher values from ferns to woody and herbaceous species and, among angiosperms, a tendency towards greater photosynthesis in crop species (although constrained by growth form). The causes of such photosynthesis variation are discussed. Moreover, crop and herbaceous species present a shift in photosynthesis limitations towards lower mesophyll diffusion constraints, under both well-watered and water-stress conditions. These particular photosynthesis characteristics in crops present several implications for the possible improvement of CO2 assimilation and water use efficiency, providing new guidelines for future engineering and management in agriculture.

The response of mesophyll conductance to short-term variation in CO2 in the C4 plants Setaria viridis and Zea mays.

Mesophyll conductance (gm) limits rates of C3 photosynthesis but little is known about its role in C4 photosynthesis. If gm were to limit C4 photosynthesis, it would likely be at low CO2 concentrations (pCO2). However, data on C4-gm across ranges of pCO2 are scarce. We describe the response of C4-gm to short-term variation in pCO2, at three temperatures in Setaria viridis, and at 25 °C in Zea mays. Additionally, we quantified the effect of finite gm calculations of leakiness (ϕ) and the potential limitations to photosynthesis imposed by stomata, mesophyll, and carbonic anhydrase (CA) across pCO2. In both species, gm increased with decreasing pCO2. Including a finite gm resulted in either no change or increased ϕ compared with values calculated with infinite gm depending on whether the observed 13C discrimination was high (Setaria) or low (Zea). Post-transitional regulation of the maximal PEP carboxylation rate and PEP regeneration limitation could influence estimates of gm and ϕ. At pCO2 below ambient, the photosynthetic rate was limited by CO2 availability. In this case, the limitation imposed by the mesophyll was similar or slightly lower than stomata limitation. At very low pCO2, CA further constrained photosynthesis. High gm could increase CO2 assimilation at low pCO2 and improve photosynthetic efficiency under situations when CO2 is limited, such as drought.

Mesophyll conductance in Zea mays responds transiently to CO2 availability: implications for transpiration efficiency in C4 crops.

Mesophyll conductance (gm ) describes the movement of CO2 from the intercellular air spaces below the stomata to the site of initial carboxylation in the mesophyll. In contrast with C3 -gm , little is currently known about the intraspecific variation in C4 -gm or its responsiveness to environmental stimuli. To address these questions, gm was measured on five maize (Zea mays) lines in response to CO2 , employing three different estimates of gm . Each of the methods indicated a significant response of gm to CO2 . Estimates of gm were similar between methods at ambient and higher CO2 , but diverged significantly at low partial pressures of CO2 . These differences are probably driven by incomplete chemical and isotopic equilibrium between CO2 and bicarbonate under these conditions. Carbonic anhydrase and phosphoenolpyruvate carboxylase invitro activity varied significantly despite similar values of gm and leaf anatomical traits. These results provide strong support for a CO2 response of gm in Z.mays, and indicate that gm in maize is probably driven by anatomical constraints rather than by biochemical limitations. The CO2 response of gm indicates a potential role for facilitated diffusion in C4 -gm . These results also suggest that water-use efficiency could be enhanced in C4 species by targeting gm .

Calibration matters: On the procedure of using the chlorophyll fluorescence method to estimate mesophyll conductance

Estimates of mesophyll conductance (gm), when calculated from chlorophyll fluorescence, are uncertain, especially when the photosystem II (PSII) operating efficiency is measured from the traditional single saturation pulse methodology. The multiphase flash method has recently been recommended to replace the single saturation pulse method, allowing a more reliable estimation of gm. Also, many researchers still directly use the PSII operating efficiency to derive linear electron transport rate J (that is required to estimate gm), without appropriate calibration using measurements under non-photorespiratory conditions. Here we demonstrate for tomato and rice that (i) using the multiphase flash method did not yield realistic estimates of gm if no calibration was conducted; and (ii) using the single saturation pulse method still gave reasonable estimates of gm when calibration based on the non-photorespiratory measurements was properly conducted. Therefore, conducting calibration based on data under non-photorespiratory conditions was indispensable for a reliable estimation of gm, regardless whether the multiphase flash or the single saturation pulse method was used for measuring the PSII operating efficiency. Other issues related to the procedure of using the chlorophyll fluorescence method to estimate gm were discussed.

Determining Near-Surface Soil Heat Flux Density Using the Gradient Method: A Thermal Conductivity Model–Based Approach

Abstract In the gradient method, soil heat flux density at a known depth G is determined as the product of soil thermal conductivity λ and temperature T gradient. While measuring λ in situ is difficult, many field studies readily support continuous, long-term monitoring of soil T and water content θ in the vadose zone. In this study, the performance of the gradient method is evaluated for estimating near-surface G using modeled λ and measured T. Hourly λ was estimated using a model that related λ to θ, soil bulk density ρb, and texture at 2-, 6-, and 10-cm depths. Soil heat flux Gm was estimated from modeled λ and measured T gradient (from thermocouples). The Gm results were evaluated with heat flux data GHP determined using independent measured λ and T gradient from heat-pulse probes. The λ model performed well at the three depths with 3.3%–7.4% errors. The Gm estimates were similar to GHP (agreed to within 15.1%), with the poorest agreement at the 2-cm soil depth, which was caused mainly by the relatively greater variability in ρb. Accounting for temporal variations in ρb (with core method) improved the accuracies of λ and Gm at the 2-cm depth. Automated θ monitoring approaches (e.g., time domain reflectometry), rather than gravimetric sampling, captured the temporal dynamics of near-surface λ and G well. It is concluded that with continuous θ and T measurements, the λ model–based gradient method can provide reliable near-surface G. Under conditions of soil disturbance or deformation, including temporally variable ρb, data improves the accuracy of G data.

A high breakdown, high efficiency and bounded influence modified GM estimator based on support vector regression

ABSTRACTRegression analysis aims to estimate the approximate relationship between the response variable and the explanatory variables. This can be done using classical methods such as ordinary least squares. Unfortunately, these methods are very sensitive to anomalous points, often called outliers, in the data set. The main contribution of this article is to propose a new version of the Generalized M-estimator that provides good resistance against vertical outliers and bad leverage points. The advantage of this method over the existing methods is that it does not minimize the weight of the good leverage points, and this increases the efficiency of this estimator. To achieve this goal, the fixed parameters support vector regression technique is used to identify and minimize the weight of outliers and bad leverage points. The effectiveness of the proposed estimator is investigated using real and simulated data sets.

Methods of mesophyll conductance estimation: its impact on key biochemical parameters and photosynthetic limitations in phosphorus-stressed soybean across CO2.

Despite the development of various methods, the rapid estimation of mesophyll conductance (gm ) for a large number of samples is still a daunting challenge. Although the accurate estimation of gm is critical to partition photosynthetic limitations by stomatal (Ls ) and mesophyll (Lm ) conductance and by photo-biochemical (Lb ) processes, the impact of various gm estimation methods on this is ambiguous. As phosphorus (P) starvation and elevated CO2 (eCO2 ) strongly affect photosynthetic processes, their combined effect on the proportional changes in these limitations are not well understood. To investigate this, while also evaluating distinct recent methods of gm estimation sharing few common theories and assumptions, soybean was grown under a range of P nutrition at ambient and eCO2 . Methods significantly affected gm and carboxylation efficiency (VCmax ) but not other photosynthetic parameters. In all the methods, all photosynthetic parameters responded similarly to treatments. However, the percentage difference between VCmax assuming finite and infinite gm was highly inconsistent among methods. The primary mechanism responsible for P limitation to soybean photosynthesis was not CO2 diffusion limitations but Lb comprised of reduced chlorophyll, photochemistry and biochemical processes. The eCO2 decreased Lb but increased Lm without affecting Ls across leaf P concentration. Although each method explored advances of our understanding about gm variability, they all require assumptions of varying degrees, which lead to the discrepancy in the gm values. Among the methods, the oxygen sensitivity-based gm estimation appeared to be suitable for the quick assessment of a large number of samples or genotypes. Digital tools are provided for the easy estimation of gm for some methods.

Inconsistency of mesophyll conductance estimate causes the inconsistency for the estimates of maximum rate of Rubisco carboxylation among the linear, rectangular and non-rectangular hyperbola biochemical models of leaf photosynthesis—A case study of CO2 enrichment and leaf aging effects in soybean

The responses of CO2 assimilation to [CO2] (A/Ci) were investigated at two developmental stages (R5 and R6) and in several soybean cultivars grown under two levels of CO2, the ambient level of 370μbar versus the elevated level of 550μbar. The A/Ci data were analyzed and compared by either the combined iterations or the separated iterations of the Rubisco-limited photosynthesis (Ac) and/or the RuBP-limited photosynthesis (Aj) using various curve-fitting methods: the linear 2-segment model; the non-rectangular hyperbola model; the rectangular hyperbola model; the constant rate of electron transport (J) method and the variable J method. Inconsistency was found among the various methods for the estimation of the maximum rate of carboxylation (Vcmax), the mitochondrial respiration rate in the light (Rd) and mesophyll conductance (gm). The analysis showed that the inconsistency was due to inconsistent estimates of gm values that decreased with an instantaneous increase in [CO2], and varied with the transition Ci cut-off between Rubisco-limited photosynthesis and RuBP-regeneration-limited photosynthesis, and due to over-parameters for non-linear curve-fitting with gm included. We proposed an alternate solution to A/Ci curve-fitting for estimates of Vcmax, Rd, Jmax and gm with the various A/Ci curve-fitting methods. The study indicated that down-regulation of photosynthetic capacity by elevated [CO2] and leaf aging was due to partially the decrease in the maximum rates of carboxylation and partially the decrease in gm. Mesophyll conductance lowered photosynthetic capacity by 18% on average for the case of soybean plants.

Constrained Robust Estimation of Power System State Variables and Transformer Tap Positions Under Erroneous Zero-Injections

This paper presents an equally constrained robust estimator of both the state and the transformer tap positions of a power system able to withstand all types of outliers, including bad leverage points and erroneous zero-injections. The statistical robustness of the estimator stems from the application of the Schweppe-type Huber GM estimator (SHGM) while its numerical robustness originates from the use of an orthogonal iteratively re-weighted least-squares algorithm together with the Van Loan's method for processing the equality constraints. The good performance of the new estimator, termed EC-SHGM estimator for short, is demonstrated on a small test system and on the Brazilian Southern power system with increasing size ranging from 139 buses to 1916 buses. It is shown that it exhibits superior convergence properties in all tested cases while the WLS method may suffer from numerical instabilities or even divergence problems when large weights are assigned to zero power injections modeling false information.

Generalized shrunken type-GM estimator and its application

The parameter estimation problem in linear model is considered when multicollinearity and outliers exist simultaneously. A class of new robust biased estimator, Generalized Shrunken Type-GM Estimation, with their calculated methods are established by combination of GM estimator and biased estimator include Ridge estimate, Principal components estimate and Liu estimate and so on. A numerical example shows that the most attractive advantage of these new estimators is that they can not only overcome the multicollinearity of coefficient matrix and outliers but also have the ability to control the influence of leverage points.