The UNIFORM C^(0)ESTIMATE AND WEIGHTED ESTIMATE OF GENERALIZED CHRISTOFFEL-MINKOWSKI PROBLEMS

In this paper,we consider generalized Christo®el-Minkowski problems as followsσ_(k)(u_(ij)+uδ_(ij))/σ_(l)(u_(ij)+uδ_(ij))=|u^(p-1)f(x),x∈S^(n),where 0≤l≤k≤n,p-1>0 and f is positive,and we establish the weighted gradient estimate and uniform C^(0)estimate for the positive convex even solutions,which is a generalization of Guan-Xia[1]and Guan[2].

Parameter Estimation of a Valve-Controlled Cylinder System Model Based on Bench Test and Operating Data Fusion

The accurate estimation of parameters is the premise for establishing a high-fidelity simulation model of a valve-controlled cylinder system.Bench test data are easily obtained,but it is challenging to emulate actual loads in the research on parameter estimation of valve-controlled cylinder system.Despite the actual load information contained in the operating data of the control valve,its acquisition remains challenging.This paper proposes a method that fuses bench test and operating data for parameter estimation to address the aforementioned problems.The proposed method is based on Bayesian theory,and its core is a pool fusion of prior information from bench test and operating data.Firstly,a system model is established,and the parameters in the model are analysed.Secondly,the bench and operating data of the system are collected.Then,the model parameters and weight coefficients are estimated using the data fusion method.Finally,the estimated effects of the data fusion method,Bayesian method,and particle swarm optimisation(PSO)algorithm on system model parameters are compared.The research shows that the weight coefficient represents the contribution of different prior information to the parameter estimation result.The effect of parameter estimation based on the data fusion method is better than that of the Bayesian method and the PSO algorithm.Increasing load complexity leads to a decrease in model accuracy,highlighting the crucial role of the data fusion method in parameter estimation studies.

LEAST SQUARES ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESSES DRIVEN BY THE WEIGHTED FRACTIONAL BROWNIAN MOTION

In this article, we study a least squares estimator （LSE） of θ for the Ornstein- Uhlenbeck process X0=0,dXt=θXtdt＋dBt^ab, t ≥ 0 driven by weighted fractional Brownian motion B^a,b with parameters a, b. We obtain the consistency and the asymptotic distribution of the LSE based on the observation {Xs, s∈[0,t]} as t tends to infinity.

Recursive weighted least squares estimation algorithm based on minimum model error principle

Kalman filter is commonly used in data filtering and parameters estimation of nonlinear system,such as projectile's trajectory estimation and control.While there is a drawback that the prior error covariance matrix and filter parameters are difficult to be determined,which may result in filtering divergence.As to the problem that the accuracy of state estimation for nonlinear ballistic model strongly depends on its mathematical model,we improve the weighted least squares method(WLSM)with minimum model error principle.Invariant embedding method is adopted to solve the cost function including the model error.With the knowledge of measurement data and measurement error covariance matrix,we use gradient descent algorithm to determine the weighting matrix of model error.The uncertainty and linearization error of model are recursively estimated by the proposed method,thus achieving an online filtering estimation of the observations.Simulation results indicate that the proposed recursive estimation algorithm is insensitive to initial conditions and of good robustness.

ERRATUM TO： LEAST SQUARES ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESSES DRIVEN BY THE WEIGHTED FRACTIONAL BROWNIAN MOTION （ACTA MATHEMATICA SCIENTIA 2016,36B （2） ：394-408）

We give a correction of Theorem 2.2 of Shen, Yin and Yan （2016）.

Wavelet Density Estimation and Statistical Evidences Role for a GARCH Model in the Weighted Distribution

We consider n observations from the GARCH-type model: Z = UY, where U and Y are independent random variables. We aim to estimate density function Y where Y have a weighted distribution. We determine a sharp upper bound of the associated mean integrated square error. We also make use of the measure of expected true evidence, so as to determine when model leads to a crisis and causes data to be lost.

Generalized weighted functional proportional mean combining forecasting model and its method of parameter estimation

A new kind of combining forecasting model based on the generalized weighted functional proportional mean is proposed and the parameter estimation method of its weighting coefficients by means of the algorithm of quadratic programming is given. This model has extensive representation. It is a new kind of aggregative method of group forecasting. By taking the suitable combining form of the forecasting models and seeking the optimal parameter, the optimal combining form can be obtained and the forecasting accuracy can be improved. The effectiveness of this model is demonstrated by an example.

STUDY ON FREQUENCY ESTIMATION BASED ON WEIGHTED LEAST SQUARE METHOD WITH THREE FOURIER COEFFICIENTS

In this paper,a sinusoidal signal frequency estimation algorithm is proposed by weighted least square method.Based on the idea of Provencher,three biggest Fourier coefficients in the maximum periodogram are considered,the Fourier coefficients can be written as three equations about the amplitude,phase,and frequency,and the frequency is estimated by solving equations.Because of the error of measurement,weighted least square method is used to solve the frequency equation and get the signal frequency.It is shown that the proposed estimator can approach the Cramer-Rao Bound(CRB)with a low Signal-to-Noise Ratio(SNR)threshold and has a higher accuracy.

Weighted Likelihood Estimation Method Based on the Multidimensional Nominal Response Model

The Monte Carlo study evaluates the relative accuracy of Warm＇s （1989） weighted likelihood estimate （WLE） compared to the maximum likelihood estimate （MLE） using the nominal response model. And the results indicate that WLE was more accurate than MLE.

Intention Estimation of Adversarial Spatial Target Based on Fuzzy Inference

Estimating the intention of space objects plays an important role in air-craft design,aviation safety,military and otherfields,and is an important refer-ence basis for air situation analysis and command decision-making.This paper studies an intention estimation method based on fuzzy theory,combining prob-ability to calculate the intention between two objects.This method takes a space object as the origin of coordinates,observes the target’s distance,speed,relative heading angle,altitude difference,steering trend and etc.,then introduces the spe-cific calculation methods of these parameters.Through calculation,values are input into the fuzzy inference model,andfinally the action intention of the target is obtained through the fuzzy rule table and historical weighted probability.Ver-ified by simulation experiment,the target intention inferred by this method is roughly the same as the actual behavior of the target,which proves that the meth-od for identifying the target intention is effective.

GRADIENT ESTIMATES AND ENTROPY FORMULAE FOR WEIGHTED p-HEAT EQUATIONS ON SMOOTH METRIC MEASURE SPACES

Let （M,g, e^-fdv） be a smooth metric measure space. In this paper, we con- sider two nonlinear weighted p-heat equations. Firstly, we derive a Li-Yau type gradient estimates for the positive solutions to the following nonlinear weighted p-heat equationand f is a smooth function on M under the assumptionthat the m-dimensional nonnegative Bakry-Emery Ricci curvature. Secondly, we show an entropy monotonicity formula with nonnegative m-dimensional Bakry-Emery Ricci curva- ture which is a generalization to the results of Kotschwar and Ni [9], Li [7].

A sharp gradient estimate for the weighted p-Laplacian

Let M be an n-dimensional complete noncompact Riemannian manifold with sectional curvature bounded from below, dμ = e^h（x） dV（x） the weighted measure and △μ,p the weighted p-Laplacian. In this paper we consider the non-linear elliptic equation △μ,pu=-λμ,p｜u｜^p-2ufor p ∈ （1, 2）. We derive a sharp gradient estimate for positive smooth solutions of this equation. As applications, we get a Harnack inequality and a Liouville type theorem..

Ultrasound estimation of fetal weight in twins by artificial neural network

This study was undertaken to determine the accuracy of using Ultrasound (US) estimation of twin fetuses by use of Artificial Neural Network. At First, as the training group, we performed US examinations on 186 healthy singleton fetuses within 3 days of delivery. Three input variables were used to construct the ANN model: abdominal circumference (AC), ab-dominal diameter (AD), biparietal diameter (BPD). Then, a total of 121 twin fetuses were assessed sub-sequently as the validation group. In validation group, the mean absolute error and the mean absolute per-cent error between estimated fetal weight and actual fetal weight was 261.77 g and 7.81%, respectively. Results show that, twin estimation of birth weight by ultrasound correlates fairly well with the actual weights of twin fetuses.

The RAMA Ped Card： Does it work for actual weight estimation in child patients at the emergency department

BACKGROUND: In emergency conditions, the actual weight of infants and young children are essential for treatments. The RAMATHIBODI Pediatric Emergency Drug Card or RAMA Ped Card has also been developed to estimate actual weight of the subjects. This study aimed to validate the RAMA Ped Card in correctly identifying the actual weight of infants and young adults.METHODS: This study was a prospective study. We enrolled all consecutive patients under 15 years of age who visited the emergency department(ED). All eligible patients' actual weight and height were measured at the screening point of the ED. The weight of each patient was also measured using the unlabeled RAMA Ped Card. The Cohen's kappa values and agreement percentages were calculated.RESULTS: During the study period, there were 345 eligible patients. The RAMA Ped Card had a 61.16% agreement with the actual weight with a kappa of 0.54(P<0.01), while the agreement with the actual height had a kappa of 0.90 and 91.59% agreement. Sub-group analysis found kappa scores with good range in two categories: in cases of accidents and in the infant group(kappa of 0.68 and 0.65, respectively).CONCLUSION: The RAMA Ped Card had a fair correlation with the actual weight in child patients presenting at the ED. Weight estimation in infant patients and children who presented with accidents were more accurate.

Hamilton-Souplet-Zhang's gradient estimates for two weighted nonlinear parabolic equations

In this paper, we consider gradient estimates for positive solutions to the following weighted nonlinear parabolic equations on a complete smooth metric measure space with only Bakry-Émery Ricci tensor bounded below: One is $${u_t} = {\Delta _f}u + au\log u + bu$$ with a, b two real constants, and another is $${u_t} = {\Delta _f}u + \lambda {u^\alpha }$$ with λ, α two real constants. We obtain local Hamilton-Souplet-Zhang type gradient estimates for the above two nonlinear parabolic equations. In particular, our estimates do not depend on any assumption on f.

Weighted Maximum Likelihood Technique for Logistic Regression

In this paper, a weighted maximum likelihood technique (WMLT) for the logistic regression model is presented. This method depended on a weight function that is continuously adaptable using Mahalanobis distances for predictor variables. Under the model, the asymptotic consistency of the suggested estimator is demonstrated and properties of finite-sample are also investigated via simulation. In simulation studies and real data sets, it is observed that the newly proposed technique demonstrated the greatest performance among all estimators compared.

Estimation of Weight and Lipid Composition in Preimplantation Embryos from Jersey and Beef Breeds of Cattle

Cryopreservation is the main functional means for storage of excess embryos produced from artificial reproductive technologies;the process assumes embryos chemical nature is highly conserved across embryos of the same species. However, in practice there appears to be a high degree of variability in embryo tolerance to cryopreservation, suggesting potential differences in embryo chemistry. The objective of the current study was to develop reproducible means of estimating relative embryos weight and associating those weights to lipid content. Relative embryo weights of frozen/thawed in-vivo Jersey and Crossbred beef breed embryos were determined using a modified specific gravity chamber. Embryo weights were then correlated with lipid content. Results suggest that beef cattle embryos are 20% - 27% heavier than Jersey embryos

Unbiased Estimation Formula of Unit Weight Standard Deviation in Regularization Solution

Regularization method is an effective method for solving ill\|posed equation. In this paper the unbiased estimation formula of unit weight standard deviation in the regularization solution is derived and the formula is verified with numerical case of 1 000 sample data by use of the typical ill\|posed equation, i.e. the Fredholm integration equation of the first kind.

WEIGHTED WEAK TYPE ESTIMATES INVOLVING SPACES GENERATED BY BLOCKS

The problem studied in this paper is how to establish weighted estimates of weak type near L^1 for those operators that are not of weak type(1,1).

The “PAWPER-on-a-page”: Increasing global access to a low-cost weight estimation system

BACKGROUND: The PAWPER tape is one of the most accurate weight estimation systems available today, but international access to the tape is limited because it has no commercial distribution. For this reason, the "PAWPER-on-a-page" concept was devised: downloadable image fi les that allow users to print and assemble their own tapes. However, the feasibility of this method is dependent on users being able to produce accurate tapes. This study was devised to determine whether untrained participants could print and assemble the "PAWPER-on-a-page" easily and accurately.METHODS: Doctor and nurse volunteers downloaded the "PAWPER-on-a-page" and "PAWPER XL-on-a-page" image files and printed copies on a home-printer and also at a commercial printer. One copy of each tape was then assembled according to instructions from an online video. The accuracy of printing and assembly, the time taken for assembly and the cost were then evaluated.RESULTS: There were 32 participants. The median time for assembly was 8 minutes 19 seconds and 7 minutes 31 seconds for the "PAWPER-on-a-page" and "PAWPER XL-on-a-page" respectively, with a median cost of USD 0.09 and USD 1.00 respectively. For the assembled tapes, 71.9% of the "PAWPER-on-a-page" tapes and 65.6% of the "PAWPER XL-on-a-page" achieved the required accuracy of 0.2%. Printing errors, related to scaling, were common, but easily detectable.CONCLUSION: The "PAWPER-on-a-page" system can be easily, quickly, affordably and accurately printed and assembled by end users. Stringent double checking of the printed and fully assembled tapes is essential to ensure accuracy.