A new relative efficiency in parameter estimation for linear model

A new relative efficiency of parameter estimation for generalized Gauss-Markov linear model was proposed. Its lower bound was also derived. Its properties were explored in comparison with three currently very popular relative efficiencies. The new relative efficiency not only reflects sensitively the error and loss caused by the substitution of the least square estimator for the best linear unbiased estimator, but also overcomes the disadvantage of weak dependence on the design matrix.

Efficient fidelity estimation:alternative derivation and related applications

In[Phys.Rev.A 107012427(2023)],Baldwin and Jones prove that Uhlmann–Jozsa’s fidelity between two quantum statesρandσ,i.e.,F(ρ,σ)=(Tr√√ρσ√ρ)^(2),can be written in a simplified form as F(ρ,σ)=(Tr√ρσ)^(2).In this article,we give an alternative proof of this result,using a function power series expansion and the properties of the trace function.Our approach not only reinforces the validity of the simplified expression but also facilitates the exploration of novel dissimilarity functions for quantum states and more complex trace functions of density operators.

Sieve MLE for Generalized Partial Linear Models with Type Ⅱ Interval-censored Data

This article concerded with a semiparametric generalized partial linear model （GPLM） with the type Ⅱ censored data. A sieve maximum likelihood estimator （MLE） is proposed to estimate the parameter component, allowing exploration of the nonlinear relationship between a certain covariate and the response function. Asymptotic properties of the proposed sieve MLEs are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. Moreover, the estimators of the unknown parameters are asymptotically normal and efficient, and the estimator of the nonparametric function has an optimal convergence rate.

Estimation method of glottal vocal efficiency based on conversion function of voice source

This investigation was designed to approach a novel estimation method of glottal vocal efficiency (GVE) based on conversion function of voice source. The conversion function of voice source was defined the ratio of supra-glottal acoustic voice source signal to the glottal air volume flow velocity waveform in frequency domain. A carefully designed in vivo canine larynx experiment and several human experiments including different vowels, pressed, falsetto, breath and typical laryngeal diseases were adopted to demonstrate this alternative GVE method. Compared with other vocal efficiency, it is shown that this method could eliminate the contribution from the super vocal tract transmission and resonance to GVE, and reflect the differences of phonation modes. The average magnitude of this conversion function in frequency domain represents GVE, and the variation of the magnitude in fundamental frequency is identical to AC/DC value.

Composite Quantile Estimation for Kink Model with Longitudinal Data

Kink model is developed to analyze the data where the regression function is two-stage piecewise linear with respect to the threshold covariate but continuous at an unknown kink point.In quantile regression for longitudinal data,kink point where the kink effect happens is often assumed to be heterogeneous across different quantiles.However,the kink point tends to be the same across different quantiles,especially in a region of neighboring quantile levels.Incorporating such homogeneity information could increase the estimation efficiency of the common kink point.In this paper,we propose a composite quantile estimation approach for the common kink point by combining information from multiple neighboring quantiles.Asymptotic normality of the proposed estimator is studied.In addition,we also develop a sup-likelihood-ratio test to check the existence of the kink effect at a given quantile level.A test-inversion confidence interval for the common kink point is also developed based on the quantile rank score test.The simulation studies show that the proposed composite kink estimator is more efficient than the single quantile regression estimator.We also illustrate the proposed method via an application to a longitudinal data set on blood pressure and body mass index.

Efficient estimation for additive hazards regression with bivariate current status data

This paper discusses efficient estimation for the additive hazards regression model when only bivariate current status data are available. Current status data occur in many fields including demographical studies and tumorigenicity experiments （Keiding, 1991; Sun, 2006） and several approaches have been proposed for the additive hazards model with univariate current status data （Linet M., 1998; Martinussen and Scheike, 2002）. For bivariate data, in addition to facing the same problems as those with univariate data, one needs to deal with the association or correlation between two related failure time variables of interest. For this, we employ the copula model and an efficient estimation procedure is developed for inference. Simulation studies are performed to evaluate the proposed estimates and suggest that the approach works well in practical situations. An illustrative example is provided.

Efficient Estimation of a Varying-coefficient Partially Linear Binary Regression Model

This article considers a semiparametric varying-coefficient partially linear binary regression model. The semiparametric varying-coefficient partially linear regression binary model which is a generalization of binary regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A Sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. One of our main objects is to estimate nonparametric component and the unknowen parameters simultaneously. It is easier to compute, and the required computation burden is much less than that of the existing two-stage estimation method. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estimator for the unknown smooth function is obtained, and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies are carried out to investigate the performance of the proposed method.

Efficient Estimation for Semiparametric Varying-Coefficient Partially Linear Regression Models with Current Status Data

This article considers a semiparametric varying-coefficient partially linear regression model with current status data. The semiparametric varying-coefficient partially linear regression model which is a generalization of the partially linear regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A Sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estimator for the unknown smooth function is obtained and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies are conducted to examine the small-sample properties of the proposed estimates and a real dataset is used to illustrate our approach.

ESTIMATION AND INFERENCE FOR VARYING-COEFFICIENT REGRESSION MODELS WITH ERROR-PRONE COVARIATES

This paper studies the estimation and inference for a class of varying-coefficient regression models with error-prone covariates.The authors focus on the situation where the covariates are unobserved,there are no repeated measurements,and the covariance matrix of the measurement errors is unknown,but some auxiliary information is available.The authors propose an instrumental variable type local polynomial estimator for the unknown varying-coefficient functions,and show that the estimator achieves the optimal nonparametric convergence rate,is asymptotically normal,and avoids using undersmoothing to allow the bandwidths to be selected using data-driven methods.A simulation is carried out to study the finite sample performance of the proposed estimator,and a real date set is analyzed to illustrate the usefulness of the developed methodology.

Using a simulation analysis to evaluate the impact of crop mapping error on crop area estimation from stratified sampling

To analyze the efficiency of area estimations(i.e.estimation accuracy and variation of estimation)impacted by crop mapping error,we simulated error at eight levels for thematic maps using a stratified sampling estimation methodology.The results show that the estimation efficiency is influenced by the combination of the sample size and the error level.Evaluating the trade-offs between sample size and error level showed that reducing the crop mapping error level provides the most benefit(i.e.higher estimation efficiency).Further,sampling performance differed based on the heterogeneity of the crop area.The results demonstrated that the influence of increasing the error level on estimation efficiency is more detrimental in heterogeneous areas than in homogeneous ones.Therefore,to obtain higher estimation efficiency,a larger sample size and lower error level or both are needed,especially in heterogeneous areas.We suggest that existing land-cover maps should first be used to determine the heterogeneity of the area.The appropriate sample size for these areas then can be determined according to all three factors:heterogeneity,expected estimation efficiency,and sampling budget.Overall,extending our understanding of the impacts of crop mapping error is necessary for decision making to improve our ability to effectively estimate crop area.

ON ASYMPTOTICALLY EFFICIENT ESTIMATION FOR A SEMIPARAMETRIC REGRESSION MODEL

Consider the model Y=Xτβ+g(T)+ε. Here g is a smooth but unknown function, β is a k×1 parameter vector to be estimated and ε, is an random error with mean 0 and variance σ2. The asymptotically efficient estimator of β is constructed on the basis of the model Yi=Xτiβ+g(Ti)+εi, i=1,…,n, when the density functions of (X,T) and ε are known or unknown.Finally, an asymptotically normal estimator of σ2 is given.

TWO-VALUED RESPONSE TECHNIQUE OF POLYCHOTOMOUS SENSITIVE QUESTION

The randomized response （RR） technique is an effective survey method when collecting sensitive information. This paper proposes a new non-randomized response model for survey sampling with polychotomous sensitive questions： Two-valued response technique. The proportion of the sensitive attribute and its estimator＇s variance are estimated under the simple random sampling without replacement and with replacement designs. The relation between the efficiency and the protection of privacy is discussed. The result indicates that the efficiency is in conflict with protection of privacy in the new proposed model, which is the same as that in the RR technique, but the new technique has better characteristics in sociological practice aspects than the RR technique, because it is of low cost, saving time and being operated easily.

More Efficient Estimators for Marginal Additive Hazards Model in Case-cohort Studies with Multiple Outcomes

Case-cohort study designs are widely used to reduce the cost of large cohort studies. When several diseases are of interest, we can use the same subcohort. In this paper, we will study the casecohort design of marginal additive hazards model for multiple outcomes by a more efficient version. Instead of analyzing each disease separately, ignoring the additional exposure measurements collected on subjects with other diseases, we propose a new weighted estimating equation approach to improve the efficiency by utilizing as much information collected as possible. The consistency and asymptotic normality of the resulting estimator are established. Simulation studies are conducted to examine the finite sample performance of the proposed estimator, which confirm the efficiency gains.

Regression Analysis of Right-censored Failure Time Data with Missing Censoring Indicators

This paper discusses regression analysis of right-censored failure time data when censoring indicators are missing for some subjects. Several methods have been developed for the analysis under different situations and especially, Goetghebeur and Ryan considered the situation where both the failure time and the censoring time follow the proportional hazards models marginally and developed an estimating equation approach. One limitation of their approach is that the two baseline hazard functions were assumed to be proportional to each other. We consider the same problem and present an efficient estimation procedure for regression parameters that does not require the proportionality assumption. An EM algorithm is developed and the method is evaluated by a simulation study, which indicates that the proposed methodology performs well for practical situations. An illustrative example is provided.

Combining estimators of a common parameter across samples

In many settings,multiple data collections and analyses on the same topic are summarised separately through statistical estimators of parameters and variances,and yet there are scientificreasons for sharing some statistical parameters across these different studies.This paper summarises what is known from large-sample theory about when estimators of a common structuralparameter from several independent samples can be combined functionally,or more specificallylinearly,to obtain an asymptotically efficient estimator from the combined sample.The main ideais that such combination can be done when the separate-sample nuisance parameters,if anyexist,vary freely and independently of one another.The issues are illustrated using data from amulti-centre lung cancer clinical trial.Examples are presented to show that separate estimatorscannot always be combined in this way,and that the functionally combined separate estimators may have low or 0 efficiency compared to the unified analysis that could be performed bypooling the datasets.

INFORMATION CHARACTERIZATION OF COMMUNICATION CHANNELS FOR SYSTEM IDENTIFICATION

This paper studies identification of systems in which the system output is quantized, transmitted through a digital communication channel, and observed afterwards. The concept of the CR Ratio is introduced to characterize impact of communication channels on identification. The relationship between the CR Ratio and Shannon channel capacity is discussed. Identification algorithms are further developed when the channel error probability is unknown.