Performance Of Different Estimators Research Articles

Minimum Lq‐distance estimators for non‐normalized parametric models

AbstractWe propose and investigate a new estimation method for the parameters of models consisting of smooth density functions on the positive half axis. The procedure is based on a recently introduced characterization result for the respective probability distributions, and is to be classified as a minimum distance estimator, incorporating as a distance function the Lq‐norm. Throughout, we deal rigorously with issues of existence and measurability of these implicitly defined estimators. Moreover, we provide consistency results in a common asymptotic setting, and compare our new method with classical estimators for the exponential, the Rayleigh and the Burr Type XII distribution in Monte Carlo simulation studies. We also assess the performance of different estimators for non‐normalized models in the context of an exponential‐polynomial family.

Assessing Heterogeneity of Treatment Effects in Observational Studies.

Here we describe methods for assessing heterogeneity of treatment effects over prespecified subgroups in observational studies, using outcome-model-based (g-formula), inverse probability weighting, doubly robust, and matching estimators of subgroup-specific potential outcome means, conditional average treatment effects, and measures of heterogeneity of treatment effects. We compare the finite-sample performance of different estimators in simulation studies where we vary the total sample size, the relative frequency of each subgroup, the magnitude of treatment effect in each subgroup, and the distribution of baseline covariates, for both continuous and binary outcomes. We find that the estimators' bias and variance vary substantially in finite samples, even when there is no unobserved confounding and no model misspecification. As an illustration, we apply the methods to data from the Coronary Artery Surgery Study (August 1975-December 1996) to compare the effect of surgery plus medical therapy with that of medical therapy alone for chronic coronary artery disease in subgroups defined by previous myocardial infarction or left ventricular ejection fraction.

Statistical Properties and Estimation of Power-Transmuted Inverse Rayleigh Distribution

Abstract A three-parameter continuous distribution is constructed, using a power transformation related to the transmuted inverse Rayleigh (TIR) distribution. A comprehensive account of the statistical properties is provided, including the following: the quantile function, moments, incomplete moments, mean residual life function and Rényi entropy. Three classical procedures for estimating population parameters are analysed. A simulation study is provided to compare the performance of different estimates. Finally, a real data application is used to illustrate the usefulness of the recommended distribution in modelling real data.

Bayesian Inference for Reliability Function of Gompertz Distribution

In this paper, some Bayes estimators of the reliability function of Gompertz distribution have been derived based on generalized weighted loss function. In order to get a best understanding of the behaviour of Bayesian estimators, a non-informative prior as well as an informative prior represented by exponential distribution is considered. Monte-Carlo simulation have been employed to compare the performance of different estimates for the reliability function of Gompertz distribution based on Integrated mean squared errors. It was found that Bayes estimators with exponential prior information under the generalized weighted loss function were generally better than the estimators based on Jeffreys prior information.

On the Alpha Power Transformed Power Inverse Lindley Distribution

In this paper, we introduce a new generalization of the power inverse Lindley distribution referred to as the alpha power transformed power inverse Lindley (APTPIL). The APTPIL model provides a better fit than the power inverse Lindley distribution. It includes the alpha power transformed inverse Lindley, power inverse Lindley and inverse Lindley as special sub models. Various properties of the APTPIL distribution including moments, incomplete moments, quantiles, entropy, and stochastic ordering are obtained. Maximum likelihood, maximum products of spacings, and ordinary and weighted least squares methods of estimation are utilized to obtain the estimators of the population parameters. Extensive numerical simulation is performed to examine and compare the performance of different estimates. Important data set is employed to show how the proposed model works in practice.

New Moment Estimators of the Effective Spread Based on Daily High and Low Prices

In the paper we propose five new moment estimators for effective spread based on the covariance estimator of Roll (1984) and the High-Low estimator recently developed by Corwin and Schultz (2012, \textit{J. Finance}, Vol.67, 719-760), and further investigate theoretically the statistical properties of six bid-ask spread estimators including Corwin and Schultz's estimator. The biases and mean squared errors (MSE) of these six estimators have been derived and compared with each other asymptotically, which, together with the subsequent simulation studies and empirical examples, reveal explicitly the superior performance of new developed High-Low estimators over Corwin and Schultz's estimator. Furthermore this paper also puts forward GMM estimators constructed by three or more moment conditions, which also perform well compared with the six High-Low estimators. The method discussed here is different to the existing literatures which usually resort to the correlation between the bid-ask spread estimators with a benchmark calculated from high-frequency data as they compare the performance of different estimators.

Real-Time Source-Independent Quantum Random-Number Generator with Squeezed States

Random numbers are a fundamental ingredient for many applications including simulation, modelling and cryptography. Sound random numbers should be independent and uniformly distributed. Moreover, for cryptographic applications they should also be unpredictable. We demonstrate a real-time self-testing source independent quantum random number generator (QRNG) that uses squeezed light as source. We generate secure random numbers by measuring the quadratures of the electromagnetic field without making any assumptions on the source; only the detection device is trusted. We use a homodyne detection to alternatively measure the Q and P conjugate quadratures of our source. Using the entropic uncertainty relation, measurements on P allow us to estimate a bound on the min-entropy of Q conditioned on any classical or quantum side information that a malicious eavesdropper may detain. This bound gives the minimum number of secure bits we can extract from the Q measurement. We discuss the performance of different estimators for this bound. We operate this QRNG with a squeezed state and we compare its performance with a QRNG using thermal states. The real-time bit rate was 8.2 kb/s when using the squeezed source and between 5.2-7.2 kb/s when the thermal state source was used.

Estimation in the Complementary Exponential Geometric Distribution Based on Progressive Type-II Censored Data

Complementary exponential geometric distribution has many applications in survival and reliability analysis. Due to its importance, in this study, we are aiming to estimate the parameters of this model based on progressive type-II censored observations. To do this, we applied the stochastic expectation maximization method and Newton–Raphson techniques for obtaining the maximum likelihood estimates. We also considered the estimation based on Bayesian method using several approximate: MCMC samples, Lindely approximation and Metropolis–Hasting algorithm. In addition, we considered the shrinkage estimators based on Bayesian and maximum likelihood estimators. Then, the HPD intervals for the parameters are constructed based on the posterior samples from the Metropolis–Hasting algorithm. In the sequel, we obtained the performance of different estimators in terms of biases, estimated risks and Pitman closeness via Monte Carlo simulation study. This paper will be ended up with a real data set example for illustration of our purpose.

Parameter Estimation of Lindley Distribution Based on Progressive Type-II Censored Competing Risks Data with Binomial Removals

The competing risk model based on Lindley distribution is discussed under the progressive type-II censored sample data with binomial removals. The maximum likelihood estimation of the unknown parameters of the distribution is established. Using the Lindley approximation method, we also obtain the Bayesian estimation of the unknown parameters of the distribution under different loss functions. The performance of different estimates is studied in this article. A real practical dataset is analyzed for illustration.

Bayesian Approach of Estimating Shape Parameter of Log Logistic Distribution

In this research, Log logistic distribution under Bayesian paradigm is studied. Posterior distribution has been derived using Uniform and Jeffrey’s’ priors. The three loss functions taken up are squared error loss function (SELF), weighted balanced loss function (WBLF) and precautionary loss function (PLF). The performance of an estimator is assessed on the basis of its relative posterior risk. An extensive simulation was carried out to illustrate the applicability of this research and to compare the performance of different estimators. The study indicated that for estimation of the shape parameter using Bayesian estimation technique, the precautionary loss function can effectively be employed. Keywords : Bayesian estimation, Log logistic distribution, Uniform prior, Jeffrey’s prior, loss functions.

Asymptotic comparison of three spread estimators based on Roll’s model

In this paper we theoretically investigate the statistical properties of three popular bid–ask spread estimators, i.e., the covariance estimator of Roll (1984), the High–Low (HL) estimator based on daily high and low prices developed by Corwin and Schultz (2012) and the Close–High–Low (CHL) estimator recently proposed by Abdi and Ranaldo (2017). The biases and mean squared errors (MSE) of these three estimators have been derived and compared with each other asymptotically, which reveals explicitly the superior performance of HL and CHL estimators over Roll’s estimator. Moreover, if the volatility is relatively small compared to the spread, the performance of the CHL estimator is superior to the HL method. Then the subsequent simulation studies and bootstrap analysis on empirical examples also verify the theoretical results. The comparison method discussed here is different from the existing literature, which usually resorts to the correlation between the bid–ask spread estimators with a benchmark calculated from high-frequency data as they compare the performance of different estimators.

MODELLING SENSITIVE ISSUES ON SUCCESSIVE WAVES

Abstract This paper addresses the problem of estimation of population mean of sensitive character using non-sensitive auxiliary variable at current wave in two wave successive sampling. A general class of estimator is proposed and studied under randomized and scrambled response model. Many existing estimators have been modified to work for sensitive population mean estimation. The modified estimators became the members of proposed general class of estimators. The detail properties of all the estimators have been discussed. Their behaviour under randomized and scrambled response techniques have been elaborated. Numerical illustrations including simulation have been accompanied to judge the performance of different estimators. Finally suitable recommendations are forwarded.

Panel Data Estimation for Correlated Random Coefficients Models

This paper considers methods of estimating a static correlated random coefficient model with panel data. We mainly focus on comparing two approaches of estimating unconditional mean of the coefficients for the correlated random coefficients models, the group mean estimator and the generalized least squares estimator. For the group mean estimator, we show that it achieves Chamberlain (1992) semi-parametric efficiency bound asymptotically. For the generalized least squares estimator, we show that when T is large, a generalized least squares estimator that ignores the correlation between the individual coefficients and regressors is asymptotically equivalent to the group mean estimator. In addition, we give conditions where the standard within estimator of the mean of the coefficients is consistent. Moreover, with additional assumptions on the known correlation pattern, we derive the asymptotic properties of panel least squares estimators. Simulations are used to examine the finite sample performances of different estimators.

Low noise sensitivity analysis of -minimization in oversampled systems

Abstract The class of $\ell _q$-regularized least squares (LQLS) are considered for estimating $\beta \in \mathbb{R}^p$ from its $n$ noisy linear observations $y=X\beta + w$. The performance of these schemes are studied under the high-dimensional asymptotic setting in which the dimension of the signal grows linearly with the number of measurements. In this asymptotic setting, phase transition (PT) diagrams are often used for comparing the performance of different estimators. PT specifies the minimum number of observations required by a certain estimator to recover a structured signal, e.g. a sparse one, from its noiseless linear observations. Although PT analysis is shown to provide useful information for compressed sensing, the fact that it ignores the measurement noise not only limits its applicability in many application areas, but also may lead to misunderstandings. For instance, consider a linear regression problem in which $n>p$ and the signal is not exactly sparse. If the measurement noise is ignored in such systems, regularization techniques, such as LQLS, seem to be irrelevant since even the ordinary least squares (OLS) returns the exact solution. However, it is well known that if $n$ is not much larger than $p$, then the regularization techniques improve the performance of OLS. In response to this limitation of PT analysis, we consider the low-noise sensitivity analysis. We show that this analysis framework (i) reveals the advantage of LQLS over OLS, (ii) captures the difference between different LQLS estimators even when $n>p$, and (iii) provides a fair comparison among different estimators in high signal-to-noise ratios. As an application of this framework, we will show that under mild conditions LASSO outperforms other LQLS even when the signal is dense. Finally, by a simple transformation, we connect our low-noise sensitivity framework to the classical asymptotic regime in which $n/p \rightarrow \infty$, and characterize how and when regularization techniques offer improvements over ordinary least squares, and which regularizer gives the most improvement when the sample size is large.

On the Alpha Power Transformed Power Lindley Distribution

In this paper, we introduce a new generalization of the power Lindley distribution referred to asthe alpha power transformed power Lindley(APTPL). The APTPL model provides a better fit than the power Lindley distribution. It includes the alpha power transformed Lindley, power Lindley, Lindley, and gamma as special submodels. Various properties of the APTPL distribution including moments, incomplete moments, quantiles, entropy, and stochastic ordering are obtained. Maximum likelihood, maximum products of spacings, and ordinary and weighted least squares methods of estimation are utilized to obtain the estimators of the population parameters. Extensive numerical simulation is performed to examine and compare the performance of different estimates. Two important data sets are employed to show how the proposed model works in practice.

Pivotal inference for the inverse Rayleigh distribution based on general progressively Type-II censored samples

ABSTRACTIn this paper, we consider the problem of estimating the scale parameter of the inverse Rayleigh distribution based on general progressively Type-II censored samples and progressively Type-II censored samples. The pivotal quantity method is used to derive the estimator of the scale parameter. Besides, considering that the maximum likelihood estimator is tough to obtain for this distribution, we derive an explicit estimator of the scale parameter by approximating the likelihood equation with Taylor expansion. The interval estimation is also studied based on pivotal inference. Then we conduct Monte Carlo simulations and compare the performance of different estimators. We demonstrate that the pivotal inference is simpler and more effective. The further application of the pivotal quantity method is also discussed theoretically. Finally, two real data sets are analyzed using our methods.

Inference Based on k-Record Values from Generalized Exponential Distribution

In this paper, the lower k-record values arising from a two parameter generalized exponential distribution is considered. The maximum likelihood estimators for the shape parameter and scale parameter are obtained. The Bayes estimates of the parameters are also developed by using Markov chain Monte Carlo method under symmetric and asymmetric loss functions. Finally, a simulation study is performed to find the performance of different estimators developed in this paper.

Parameter Estimation for the Kumaraswamy Distribution Based on Hybrid Censoring

SYNOPTIC ABSTRACTWe consider estimation of unknown parameters of a two-parameter Kumaraswamy distribution with hybrid censored samples. We obtain maximum likelihood estimates using an expectation-maximization algorithm. Bayes estimates are derived under the squared error loss function using different approximation methods. In addition, an importance sampling technique is also discussed. Interval estimation is considered as well. We conduct a simulation study to compare the performance of different estimates, and based on this study, recommendations are made. A real data set and a simulated data set are analyzed for illustration purposes.

Efficient estimation of Pareto model: Some modified percentile estimators.

The article proposes three modified percentile estimators for parameter estimation of the Pareto distribution. These modifications are based on median, geometric mean and expectation of empirical cumulative distribution function of first-order statistic. The proposed modified estimators are compared with traditional percentile estimators through a Monte Carlo simulation for different parameter combinations with varying sample sizes. Performance of different estimators is assessed in terms of total mean square error and total relative deviation. It is determined that modified percentile estimator based on expectation of empirical cumulative distribution function of first-order statistic provides efficient and precise parameter estimates compared to other estimators considered. The simulation results were further confirmed using two real life examples where maximum likelihood and moment estimators were also considered.

A comparison of manual tracing and FreeSurfer for estimating hippocampal volume over the adult lifespan.

MRI has become an indispensable tool for brain volumetric studies, with the hippocampus an important region of interest. Automation of the MRI segmentation process has helped advance the field by facilitating the volumetric analysis of larger cohorts and more studies. FreeSurfer has emerged as the de facto standard tool for these analyses, but studies validating its output are all based on older versions. To characterize FreeSurfer's validity, we compare several versions of FreeSurfer software with traditional hand-tracing. Using MRI images of 262 males and 402 females aged 38 to 84, we directly compare estimates of hippocampal volume from multiple versions of FreeSurfer, its hippocampal subfield routines, and our manual tracing protocol. We then use those estimates to assess asymmetry and atrophy, comparing performance of different estimators with each other and with brain atrophy measures. FreeSurfer consistently reports larger volumes than manual tracing. This difference is smaller in larger hippocampi or older people, with these biases weaker in version 6.0.0 than prior versions. All methods tested agree qualitatively on rightward asymmetry and increasing atrophy in older people. FreeSurfer saves time and money, and approximates the same atrophy measures as manual tracing, but it introduces biases that could require statistical adjustments in some studies.