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In recent years, model averaging, by which estimates are obtained based on not one single model but a weighted ensemble of models, has received growing attention as an alternative to model selection. To-date, methods for model averaging have been developed almost exclusively for point-valued data, despite the fact that interval-valued data are commonplace in many applications and the substantial body of literature on estimation and inference methods for interval-valued data. This paper focuses on the special case of interval time series data, and assumes that the mid-point and log-range of the interval values are modelled by a two-equation vector autoregressive with exogenous covariates (VARX) model. We develop a methodology for combining models of varying lag orders based on a weight choice criterion that minimises an unbiased estimator of the squared error risk of the model average estimator. We prove that this method yields predictors of mid-points and ranges with an optimal asymptotic property. In addition, we develop a method for correcting the range forecasts, taking into account the forecast error variance. An extensive simulation experiment examines the performance of the proposed model averaging method in finite samples. We apply the method to an interval-valued data series on crude oil future prices.

We study estimation of the correlation ρ in the multivariate linear model with uniform correlation structure. Unbiased estimator of ρ based on moment estimator proposed by Žežula (2006) is derived. Biased and unbiased estimators are compared by bias and mean square error under normal and t-distribution.

International audience; Being able to compare risk measures in practice is crucial in many applications such as in finance, insurance or environmental science. The difficulty is that the variables of interest are not always of the same nature, nor of the same type or scale. Thus the usual risk measures are often misleading and to solve this issue we propose to use the Expected Proportional Shortfall (EPS) which is scale invariant and thus, which does not depend on the unit of measurement. To estimate the EPS, an estimator of the tail index γ is required. The main asymptotic properties of our EPS estimator are provided under very general assumptions in case of d−variate β−mixing processes with Pareto-type marginals. Then, we propose a test statistic based on the EPS estimators to compare different risks, whatever their nature/type/scale are. Since the performances of the test statistic are poor when a biased estimate of γ is used, we propose to perform our EPS estimation with an asymptotically unbiased estimator for γ. The efficiency of our test statistic is illustrated in a simulation experiment and validated on an environmental dataset.

In this paper we study estimation of and inference for average treatment effects in a setting with panel data. We focus on the staggered adoption setting where units, e.g, individuals, firms, or states, adopt the policy or treatment of interest at a particular point in time, and then remain exposed to this treatment at all times afterwards. We take a design perspective where we investigate the properties of estimators and procedures given assumptions on the assignment process. We show that under random assignment of the adoption date the standard Difference-In-Differences (DID) estimator is an unbiased estimator of a particular weighted average causal effect. We characterize the exact finite sample properties of this estimand, and show that the standard variance estimator is conservative.

We consider estimation of the inverse scatter matrix Σ − 1 for a scale mixture of Wishart matrices under various Efron–Morris type losses, tr [ { Σ ˆ − 1 − Σ − 1 } 2 S k ] for k = 0 , 1 , 2 . . . , where S is the sample covariance matrix. We improve on the standard estimators a S + , where S + denotes the Moore–Penrose inverse of S and a is a positive constant, through an unbiased estimator of the risk difference between the new estimators and a S + . Thus we demonstrate that improvements over the standard estimators under a Wishart distribution can be extended under mixing. We give a unified treatment of the two cases where S is invertible ( S + = S − 1 ) and where S is singular.

To increase power or reduce the number of patients needed for a parallel groups design, the crossover design has been often used to study treatments for noncurable chronic diseases. However, in the presence of carry-over effect caused by treatments, the commonly-used estimator which ignores the carry-over effect leads to a biased estimator for estimating the treatment effect difference. A two-stage test approach aimed to address carry-over effect proposed was found to be potentially misleading. In this paper, we propose a weighted average of the commonly-used estimator and an unbiased estimator that uses only the first period of the data. We derive an optimal weight that minimizes the mean squared error (MSE) and its modified estimator. We apply Monte Carlo simulation to evaluate the performance of the proposed estimators in a variety of situations. In the simulations, we examine the estimated MSE (EMSE), percentile interval length, and coverage probability calculated from the percentile intervals among considered estimators. Simulation results show that our proposed weighted average estimator and its modified estimator lead to smaller EMSEs on average comparing to the two commonly used estimators. The coverage probabilities using our proposed estimators are reasonably close to the nominal confidence level and the interval lengths are shorter comparing to the use of the unbiased estimator that uses only the first period of the data. We apply an example that was to evaluate the efficacy of two type of bronchodilators for asthma treatment to demonstrate the use of the proposed estimators.

Accurate estimation of the Cosmic Microwave Background (CMB) angular power spectrum is enticing due to the prospect for precision cosmology it presents. Galactic foreground emissions, however, contaminate the CMB signal and need to be subtracted reliably in order to lessen systematic errors on the CMB temperature estimates. Typically bright foregrounds in a region lead to further uncertainty in temperature estimates in the area even after some foreground removal technique is performed and hence determining the underlying full-sky angular power spectrum poses a challenge. We explore the feasibility of utilizing artificial neural networks to predict the angular power spectrum of the full sky CMB temperature maps from the observed angular power spectrum of the partial sky in which CMB temperatures in some bright foreground regions are masked. We present our analysis at large angular scales with two different masks. We produce unbiased predictions of the full-sky angular power spectrum and recover the underlying theoretical power spectrum using neural networks. Our predictions are also uncorrelated to a large extent. We further show that the multipole-space covariances of the predictions of full-sky spectra made by the ANNs are much smaller than those of the estimates obtained using the pseudo-$C_\ell$ method., Comment: 10 pages, 11 figures; altered methodology, added links to references, updated analysis using latest available data, modified the write-up accordingly

With the rise of the semiconductor industry, passive components have become a foundation of the electronics industry and propelled the development of peripheral equipment and industries. This paper focused on improving the lifetime performance of products to increase product value and achieve the green production goals of energy conservation and waste reduction. We first established a relative lifetime performance index for passive component capacitors. Next, we derived the cumulative distribution function and reliability function based on the probability density function of relative lifetime to investigate the properties of the relative lifetime performance index. The results indicated that the reliability increased with the index value and that the probability of the product lifetime exceeding the minimum requirement also increased with the index value. Due to the fact that the index contains unknown parameters, using point estimates to estimate product lifetime performance may lead to misjudgment caused by sampling errors. For this reason, we propose a uniformly minimum-variance unbiased estimator for the index and derived its probability density function. In addition, we establish a fuzzy testing model based on the confidence interval to determine whether the lifetime performance of a product reaches the required performance level. Finally, we present a numerical example of passive components to demonstrate application of the proposed model. This example further demonstrates how the proposed model improves product lifetime performance, which in turn increases product value and also achieves the green objectives of energy conservation and waste reduction.

It is well known that the ordinary least squares (OLS) regression estimator is not robust. Many robust regression estimators have been proposed and inferential methods based on these estimators have been derived. However, for two independent groups, let θj(X) be some conditional measure of location for the jth group, given X, based on some robust regression estimator. An issue that has not been addressed is computing a 1 − α confidence interval for θ1(X) − θ2(X) in a manner that allows both within group and between group hetereoscedasticity. The paper reports the finite sample properties of a simple method for accomplishing this goal. Simulations indicate that, in terms of controlling the probability of a Type I error, the method performs very well for a wide range of situations, even with a relatively small sample size. In principle, any robust regression estimator can be used. The simulations are focused primarily on the Theil–Sen estimator, but some results using Yohai’s MM-estimator, as well as the Koenker and Bassett quantile regression estimator, are noted. Data from the Well Elderly II study, dealing with measures of meaningful activity using the cortisol awakening response as a covariate, are used to illustrate that the choice between an extant method based on a nonparametric regression estimator, and the method suggested here, can make a practical difference.

In this paper, we develop unbiased estimators of the finite population cumulative distribution function (CDF) using two-stage and three-stage cluster sampling. In addition, the ranked-set sampling ...

Many two-level nested simulation applications involve the conditional expectation of some response variable, where the expected response is the quantity of interest, and the expectation is with respect to the inner-level random variables, conditioned on the outer-level random variables. The latter typically represent random risk factors, and risk can be quantified by estimating the probability density function (pdf) or cumulative distribution function (cdf) of the conditional expectation. Much prior work has considered a naïve estimator that uses the empirical distribution of the sample averages across the inner-level replicates. This results in a biased estimator, because the distribution of the sample averages is over-dispersed relative to the distribution of the conditional expectation when the number of inner-level replicates is finite. Whereas most prior work has focused on allocating the numbers of outer- and inner-level replicates to balance the bias/variance tradeoff, we develop a bias-corrected pdf estimator. Our approach is based on the concept of density deconvolution, which is widely used to estimate densities with noisy observations but has not previously been considered for nested simulation problems. For a fixed computational budget, the bias-corrected deconvolution estimator allows more outer-level and fewer inner-level replicates to be used, which substantially improves the efficiency of the nested simulation.

In recent literature, a new class of unbiased Monte Carlo estimators have been proposed, which is based on truncating a telescopic representation of the expectation of a functional of the stochastic process at an independent random level. The generality of the method lies in that it can translate any sequence of asymptotically unbiased estimators into a truly unbiased estimator. However, since any independent truncation level can lead to an unbiased estimator, its optimal choice is crucial for the successful implementation of this unbiased Monte Carlo method in financial engineering applications. We develop a novel efficient algorithm to locate the optimal distribution of the random truncation level in general, which answers positively an open question posted in Rhee and Glynn (2015), and we rigorously establish the convergence and optimality of the algorithm and derive its exact complexity. Our algorithm has a much lower complexity as compared to the literature, and numerical examples confirm our findings. The proposed algorithm is shown to be also applicable to optimization problems arising in contextual areas of supply chain management.

Graphlets are induced subgraph patterns that are crucial to the understanding of the structure and function of a large network. A lot of effort has been devoted to calculating graphlet statistics where random walk-based approaches are commonly used to access restricted graphs through the available application programming interfaces (APIs). However, most of them merely consider individual networks while overlooking the strong coupling between different networks. In this article, we estimate the graphlet concentration in multiplex networks with real-world applications. An inter-layer edge connects two nodes in different layers if they actually belong to the same node. The access to a multiplex network is restrictive in the sense that the upper layer allows random walk sampling, whereas the nodes of lower layers can be accessed only through the inter-layer edges and only support random node or edge sampling. To cope with this new challenge, we define a suit of two-layer graphlets and propose novel random walk sampling algorithms to estimate the proportion of all the three-node graphlets. An analytical bound on the sampling steps is proved to guarantee the convergence of our unbiased estimator. We further generalize our algorithm to explore the tradeoff between the estimated accuracy of different graphlets when the sample budget is split into different layers. Experimental evaluation on real-world and synthetic multiplex networks demonstrates the accuracy and high efficiency of our unbiased estimators.

In this paper, inference upon stress-strength reliability is considered for unit-Weibull distributions with a common parameter under the assumption that data are observed using progressive type II censoring. We obtain di_erent estimators of system reliability using classical and Bayesian procedures. Asymptotic interval is constructed based on Fisher information matrix. Besides, boot-p and boot-t intervals are also obtained. We evaluate Bayes estimates using Lindley's technique and Metropolis-Hastings (MH) algorithm. The Bayes credible interval is evaluated using MH method. An unbiased estimator of this parametric function is also obtained under know common parameter case. Numerical simulations are performed to compare estimation methods. Finally, a data set is studied for illustration purposes.

Spatial predictions, like other supervised learning tasks, require some criterion for a predictor’s quality. Typical data-splitting schemes, such as holdouts and $k$ -fold cross-validation, ignore the fact that the training data are usually not available where predictions are being made. The common data-splitting schemes are thus biased estimates of a predictor’s performance, which in turn may lead to choosing suboptimal predictors. In this contribution, we borrow ideas from the domain adaptation machine-learning literature, to suggest the importance-weighted source risk (IWSR). IWSR is a principled approach for weighting the prediction risk, which allows the practitioner to explicitly state the target locations for prediction. IWSR essentially consists of down-weighting training locations and up-weighting target locations. We show that, unlike the usual (unweighted) empirical risk, IWSR is an unbiased estimator of the prediction error. Equipped with this risk estimator, we use it to learn a model in the empirical risk minimization framework and to evaluate the existing predictors. We show the superiority of this weighted risk, using both simulated data and an empirical control: air-temperature prediction in France.

In the logistic regression model, the variance of the maximum likelihood estimator is inflated and unstable when the multicollinearity exists in the data. There are several methods available in literature to overcome this problem. We propose a new stochastic restricted biased estimator. We study the statistical properties of the proposed estimator and compare its performance with some existing estimators in the sense of scalar mean squared criterion. An example and a simulation study are provided to illustrate the performance of the proposed estimator.

Akaike’s Bayesian information criterion (ABIC) has been widely used in inverse ill-posed problems. Little has been done to investigate its statistical aspects. We present an alternative derivation of the marginal distribution of measurements for ABIC under the assumption of normal distributions and show that the principle of ABIC is to statistically estimate the variances of measurements and prior data by maximizing the marginal distribution of measurements. The determination of the regularization parameter with ABIC is essentially equivalent to estimating the relative weighting between measurements and prior data. We prove that ABIC theoretically would produce a biased estimate of the variance of measurements. Since the prior mean is generally unknown but arbitrarily treated as zero in inverse ill-posed problems, ABIC is shown to fail to produce any reasonable estimate for the prior variance. Although ABIC is constructed under the Bayesian framework, it essentially plays more or less the same role as biased regularization from the frequentist’s point of view. ABIC error evaluation cannot be performed under the Bayesian framework but should be more appropriately done with the frequentist’s standpoint in terms of mean squared errors. ABIC is sensitive to prior distributions. In the case of non-informative prior distribution, ABIC leads to the conventional weighted least squares (LS) estimate of parameters and cannot be used to solve inverse ill-posed problems. It is not linked to the regularization parameter but only straightforwardly produces an unbiased estimator for the noise level of measurements, which is only applicable numerically for well-posed problems but not for inverse ill-posed problems. Numerical simulated examples are used to demonstrate the statistical performances of ABIC.

In this letter, target localization from range measurements corrupted by both additive and multiplicative noises is studied. First, the maximum likelihood estimator (MLE) is proposed. Then, the novel expectation maximization (EM) algorithm with guaranteed convergence is proposed to find the MLE. It is shown that the expectation step can be calculated componentwisely, and the maximization step can be solved via the Majorization-Minimization (MM) approach. The algorithm is termed as R-EM-MM. To provide a benchmark performance of R-EM-MM, the theoretical performance of unbiased estimator, i.e., Cramer Rao bound (CRB) is derived. In addition, the enhanced R-EM-MM (E-R-EM-MM) is proposed to jointly learn the noise statistics and perform target localization. Finally, numerical simulations are conducted to demonstrate the near optimal performance, compared with CRB and other state-of-art method.

Different methods have been suggested for calculating “exact” confidence intervals for a standardized mean difference using the noncentral t distributions. Two methods are provided in Hedges and Olkin (1985, “H”) and Steiger and Fouladi (1997, “S”). Either method can be used with a biased estimator, d, or an unbiased estimator, g, of the population standardized mean difference (methods abbreviated Hd, Hg, Sd, and Sg). Coverages of each method were calculated from theory and estimated from simulations. Average coverages of 95% confidence intervals across a wide range of effect sizes and across sample sizes from 5 to 89 per group were always between 85 and 98% for all methods, and all were between 94 and 96% with sample sizes greater than 40 per group. The best interval estimation was the Sd method, which always produced confidence intervals close to 95% at all effect sizes and sample sizes. The next best was the Hg method, which produced consistent coverages across all effect sizes, although coverage was reduced to 93–94% at sample sizes in the range 5–15. The Hd method was worse with small sample sizes, yielding coverages as low as 86% at n = 5. The Sg method produced widely different coverages as a function of effect size when the sample size was small (93–97%). Researchers using small sample sizes are advised to use either the Steiger & Fouladi method with d or the Hedges & Olkin method with g as an interval estimation method.

Ranked set sampling (RSS) is a method of sampling that can be advantageous when quantification of all sampling units is costly but when small sets of units can be ranked according to the character ...

In this paper, a study of the day-ahead unit commitment problem with stochastic wind power generation is presented, which considers conditional, and correlated wind power forecast errors through a distributionally robust optimization approach. Firstly, to capture the characteristics of random wind power forecast errors, the least absolute shrinkage, and selection operator (Lasso) is utilized to develop a robust conditional error estimator, while an unbiased estimator is used to obtain the covariance matrix. The conditional error, and the covariance matrix are then used to construct an enhanced ambiguity set. Secondly, we develop an equivalent mixed integer semidefinite programming (MISDP) formulation of the two-stage distributionally robust unit commitment model with a polyhedral support of random variables. Further, to efficiently solve this problem, a novel cutting plane algorithm that makes use of the extremal distributions identified from the second-stage semidefinite programming (SDP) problems is introduced. Finally, numerical case studies show the advantage of the proposed model in capturing the spatiotemporal correlation in wind power generation, as well as the economic efficiency, and robustness of dispatch decisions.

A randomly truncated sample appears when the independent variables T and L are observable if L ＜ T. The truncated version Kaplan-Meier estimator is known to be the standard estimation method for the marginal distribution of T or L. The inverse probability weighted (IPW) estimator was suggested as an alternative and its agreement to the truncated version Kaplan-Meier estimator has been proved. This paper centers on the weak convergence of IPW estimators and variance decomposition. The paper shows that the asymptotic variance of an IPW estimator can be decomposed into two sources. The variation for the IPW estimator using known weight functions is the primary source, and the variation due to estimated weights should be included as well. Variance decomposition establishes the connection between a truncated sample and a biased sample with know probabilities of selection. A simulation study was conducted to investigate the practical performance of the proposed variance estimators, as well as the relative magnitude of two sources of variation for various truncation rates. A blood transfusion data set is analyzed to illustrate the nonparametric inference discussed in the paper.

An important parameter describing the state of capital markets, investment opportunity sets, and asset pricing is the unobservable market risk price. The estimated risk price depends upon the selected asset set, the number of assets, the investment horizon, and the sample period. We document the large theoretical and empirical probability of an unacceptably negative sample estimate for the unbiased estimator of the squared risk price. We address admissibility and dominance under quadratic loss of alternative estimators, concluding that an optimized shrinkage estimator has the smallest expected quadratic loss compared with our alternative estimators. Using market data, we examine estimates for more inclusive investment opportunity sets and provide upper bounded estimates of the risk price and resultant unique Sharpe measure, to complement the existing literature’s Sharpe measure bounds and equity premium estimates. Finally, we examine time series properties, behavior in the business cycle, and relation to some recently advocated economic factors.

Debate on the use of lagged dependent variables has a long history in political science. The latest contribution to this discussion is Wilkins (2018, Political Science Research and Methods, 6, 393–411), which advocates the use of an ADL(2,1) model when there is serial dependence in the outcome and disturbance. While this specification does offer some insurance against serially correlated disturbances, this is never the best (linear unbiased estimator) approach and should not be pursued as a general strategy. First, this strategy is only appropriate when the data-generating process (DGP) actually implies a more parsimonious model. Second, when this is not the DGP—e.g., lags of the predictors have independent effects—this strategy mischaracterizes the dynamic process. We clarify this issue and detail a Wald test that can be used to evaluate the appropriateness of the Wilkins approach. In general, we argue that researchers need to always: (i) ensure models are dynamically complete and (ii) test whether more restrictive models are appropriate.

We use the jackknife to bias correct the log-periodogram regression(LPR) estimator of the fractional parameter in a stationary fractionally integrated model. The weights for the jackknife estimator are chosen in such a way that bias reduction is achieved without the usual increase in asymptotic variance, with the estimator viewed as `optimal' in this sense. The theoretical results are valid under both the non-overlapping and moving-block sub-sampling schemes that can be used in the jackknife technique, and do not require the assumption of Gaussianity for the data generating process. A Monte Carlo study explores the finite sample performance of different versions of the jackknife estimator, under a variety of scenarios. The simulation experiments reveal that when the weights are constructed using the parameter values of the true data generating process, a version of the optimal jackknife estimator almost always out-performs alternative semi-parametric bias-corrected estimators. A feasible version of the jackknife estimator, in which the weights are constructed using estimates of the unknown parameters, whilst not dominant overall, is still the least biased estimator in some cases. Even when misspecified short run dynamics are assumed in the construction of the weights, the feasible jackknife still shows significant reduction in bias under certain designs. As is not surprising, parametric maximum likelihood estimation out-performs all semi-parametric methods when the true values of the short memory parameters are known, but is dominated by the semi-parametric methods (in terms of bias) when the short memory parameters need to be estimated, and in particular when the model is misspecified., Comment: 57 pages

In the small area estimation, the empirical best linear unbiased predictor (EBLUP) in the linear mixed model is useful because it gives a stable estimate for a mean of a small area. For measuring uncertainty of EBLUP, much of research is focused on second-order unbiased estimation of mean squared prediction errors in the univariate case. In this paper, we consider the multivariate Fay–Herriot model where the covariance matrix of random effects is fully unknown, and obtain a confidence region of the small area mean that is based on the Mahalanobis distance centered around EBLUP and has second-order correction. A positive-definite, consistent and second-order unbiased estimator of the covariance matrix of the random effects is also suggested. The performance is investigated through simulation study.

Average precision (AP) and many other related evaluation indices have been employed ubiquitously in classification tasks for a long time. However, they have defects and can hardly provide both overall evaluations and individual evaluations. In practice, we have to strike a balance between whole and individual performances to satisfy diverse demands. To this end, we propose a new index for multiclass classification tasks, named ${R^{\prime }}$ , which is an unbiased estimator of AP. Specifically, we improve the R index by taking the numerical differences between the real labels and predicted labels of each class into consideration. We evaluate its effectiveness and robustness on the MNIST and CIFAR-10 datasets. Experimental results show that it is positively correlated with some related indices. More importantly, we can obtain both overall and individual evaluations, which can be beneficial for improving training processes and model selection. Furthermore, as an evaluation architecture, the index can be promoted to evaluate any classification task, thereby implying broad application prospects.

Background In infectious disease transmission dynamics, the high heterogeneity in individual infectiousness indicates that few index cases generate large numbers of secondary cases, which is commonly known as superspreading events. The heterogeneity in transmission can be measured by describing the distribution of the number of secondary cases as a negative binomial (NB) distribution with dispersion parameter, k. However, such inference framework usually neglects the under-ascertainment of sporadic cases, which are those without known epidemiological link and considered as independent clusters of size one, and this may potentially bias the estimates. Methods In this study, we adopt a zero-truncated likelihood-based framework to estimate k. We evaluate the estimation performance by using stochastic simulations, and compare it with the baseline non-truncated version. We exemplify the analytical framework with three contact tracing datasets of COVID-19. Results We demonstrate that the estimation bias exists when the under-ascertainment of index cases with 0 secondary case occurs, and the zero-truncated inference overcomes this problem and yields a less biased estimator of k. We find that the k of COVID-19 is inferred at 0.32 (95%CI: 0.15, 0.64), which appears slightly smaller than many previous estimates. We provide the simulation codes applying the inference framework in this study. Conclusions The zero-truncated framework is recommended for less biased transmission heterogeneity estimates. These findings highlight the importance of individual-specific case management strategies to mitigate COVID-19 pandemic by lowering the transmission risks of potential super-spreaders with priority.

In the last two decades, doubly robust estimators (DREs) have been developed for causal inference on various target parameters derived from different study designs. The approach combines propensity score and outcome models of the confounding variables. It yields unbiased estimator of the target parameter if at least one of the two models is correctly specified, a desirable property and an improvement on the inverse propensity score weighted estimate. However, in practice it is difficult to know what the correct model could be and both propensity score and outcome models may be incorrectly specified. Furthermore, it is known that DRE may fail and give estimates with large bias and variance, even when the propensity and/or outcome models are mildly misspecified. To reduce such risk and increase robustness in inference, we propose an enhanced DRE method utilizing semiparametric models with nonparametric monotone link functions for both the propensity score and the outcome models. The models are estimated using an iterative procedure incorporating the pool adjacent violators algorithm. We then study the asymptotic properties of the enhanced DREs. Simulation studies, performed to evaluate their finite sample performance, demonstrated clear superiority to several commonly used doubly robust procedures with reduced bias and increased efficiency even with both models are misspecified, thus enhancing the robustness of DRE. The method is then applied to analyzing a clinical trial from the AIDS Clinical Trials Group and the National Epidemiology Follow-up Study.

The ratio, product, difference estimators, and unbiased estimator under systematic sampling scheme has been studied in the presence of measurement error. The methods of estimation have been propose...

Our purpose is twofold: to present a prototypical example of the conditioning technique to obtain the best estimator of a parameter and to show that this technique resides in the structure of an inner product space. The technique uses conditioning of an unbiased estimator on a sufficient statistic. This procedure is founded upon the conditional variance formula, which leads to an inner product space and a geometric interpretation. The example clearly illustrates the dependence on the sampling methodology. These advantages show the power and centrality of this process.

PurposeThis study aims to focus on proposing a new memory-type chart called progressive mean exponentially weighted moving average (PMEWMA) control chart. This memory-type chart is an improvement on the existing progressive mean control chart, to detect small and moderate shifts in a process.Design/methodology/approachThe PMEWMA control chart is developed by using a cumulative average of the exponentially weighted moving average scheme known as the progressive approach. This scheme is designed based on the assumption that data follow a normal distribution. In addition, the authors investigate the robustness of the proposed chart to the normality assumption.FindingsThe variance and the mean of the scheme are computed, and the mean is found to be an unbiased estimator of the population mean. The proposed chart's performance is compared with the existing charts in the literature by using the average run-length as the performance measure. Application examples from the petroleum and bottling industry are also presented for practical considerations. The comparison shows that the PMEWMA chart is quicker in detecting small shifts in the process than the other memory-type charts covered in this study. The authors also notice that the PMEWMA chart is affected by higher kurtosis and skewness.Originality/valueA new memory-type scheme is developed in this research, which is efficient in detecting small and medium shifts of a process mean.

U -statistics enjoy good properties such as asymptotic normality, unbiasedness and minimal variance among unbiased estimators. The estimation of their variance is often of interest, for instance to derive asymptotic tests. It is well-known that an unbiased estimator of the variance of a U -statistic can be formulated explicitly as a U -statistic itself, but specific dependencies on the sample size make asymptotic statements difficult. Here, we solve the issue by decomposing the variance estimator into a linear combination of U -statistics with fixed kernel size, consequently obtaining a straightforward statement on the asymptotic distribution. We subsequently demonstrate a central limit theorem for the studentized estimator. We show that it leads to a hypothesis test which compares the error estimates of two prediction algorithms and permits construction of an asymptotically exact confidence interval for the true difference of errors. The test is illustrated by a real data application and a simulation study.

A measure of interrater absolute agreement for ordinal scales is proposed capitalizing on the dispersion index for ordinal variables proposed by Giuseppe Leti. The procedure allows to overcome the limits affecting traditional measures of interrater agreement in different fields of application. An unbiased estimator of the proposed measure is introduced and its sampling properties are investigated. In order to construct confidence intervals for interrater absolute agreement both asymptotic results and bootstrapping methods are used and their performance is evaluated. Simulated data are employed to demonstrate the accuracy and practical utility of the new procedure for assessing agreement. Finally, an application to a real case is provided.

Distinguishing substantively meaningful spillover effects from correlated residuals is of great importance in cross-sectional studies. Both forms of spatial dependence not only hold different implications for the choice of an unbiased estimator but also for the validity of inferences. To guide model specification, different empirical strategies involve the estimation of an unrestricted spatial Durbin model and subsequently use the Wald test to scrutinize the nonlinear restriction of common factors implied by pure error dependence. However, the Wald test’s sensitivity to algebraically equivalent formulations of the null hypothesis receives scant attention in the context of cross-sectional analyses. This article shows analytically that the noninvariance of the Wald test to such reparameterizations stems from the application of a Taylor series expansion to approximate the restriction’s sampling distribution. While asymptotically valid, Monte Carlo simulations reveal that alternative formulations of the common factor restriction frequently produce conflicting conclusions in finite samples. An empirical example illustrates the substantive implications of this problem. Consequently, researchers should either base inferences on bootstrap critical values for the Wald statistic or use the likelihood ratio test which is invariant to such reparameterizations when deciding on the model specification that adequately reflects the spatial process generating the data.

In this article, we propose a simple estimator of cross-covariance matrices for a multi-variate time series with an unknown mean based on a linear combination of the circular sample cross-covariance estimator. Our estimator is exactly unbiased when the data generating process follows a vector moving average (VMA) model with an order less than one half of the sampling period, and is nearly unbiased if such VMA model can approximate the data generating process well. In addition, our estimator is shown to be asymptotically equivalent to the conventional sample cross-covariance estimator. Via simulation, we show that the proposed estimator can to a large extent eliminate the finite sample bias of cross-covariance estimates, while not necessarily increase the mean squared error.

In a multiple linear regression model, the ordinary least squares estimator is inefficient when the multicollinearity problem exists. Many authors have proposed different estimators to overcome the multicollinearity problem for linear regression models. This paper introduces a new regression estimator, called the Dawoud&ndash, Kibria estimator, as an alternative to the ordinary least squares estimator. Theory and simulation results show that this estimator performs better than other regression estimators under some conditions, according to the mean squares error criterion. The real-life datasets are used to illustrate the findings of the paper.

In this work, we consider the deterministic optimization using random projections as a statistical estimation problem, where the squared distance between the predictions from the estimator and the true solution is the error metric. In approximately solving a large scale least squares problem using Gaussian sketches, we show that the sketched solution has a conditional Gaussian distribution with the true solution as its mean. Firstly, tight worst case error lower bounds with explicit constants are derived for any estimator using the Gaussian sketch, and the classical sketching is shown to be the optimal unbiased estimator. For biased estimators, the lower bound also incorporates prior knowledge about the true solution. Secondly, we use the James-Stein estimator to derive an improved estimator for the least squares solution using the Gaussian sketch. An upper bound on the expected error of this estimator is derived, which is smaller than the error of the classical Gaussian sketch solution for any given data. The upper and lower bounds match when the SNR of the true solution is known to be small and the data matrix is well conditioned. Empirically, this estimator achieves smaller error on simulated and real datasets, and works for other common sketching methods as well., Comment: This work has been submitted to the IEEE Journal on Selected Areas in Information Theory (JSAIT) - Special Issue on Estimation and Inference, and is awaiting review. This document contains 37 pages and 14 figures

Estimation under equality restrictions is an age old problem and has been considered by several researchers in the past due to practical applications and theoretical challenges involved in it. Part...

This study develops a nearly unbiased estimator of the ratio of the contemporary effective mother size to the census size in a population, as a proxy of the ratio of contemporary effective size (or effective breeding size) to census size (Ne/N or Nb/N). The proposed estimator is based on both known mother–offspring (MO) and maternal‐sibling (MS) relationships observed within the same cohort, in which sampled individuals in the cohort probably share MO relationships with sampled mothers. The rationale is that the frequency of MO and MS pairs contains information regarding the contemporary effective mother size and the (mature) census size, respectively. Therefore, the estimator can be obtained only from genetic data. We also evaluate the performance of the estimator by running an individual‐based model. The results of this study provide the following: (a) parameter range for satisfying the unbiasedness, and (b) guidance for sample sizes to ensure the required accuracy and precision, especially when the order of the ratio is available. Furthermore, the results demonstrate the usefulness of a sibship assignment method for genetic monitoring, providing insights for interpreting environmental and/or anthropological factors fluctuating Ne/N (or Nb/N), especially in the context of conservation biology and wildlife management., We developed a nearly unbiased estimator of the ratio of the contemporary effective mother size to the census size in a population, as a proxy of Ne/N. The proposed estimator is based on a known mother–offspring (MO) relationship and on a known maternal‐sibling (MS) relationship found within the same cohort, in which sampled individuals in the cohort potentially share MO relationships with sampled mothers.

This article addresses the problem of fast and accurate chirp signal parameter estimation in fractional Fourier domains. By employing a perturbation analysis, it is shown that the fractional Fourier transform can be used as an effective tool to yield an asymptotically minimum-variance unbiased estimator of the chirp parameters. Furthermore, it is shown that the asymptotic performance of the fractional-Fourier-transform-based chirp-rate estimator depends only on the actual chirp rate, not the initial frequency. Consequently, the chirp-rate estimation can be done in only one-dimensional search space, which greatly reduces the computational cost. In order to validate theoretical outcomes, we propose a fast and powerful method for the estimation of chirp rates in the fractional Fourier domains based on the golden section search. Extensive computer simulations confirm the theoretical results by demonstrating that the estimation performance of the chirp rate achieves the Cramer–Rao lower bound for both single- and multicomponent chirps. Consequently, we assert that the proposed method of chirp parameter estimation in the fractional Fourier domains is the minimum-variance unbiased estimator, requiring minimal computational cost.

We consider estimating an expected infinite-horizon cumulative discounted cost/reward contingent on an underlying stochastic process by Monte Carlo simulation. An unbiased estimator based on truncating the cumulative cost at a random horizon is proposed. Explicit forms for the optimal distributions of the random horizon are given, and explicit expressions for the optimal random truncation level are obtained, leading to a full analysis of the bias-variance tradeoff when comparing this new class of randomized estimators with traditional fixed truncation estimators. Moreover, we characterize when the optimal randomized estimator is preferred over a fixed truncation estimator by considering the tradeoff between bias and variance. This comparison provides guidance on when to choose randomized estimators over fixed truncation estimators in practice. Numerical experiments substantiate the theoretical results.

Summary In this paper, we develop a model averaging method to estimate a high-dimensional covariance matrix, where the candidate models are constructed by different orders of polynomial functions. We propose a Mallows-type model averaging criterion and select the weights by minimizing this criterion, which is an unbiased estimator of the expected in-sample squared error plus a constant. Then, we prove the asymptotic optimality of the resulting model average covariance estimators. Finally, we conduct numerical simulations and a case study on Chinese airport network structure data to demonstrate the usefulness of the proposed approaches.

In the astronomical speckle interferometry, low-light CCD cameras such as the electron bombarded/multiplying CCDs (EB/EMCCDs) are being widely used for taking the faint speckle images. The detector noise affects the power spectral estimate of the astronomical object as well as the speckle noise does. The estimation errors of the object power spectrum are results of the propagation of the random fluctuations due to those noises. We have formulated a method for correcting and evaluating the estimation errors based on our detection model developed for EB/EMCCDs and the conventional model of the speckle noise. In our method, the error correction and evaluation are accomplished with the aid of the auxiliary data known as the dark and flat frames. The unbiased estimator of the object power spectrum and its SNR evaluator as derived above are verified using simulated data, where we have adopted the values of the detector parameters as obtained by measuring the actually used EMCCD camera in our observations. The results of the simulated experiments show that, within the diffraction cutoff frequency, our power spectral estimator is unbiased, and our SNR evaluator for that is useful except below the seeing cutoff.

One eminent disadvantage of many existing optimal estimators/class of estimators is that they are typically biased. In this article, we proposed an optimum class of unbiased estimators for estimating the population mean under simple random sampling without replacement (SRSWOR) scheme. Proposed class is a blend of three concepts: 1) information on auxiliary variable, 2) the ranks of auxiliary variable and 3) Hartley-Ross type unbiased estimation procedure. Expressions for the bias and the minimum variance of the new class are derived up to first degree of approximation. To highlight the application of proposed class, five real data sets are used. Numerical findings confirm that the new class behaves efficiently as compared to traditional unbiased estimator and other almost unbiased estimators under study. In addition, Monte Carlo simulation study is conducted through two real populations to assess the performance of proposed class against competitors. On the basis of theoretical and numerical findings, it is concluded that new proposed class can generate optimum unbiased estimators under SRSWOR scheme. Therefore, use of proposed class is recommended for future applications.

We consider hypothesis testing for high-dimensional covariance structures in which the covariance matrix is a (i) scaled identity matrix, (ii) diagonal matrix, or (iii) intraclass covariance matrix. Our purpose is to systematically establish a nonparametric approach for testing the high-dimensional covariance structures (i)–(iii). We produce a new common test statistic for each covariance structure and show that the test statistic is an unbiased estimator of its corresponding test parameter. We prove that the test statistic establishes the asymptotic normality. We propose a new test procedure for (i)–(iii) and evaluate its asymptotic size and power theoretically when both the dimension and sample size increase. We investigate the performance of the proposed test procedure in simulations. As an application of testing the covariance structures, we give a test procedure to identify an eigenvector. Finally, we demonstrate the proposed test procedure by using a microarray data set.