Search

We propose a new estimation procedure of the conditional density for independent and identically distributed data. Our procedure aims at using the data to select a function among arbitrary (at most countable) collections of candidates. By using a deterministic Hellinger distance as loss, we prove that the selected function satisfies a non-asymptotic oracle type inequality under minimal assumptions on the statistical setting. We derive an adaptive piecewise constant estimator on a random partition that achieves the expected rate of convergence over (possibly inhomogeneous and anisotropic) Besov spaces of small regularity. Moreover, we show that this oracle inequality may lead to a general model selection theorem under very mild assumptions on the statistical setting. This theorem guarantees the existence of estimators possessing nice statistical properties under various assumptions on the conditional density (such as smoothness or structural ones). [ABSTRACT FROM AUTHOR]

The strong diagnosability and conditional diagnosability are both novel concepts for measuring the reliability and fault tolerance of multicomputers. The optical multi-mesh hypercube (OMMH) networks, which integrate satisfactory features of both hypercubes and meshes and circumvent the lack of scalability of hypercubes and the large diameter of meshes, are promising optical interconnection topologies. For-OMMH networks, this study shows that the strong diagnosability is, and the conditional diagnosability isif either (a), or (b)and. [ABSTRACT FROM AUTHOR]

This article analyzes the effect of the expected closeness on turnout for 56 direct-democratic votes held in Switzerland between 2012 and 2015. It is the first study to measure the expected closeness by using data obtained from prediction markets. It clarifies empirically the relation between the expected closeness and the levels of turnout in direct democratic votes showing that the expected closeness of the result exerts a positive effect on participation levels. [ABSTRACT FROM AUTHOR]

In this paper we analyze Murakami's family of fifth order methods for the solution of nonlinear equations. We show how to find the best performer by using a measure of closeness of the extraneous fixed points to the imaginary axis. We demonstrate the performance of these members as compared to the two members originally suggested by Murakami. We found several members for which the extraneous fixed points are on the imaginary axis, only one of these has 6 such points (compared to 8 for the other members). We show that this member is the best performer. [ABSTRACT FROM AUTHOR]

Cognitive radio combined with multiple-input multiple-output (MIMO) communications provides high data rate, efficiency and high reliability. One of the most important challenges in MIMO communication is combating MIMO multipath channel. MIMO blind equalizers and channel estimators combat MIMO multipath channels without the use of training or pilot sequences. First, the multipath channel is converted into instantaneous mixture channel (IMC), using second-order statistics of the data. Then using higher-order statistics, these mixtures are separated. However, proper selection of IMC is a major challenge. In this paper, a novel blind algorithm for choosing the best IMC is proposed. The proposed algorithm is based on the cumulant value of the received signal. [ABSTRACT FROM AUTHOR]

Recently, estimators have been developed to estimate occupancy probabilities when false-positive detections occur during presence-absence surveys. Some of these estimators combine different types of survey data to improve estimates of occupancy. With these estimators, there is a trade-off between the number of sample units surveyed, and the number and type of surveys at each sample unit. Guidance on efficient design of studies when false positives occur is unavailable., For a range of scenarios, I identified survey designs that minimized the mean square error of the estimate of occupancy. I considered an approach that uses one survey method and two observation states and an approach that uses two survey methods. For each approach, I used numerical methods to identify optimal survey designs when model assumptions were met and parameter values were correctly anticipated, when parameter values were not correctly anticipated and when the assumption of no unmodelled detection heterogeneity was violated., Under the approach with two observation states, false-positive detections increased the number of recommended surveys, relative to standard occupancy models. If parameter values could not be anticipated, pessimism about detection probabilities avoided poor designs. Detection heterogeneity could require more or fewer repeat surveys, depending on parameter values. If model assumptions were met, the approach with two survey methods was inefficient. However, with poor anticipation of parameter values, with detection heterogeneity or with removal sampling schemes, combining two survey methods could improve estimates of occupancy., Ignoring false positives can yield biased parameter estimates, yet false positives greatly complicate the design of occupancy studies. Specific guidance for major types of false-positive occupancy models, and for two assumption violations common in field data, can conserve survey resources. This guidance can be used to design efficient monitoring programmes and studies of species occurrence, species distribution or habitat selection, when false positives occur during surveys. [ABSTRACT FROM AUTHOR]

Weapon systems accuracy is a vitally important tactical and technical index, which has a significant impact on the process of the weapon systems design and test. Based on different accuracy criteria, we proposed a new evaluation method for the weapon systems accuracy. First, a new bootstrap method, using the correlation coefficient criterion, is presented to evaluate a weapon systems accuracy when the sample size n satisfied n ≥ 10 . Second, measures for weapon systems accuracy are introduced to represent the different performance of weapon systems. Furthermore, an attributes matrix is proposed to combine the above measures. Third, inspired by the Pitman's closeness measure, we designed a weapon systems accuracy attributes competition matrix to contain the entire pairwise competition results, and then its positive eigenvector is employed to the weapon systems accuracy evaluation. Finally, a numerical example is provided to illustrate the effectiveness and feasibility of the proposed method. It is shown that the new evaluation method can not only evaluate the weapon systems accuracy before and after improvement, but also rank the accuracy of the designed weapon systems to the evaluated weapon systems. [ABSTRACT FROM AUTHOR]

Pitman’s Closeness Measure plays an important role in multiple-attribute estimation ranking. However, its non-transitivity problem brings inconvenience for multiple-attribute estimation ranking. Therefore, the multiple-attribute competition measure matrix was proposed to solve the problem of non-transitivity. Unfortunately, the multiple-attribute competition measure matrix only reflect that one estimator is better or worse that the other estimator. Nevertheless, in multiple-attribute estimation ranking, one may cares not only better or worse but also how much better or worse. To avoid the above drawback, the error spectrum is applied to represent more attributes of an estimator in that it is an aggregation of many incomprehensive measures. Then, the area error spectrum is proposed to calculate how much better or worse one estimator beats the other. And the range error spectrum is presented to solve the indistinguishable problem of the area error spectrum when one estimator’s area error spectrum equals to the other estimator’s. Furthermore, the estimation attribute matrix is designed to utilize the above proposed measures. Finally, the above two information is considered in the multiple-attribute competition measure matrix according to the estimation attribute matrix. [ABSTRACT FROM AUTHOR]

Consider a two-sampling scheme in which an initial sample is first taken from the underlying population and then by assuming a suitable restriction on this sample, some more data points are observed as a new restricted sample. This sampling scheme is used to do inference about the lower quantiles of the underlying distribution. The results are compared with those of simple random sampling in view of mean squared error and Pitman’s measure of closeness criteria for exponential and uniform distributions. It will be shown that the proposed sampling scheme would improve the performance of the point estimators of the lower quantiles of the population. [ABSTRACT FROM PUBLISHER]

In this article, we consider a sampling scheme in record-breaking data set-up, asrecord ranked set sampling. We compare the proposed sampling with the well-known sampling scheme in record values known as inverse sampling scheme when the underlying distribution follows the proportional hazard rate model. Various point estimators are obtained in each sampling schemes and compared with respect to mean squared error and Pitman measure of closeness criteria. It is observed in most of the situations that the new sampling scheme provides more efficient estimators than their counterparts. Finally, one data set has been analyzed for illustrative purposes. [ABSTRACT FROM PUBLISHER]

We develop an estimation procedure for a discrete probability mass function (pmf) with unknown support. We derive its maximum likelihood estimator under the mild and natural shape-constraint of unimodality. Shape-constrained estimation is a powerful and robust technique that additionally provides smoothing of the empirical distribution yielding gains in efficiency. We show that our unimodal estimator is consistent when the model is specified, and that it converges to the best projection of the true pmf on the unimodal class under model misspecification. We derive the limiting distribution of the the estimator, and use this to build asymptotic confidence bands for the unknown pmf when the latter is unimodal. We illustrate our approach using time-to-onset data of the Ebola virus during the 1976 outbreak in the former republic of Zaire. [ABSTRACT FROM AUTHOR]

High-dimensional data arise frequently in modern applications such as biology, chemometrics, economics, neuroscience and other scientific fields. The common features of high-dimensional data are that many of predictors may not be significant, and there exists high correlation among predictors. Generalized linear models, as the generalization of linear models, also suffer from the collinearity problem. In this paper, combining the nonconvex penalty and ridge regression, we propose the weighted elastic-net to deal with the variable selection of generalized linear models on high dimension and give the theoretical properties of the proposed method with a diverging number of parameters. The finite sample behavior of the proposed method is illustrated with simulation studies and a real data example. [ABSTRACT FROM AUTHOR]

This paper deals with an adaptive nonlinear model predictive control (NMPC) based estimator in cases of mismatch modeling, presence of perturbations and/or parameter variations. Thus, we propose an adaptive nonlinear predictive controller based on the second-order divided difference filter (DDF) for multivariable systems. The controller uses a nonlinear state-space model for parameters and state estimation and for the control law synthesis. Two nonlinear optimization layers are included in the proposed algorithm. The first optimization problem is based on the output error (OE) model with a tuning factor, and it is dedicated to minimize the error between the model and the system at each sample time by estimating unknown parameters when assuming that all system states are available. The second optimization layer is used by the centralized nonlinear predictive controller to generate the control law which minimizes the error between future setpoints and future outputs along the prediction horizon. The proposed algorithm leads to a good tracking performance with an offset-free output and an effectiveness in perturbation attenuation. Practical results on a real setup show the reliability of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper considers the performance of the unbiased ridge estimator (Crouse et al. Commun Stat Theory Methods 24:2341-2354, ) over the ordinary least squares estimator of the regression parameter using the Pitman's closeness criterion. Then, we introduce a new variance components estimator based on the unbiased ridge estimator. Furthermore we show that the new variance components estimator has smaller mean squared error than the variance components estimator based on the ordinary least squares estimator. A simulation study has been presented to compare the performance of the estimators, and a numerical example has been proposed to explain the performance of the estimators. [ABSTRACT FROM AUTHOR]

For left-truncated and right-censored data, the technique proposed by Brookmeyer and Crowley (1982) is extended to construct a point-wise confidence interval for median residual lifetime. This procedure is computationally simpler than the score type confidence interval in Jeong et al. (2008) and empirical likelihood ratio confidence interval in Zhou and Jeong (2011). Further, transformations of the estimator are applied to improve the approximation to the asymptotic distribution for small sample sizes. A simulation study is conducted to investigate the accuracy of these confidence intervals and the implementation of these confidence intervals to two real datasets is illustrated. [ABSTRACT FROM PUBLISHER]

We investigate the small-sample quality of the maximum likelihood estimators (MLE) of the parameters of a zero-inflated Poisson distribution (ZIP). The finite-sample bias of the MLE is determined toO(n−1) using an analytic bias-reduction methodology based on the work of Cox and Snell (1968) and Cordeiro and Klein (1994). Monte Carlo simulations show that the MLEs have very small percentage biases for this distribution, but the analytic bias-reduction methods essentially eliminate the bias without adversely affecting the mean-squared errors of the estimators. The analytic adjustment compares favorably with the parametric bootstrap bias-corrected estimator, in terms of bias reduction itself, as well as with respect to mean-squared error and Pitman’s nearness measure. [ABSTRACT FROM AUTHOR]

Exponentially weighted moving average (EWMA) control charts have been widely recognized as an advanced statistical process monitoring tool due to their excellent performance in detecting small to moderate shifts in process parameters. In this paper, we propose a new EWMA control chart for monitoring the process dispersion based on the best linear unbiased absolute estimator (BLUAE) obtained under paired ranked set sampling (PRSS) scheme, which we name EWMA-PRSS chart. The performance of the EWMA-PRSS chart is evaluated in terms of the average run length and standard deviation of run length, estimated using Monte Carlo simulations. These control charts are compared with their existing counterparts for detecting both increases and decreases in the process dispersion. It is observed that the proposed EWMA-PRSS chart performs uniformly better than the EWMA dispersion charts based on simple random sampling and ranked set sampling (RSS) schemes. We also construct an EWMA chart based on imperfect PRSS (IPRSS) scheme, named EWMA-IPRSS chart, for detecting overall changes in the process variability. It turns out that, with reasonable assumptions, the EWMA-IPRSS chart outperforms the existing EWMA dispersion charts. A real data set is used to explain the construction and operation of the proposed EWMA-PRSS chart. [ABSTRACT FROM AUTHOR]

The Gini methodology in statistical inference and related area has got much attention in recent years. In this paper, using a characterisation based on the Gini index we develop a nonparametric test for testing exponentiality against new better than used in expectation class. We derive the exact null distribution of the proposed test statistic and then calculate the critical values for different sample sizes. Asymptotic properties of the test statistic are discussed. The test is compared with some other test by evaluating Pitman's asymptotic efficacy. We also discuss how to incorporate right-censored observations in our study. A simulation study is presented to demonstrate the performance of the testing method. Finally, we illustrated our test procedure using two real data sets. [ABSTRACT FROM AUTHOR]

In this paper, the Pitman closeness of predictors for a future order statistic coming from a two parameter exponential distribution is discussed. The optimum equivariant predictor using the Pitman closeness criterion is derived and compared with the best invariant predictor and the best unbiased predictor. The predictors are obtained on the basis of observed record values. Exact expressions for the required Pitman closeness probabilities are derived when both parameters are considered to be unknown. Similar results are obtained for the predictors of the mean of a future sample from exponential distribution. Several tables which contain numerical computations, are provided in order to compare the predictors in the sense of Pitman's measure of closeness. [ABSTRACT FROM AUTHOR]

We present an approach to quantifying errors in covariance structures in which adventitious error, identified as the process underlying the discrepancy between the population and the structured model, is explicitly modeled as a random effect with a distribution, and the dispersion parameter of this distribution to be estimated gives a measure of misspecification. Analytical properties of the resultant procedure are investigated and the measure of misspecification is found to be related to the root mean square error of approximation. An algorithm is developed for numerical implementation of the procedure. The consistency and asymptotic sampling distributions of the estimators are established under a new asymptotic paradigm and an assumption weaker than the standard Pitman drift assumption. Simulations validate the asymptotic sampling distributions and demonstrate the importance of accounting for the variations in the parameter estimates due to adventitious error. Two examples are also given as illustrations. [ABSTRACT FROM AUTHOR]

In this rejoinder we discuss the following aspects of our approach to model discrepancy: the interpretations of the two populations and adventitious error, the choice of inverse Wishart distribution, the perceived danger of justifying a model with bad fit, the relationship among our new approach, Chen's (J R Stat Soc Ser B, 41:235-248, ) approach and the existing RMSEA-based approach, and the Pitman drift assumption. [ABSTRACT FROM AUTHOR]

Background: Estimates of home-range size are frequently used to compare areal requirements of animals over time or space. Comparative studies of home-range estimators have highlighted extreme differences among general classes of methods (e.g., polygon-based and kernel density-based estimators) and sensitivity to the choice of various tuning parameters (e.g., amount of smoothing). These studies, however, have largely failed to consider how estimates of home-range size are typically used in applied research. We illustrate simulation-based methods for comparing estimators, which focus on relative differences in home-range size (over time or space), rather than their absolute magnitude. We also consider Global Positioning Technology (GPS) location data from a black bear (Ursus americanus) from northwestern Minnesota, USA, to illustrate the relevance to real-world data applications. Results: In our examples, estimates of home-range size often differed considerably in absolute magnitude. Yet, for relative differences, the choice of home-range estimator was often negligible. Furthermore, choosing the right estimator was less important than other aspects of study design (e.g., number of animals followed). Conclusion: Many questions in ecology focus on changes in space-use patterns (over space or time). For these types of questions, home-range estimators should be evaluated in terms of their ability to detect these spatial and temporal patterns. More importantly, home-range estimation should be seen as a means to an end--i.e., estimators provide indices useful for addressing interesting biological questions or hypotheses--rather than as an end to itself. [ABSTRACT FROM AUTHOR]

The purpose of the present investigation was to assess whether interpersonal closeness facilitates earlier emotion detection as the emotional expression unfolds. Female undergraduate participants were either paired with a close friend or an acquaintance (n= 92 pairs). Participants viewed morphed movies of their partner and a stranger gradually shifting from a neutral to either a sad, angry, or happy expression. As predicted, findings indicate a closeness advantage. Close friends detected the onset of their partners’ angry and sad expressions earlier than acquaintances. Additionally, close friends were more accurate than acquaintances in identifying angry and sad expressions at the onset, particularly in non-vignette conditions when these expressions were void of context. These findings suggest that closeness does indeed facilitate emotional perception, particularly in ambiguous situations for negative emotions. [ABSTRACT FROM AUTHOR]

An interconnection network's diagnosability is an important measure of its self-diagnostic capability. The classical problems of fault diagnosis are explored widely. The conditional diagnosability is proposed by Lai et al. as a new measure of diagnosability, which can better measure the diagnosability of regular interconnection networks. The conditional diagnosability is an important indicator of the robustness of a multiprocessor system in presence of failed processors. Furthermore, a multiprocessor system is strongly t -diagnos-able, if it is t -diagnosable and can achieve diagnosability t + 1 except for the case where a node's neighbors are all faulty. The conditional diagnosability and strong diagnosability were proposed later to better reflect the networks' self-diagnostic capability under more realistic assumptions. In this paper, we determine the conditional diagnosability of an n -dimensional Split-Star Network (denoted as S n 2 ), a well-known interconnection network model for multiprocessor systems, under the PMC (Preparata, Metze, and Chien) model. We show that the conditional diagnosability of S n 2 ( n ≥ 4 ) is 8 n − 23 , which is about four times of its traditional diagnosability. As a byproduct, the strong diagnosability of S n 2 is also obtained. [ABSTRACT FROM AUTHOR]

In this paper, the Bayes linear unbiased estimator (Bayes LUE) is derived under the balanced loss function. Moreover, the superiority of Bayes LUE over ordinary least square estimator is studied under the mean square error matrix criterion and Pitman closeness criterion. Furthermore, we compare Bayes LUE under the balanced loss function with Bayes LUE under the quadratic loss function. [ABSTRACT FROM PUBLISHER]

In this paper, we focus on Pitman closeness probabilities when the estimators are symmetrically distributed about the unknown parameter θ. We first consider two symmetric estimators θˆ1and θˆ2and obtain necessary and sufficient conditions for θˆ1to be Pitman closer to the common median θ than θˆ2. We then establish some properties in the context of estimation under the Pitman closeness criterion. We define Pitman closeness probability which measures the frequency with which an individual order statistic is Pitman closer to θ than some symmetric estimator. We show that, for symmetric populations, the sample median is Pitman closer to the population median than any other independent and symmetrically distributed estimator of θ. Finally, we discuss the use of Pitman closeness probabilities in the determination of an optimal ranked set sampling scheme (denoted by RSS) for the estimation of the population median when the underlying distribution is symmetric. We show that the best RSS scheme from symmetric populations in the sense of Pitman closeness is the median and randomized median RSS for the cases of odd and even sample sizes, respectively. [ABSTRACT FROM PUBLISHER]

Copyright of Sultan Qaboos University Journal for Science is the property of Sultan Qaboos University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Uniform order statistics generated by two simulation methods are compared by means of Pitman’s measure of closeness. This measure, as a probability, is shown to be asymptotically 1/2. Some results are also established for fixed points of the cumulative distribution function (CDF) for a uniform order statistic. These fixed points are important for calculations involving the joint distribution of these order statistics. [ABSTRACT FROM PUBLISHER]

This article is concerned with the prediction problems in linear mixed models (LMM). Both biased predictors and restricted predictors are introduced. It was found that the mean square error matrix (MSEM) of a predictor strongly depends on the MSEM of corresponding estimator of the fixed effects and precise formulas are obtained. As an application, we propose three new predictors to improve the best linear unbiased predictor (BLUP). The performance of the new predictors can be examined easily with the help of vast literature on the linear regression models (LM). We also illustrate our findings with a Monte Carlo simulation and a numerical example. [ABSTRACT FROM PUBLISHER]

In this paper, Pitman closeness criterion is used to compare the nearness of record values and order statistics from two independent samples to a specific population quantile of the parent distribution while the underlying distributions are the same. General expressions for the associated Pitman closeness probability are obtained when the support of the parent distribution is bounded and also unbounded. Some distribution-free results are achieved for symmetric distributions. The exponential and uniform distributions are considered for illustrative proposes and exact expressions are obtained in each case. [ABSTRACT FROM PUBLISHER]

An efficient diagnosis is very important for a multiprocessor system. The ability of identifying all the faulty devices in a multiprocessor system is known as diagnosability. The PMC model is the tested-based diagnosis with a processor performing the diagnosis by testing on the neighboring processors via the links between them. Recently, some researches such as the conditional diagnosability and the local diagnosability, are concerned with the measure which is able to better reflect fault patterns in real systems. In this paper, we propose a specific structure for local diagnosis. Under the PMC model, we design a test round controllable local diagnosis algorithm for a t ∗ -diagnosable network. For some conditional constraint, we give a conditional local diagnosis algorithm for a ( 2 t - 1 ) ∗ -diagnosable network. With our algorithm, a diagnosis is completed in k test rounds. [ABSTRACT FROM AUTHOR]

In many applications, a finite mixture is a natural model, but it can be difficult to choose an appropriate number of components. To circumvent this choice, investigators are increasingly turning to Dirichlet process mixtures (DPMs), and Pitman-Yor process mixtures (PYMs), more generally. While these models may be well-suited for Bayesian density estimation, many investigators are using them for inferences about the number of components, by considering the posterior on the number of components represented in the observed data. We show that this posterior is not consistent--that is, on data from a finite mixture, it does not concentrate at the true number of components. This result applies to a large class of nonparametric mixtures, including DPMs and PYMs, over a wide variety of families of component distributions, including essentially all discrete families, as well as continuous exponential families satisfying mild regularity conditions (such as multivariate Gaussians). [ABSTRACT FROM AUTHOR]

In this paper, we consider two independent $$k$$ -record sequences with the same distribution. We determine the closeness probability of $$k$$ -record values to a specific progressive Type-II censored order statistic. With this in mind, we first derive the exact expression for the Pitman closeness of records in general, and some special properties of the closeness probability are presented. Then, we apply the obtained results for the standard uniform and exponential distributions and exact expressions for the Pitman closeness are obtained. Finally, numerical results are displayed in figures. [ABSTRACT FROM AUTHOR]

The best linear unbiased reconstructor and the best linear invariant reconstructor of the past upper records based on observed upper record values for the location-scale family of distributions are derived. The results are obtained in detail for two-parameter exponential distribution. A comparison study is performed in terms of mean squared reconstruction error and Pitman's measure of closeness criteria. Finally, a real example is given to illustrate the proposed procedures. [ABSTRACT FROM AUTHOR]

In the past two decades, Pitman closeness (PC) criterion has been studied intensively in China. But many of research works were written in Chinese, which cannot be accessed by researchers from other countries. In this paper, we briefly summarize part of main results on the PC criterion in linear model in China. First, we present the basic model and some definitions. Then, we introduce the PC superiority for covariance adjustment estimate, and a class of biased estimates such as a kind of linear estimate, James–Stein estimate and the principal components estimate. Third, we introduce Bayesian PC superiorities for several different linear models such as ordinary univariate regression model, multivariate linear model and analysis of variance model. Finally, some results of robustness under Bayesian PC criterion are shown. [ABSTRACT FROM PUBLISHER]

We propose rank-based estimators of principal components, both in the one-sample and, under the assumption ofcommon principal components, in them-sample cases. Those estimators are obtained via a rank-based version of Le Cam’s one-step method, combined with an estimation ofcross-information quantities. Under arbitrary elliptical distributions with, in them-sample case, possibly heterogeneous radial densities, those R-estimators remain root-nconsistent and asymptotically normal, while achieving asymptotic efficiency under correctly specified radial densities. Contrary to their traditional counterparts computed from empirical covariances, they do not require any moment conditions. When based on Gaussian score functions, in the one-sample case, they uniformly dominate their classical competitors in the Pitman sense. Their AREs with respect to other robust procedures are quite high—up to 30, in the Gaussian case, with respect to minimum covariance determinant estimators. Their finite-sample performances are investigated via a Monte Carlo study. [ABSTRACT FROM AUTHOR]

The problem of estimating order-restricted scale parameters of two Gamma distributions is considered under the Pitman closeness criterion. A class of isotonic estimators including the MLE is proposed. Some properties of this class of isotonic estimators is given under the Pitman closeness criterion. In particular, some properties of the MLE naturally follow. We use simulation comparisons to examine the results. [ABSTRACT FROM AUTHOR]

The focus of this paper is on a nonlinear weighted total least squares fitting problem for the three-parameter inverse Weibull density which is frequently employed as a model in reliability and lifetime studies. As a main result, a theorem on the existence of the total least squares estimator is obtained, as well as its generalization in the lq norm (1 ⩽ q <∞). [ABSTRACT FROM AUTHOR]

New inequalities are proved for the variance of the Pitman estimators (minimum variance equivariant estimators) of θ constructed from samples of fixed size from populations F( x − θ). The inequalities are closely related to the classical Stam inequality for the Fisher information, its analog in small samples, and a powerful variance drop inequality. The only condition required is finite variance of F; even the absolute continuity of F is not assumed. As corollaries of the main inequalities for small samples, one obtains alternate proofs of known properties of the Fisher information, as well as interesting new observations like the fact that the variance of the Pitman estimator based on a sample size n scaled by n monotonically decreases in n. Extensions of the results to polynomial versions of the Pitman estimators and a multivariate location parameter are given. Also, the search for the characterization of equality conditions for one of the inequalities leads to a Cauchy-type functional equation for independent random variables, and an interesting new behavior of its solutions is described. Bibliography: 21 titles. [ABSTRACT FROM AUTHOR]

In this article, the Pitman closeness of upper and lowerk-records to progressive Type-II censored order statistics for location-scale families is investigated. In each case, the special properties of the probability of Pitman closeness are obtained and the corresponding monotonicity properties are discussed. Moreover, the closestk-record to a specific progressive Type-II censored data is obtained. Finally, for the standard exponential and standard uniform distributions, explicit expressions for the probability of Pitman closeness are derived. For various censoring schemes, the results of the numerical computations are displayed in tables. Most of the results in Ahmadi and Balakrishnan (2013) can be achieved as special cases. [ABSTRACT FROM AUTHOR]

In this note, we consider the problem of estimating an unknown parameter θ in the sense of the Pitman's measure of closeness (PMC) using the balanced loss function (BLF). We show that the PMC comparison of estimators under the BLF can be reduced to the PMC comparison under the usual absolute error loss. The Pitman-closest estimators of the location and scale parameters under BLF are also characterized. Illustrative examples are given to show the broad range applications of the obtained results. [ABSTRACT FROM AUTHOR]