A linear causal model with **correlated** **errors**, represented by a DAG with bi-directed edges, can be tested by the set of conditional independence relations implied by the model. A global Markov property specifies, by the d-separation criterion, the set of all conditional independence relations holding in any model associated with a graph. A local Markov property specifies a much smaller set of conditional independence relations which will imply all other conditional independence relations which hold under the global Markov property. For DAGs with bi-directed edges associated with arbitrary probability distributions, a local Markov property is given in Richardson (2003) which may invoke an exponential number of conditional independencies. In this paper, we show that for a class of linear structural equation models with **correlated** **errors**, there is a local Markov property which will invoke only a linear number of conditional independence relations. For general linear models, we provide a local Markov property that often invokes far fewer conditional independencies than that in Richardson (2003). The results have applications in testing linear structural equation models with **correlated** **errors**.

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It is a well-known problem that obtaining a correct bandwidth and/or smoothing parameter in non- parametric regression is difficult in the presence of **correlated** **errors**. There exist a wide variety of methods coping with this problem, but they all critically depend on a tuning procedure which requires accurate information about the correlation structure. We propose a bandwidth selection procedure based on bimodal kernels which successfully removes the correlation without requiring any prior knowledge about its structure and its parameters. Further, we show that the form of the kernel is very important when **errors** are **correlated** which is in contrast to the independent and iden- tically distributed (i.i.d.) case. Finally, some extensions are proposed to use the proposed criterion in support vector machines and least squares support vector machines for regression.

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The requirement of uncorrelated **errors** may be overly restrictive in many settings. While arbitrary correlation patterns over the **errors** may yield rather ill-behaved statistical models, there are sub- classes of models with **correlated** **errors** in which some of the nice properties of DAG models are preserved; compare McDonald (2002). In this paper we consider path diagrams in which there are no directed cycles and no ‘double’ edges of the form i → ↔ j (compare Def. 2 and 3). Since such double edges have been called ‘bows’, we call this class bow-free acyclic path diagrams (BAPs). An example of a BAP arose in our motivating example in §1.1; see Figure 1. While instrumental variable models, which are much studied in economics, contain bows, most models in other social sciences are based on BAPs. For instance, all path diagrams in Bollen (1989) are BAPs.

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The original WG and IV tests allow for heterogeneous disturbances across i but this assumption is trimmed so that tractable results may be obtained. For the same reasons, normal **errors** provide analytic formulas for the variances of the tests. Condition (1.1) ensures the existence of at least one moment condition free of correlation nuisance parameters but does not specify the true order of serial correlation. De…ne p the order of serial correlation assumed by the researcher and p the true order. As long as p p the limiting distribution of the test statistics is valid. Since inference in both tests is based on moments that are free of correlation parameters, choosing p > p means selecting fewer than possible moments for inference. For a discussion on how to estimate the order of serial correlation see Hayakawa (2010).

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Abstract: This paper considers panel data models when the **errors** are first-order serially **correlated** as well as with stochastic regression parameters. The generalized least squares (GLS) estimators for these models have been derived and examined in this paper. Moreover, an alternative estimator for GLS estimators in small samples has been proposed, this estimator is called simple mean group (SMG). The efficiency comparisons for GLS and SMG estimators have been carried out. The Monte Carlo studies indicate that SMG estimator is more reliable in most situations than the GLS estimators, especially when the model includes one or more non-stochastic parameter.

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The study of the internal structure, by means of CFAs, supported the five-factor structure in all the countries and in the total sample, as it is the case in previous studies [40,27,11,24,28,29,25]. Nevertheless, adequate goodness-of-fit indices were found after adding error correlation between items, indicating discrete values in the five-factor baseline model in all the countries. Moreover, some goodness-of-fit indices of Ireland were still not appropriate. Similar results were found in previous studies [40,32,19,26]. For instance, the study of Ortuño-Sierra et al. [40] showed that the five-factor structure was the better to fit the data, but appropriate goodness-of-fit were only reached after **correlated** **errors** were added. Thus, the five-factor structure is still questionable. In the same line, a modified five factor model allowing the reverse-worded items to cross-load on the Prosocial factor displayed significant better goodness-of-fit indices in all the countries, including the total sample, as it was the case in the study of van de Looij–Jansen et al. [26]. However, the study of factor loadings revealed that some of them were non-significant, questioning the adequacy of this model.

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Measurement invariance was examined separately for gender (male vs female), and equal sized age groups (18–30; 31–43; ≥44). First, configural invariance was tested by estimating the 1-factor model of the WEMWBS in each group without constraining factor loadings and intercepts. In the next step, metric invari- ance was tested by constraining the factor loadings to be equal in each group. Due to the categorical nature of the indicators, additional constraints were required to test metric invariance; the first threshold of each item was held equal across groups and the second threshold of the item that was used to set the metric of the factor was also held equal across groups [42]. Finally, both factor loadings and thresholds were constrained to be equal across groups to test for scalar invariance. Scalar invariance is required for comparing absolute scores across groups. In many cases, full scalar invariance cannot be obtained and one or more of the constrained model parameters need to be set free in order to improve model fit. According to recommendations from Byrne et al. [43] partial scalar invariance is obtained when at least two of the factor indicators are invariant. Testing strict measure- ment invariance, in which residual variances are fixed to one across groups, was considered less relevant for the present study since **correlated** **errors** were explicitly accounted for in the measurement model [44]. Adjust- ments to the model were informed by SEPC. In line with Cheung and Rensvold [45], we used a change in CFI of more than 0.01 as an indicator of true difference in relative model fit.

We presented the CRUMEL framework that **correlated** both the message logs and resource use data to identify **errors** and resource usage patterns. We showed that the new approach to integration of resource use data and message logs, and the use of multiple correlation algorithms can identify more events associated with system failures. The framework confirmed six groups of **errors**, identified Lustre I/O resource use counters that are **correlated** with occurrence of Lustre faults that are potential flags for online detection of failures, matched the dates when **correlated** **errors** and **correlated** resource use counters are associated with the dates of compute node hang- ups, and identified two more error groups - process **errors** and file-system **errors** - associated with compute node hang-ups.

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Das [1,2] studied robust second order rotatable designs (RSORD) and constructed second order rotatable designs with **correlated** **errors** (SORDWCE) under the auto **correlated** structure using central composite design. In this paper, a new method of construction of RSORD using balanced incomplete block designs (BIBD) is suggested. In this method the number of design points required is in some cases less than the number required in Das [1,2] method of construction of robust rotatable central composite designs (RRCCD). We may point out here that this RSORD using BIBD has 113 design points for 7-factors where as the corresponding RRCCD obtained by Rajyalakshmi and Victorbabu [3] needs 157 design points. Thus the new method leads to a 7-factor RSORD in less number of design points than the corre- sponding RRCCD. Here we also obtained the variance of the estimated response for the factors 3 ≤ v ≤ 8.

reduce the medication **errors** and prevent harms from reaching the patients. It can be reached through building safer organization endlessly improve its quality. The medication safety manual, which is considered as the foundation of the program, was the first step to be formulated to serve as guide for MOH organizations. There are medication safety officers, as well as there is a committee to medication safety in both the hospitals, primary health care and the Committee for each region as well as the main committee meets monthly in the ministry’s pharmaceutical care administration. For the eastern region, there are 10 hospitals containing medication safety officer, medication safety committee, ISMP medication safety for hospitals in 2014, medication safety committee in the region to analyze the study to develop plans and prevent their reoccurrence. In 2015, basic medication safety course was started in maternity children hospital, Dammam, where 42 nurses, 9 doctors and 7 pharmacists were the highest attendees. Medication error is an essential variable to determine patient safety services, so it is crucial to realize the weak points of health care members regarding medication error and provide an educational program to resolve them.

Abstract: Role of clinical pharmacist is to provide optimal pharmaceutical care for individual patients and optimal pharmaceutical care is attained when the right drug in the correct dosage and quality reaches the right patients at the right point in time with the right information. Any preventable event that may cause or lead to inappropriate medication use or patient harm during medication to user is called medicational error and is in the control of the health care professional, patient and consumer. In this review on medication **errors**, prescr - ibing **errors** (67 %), administration **errors** (25%), dispensing **errors** (08%) were found on the basis of review of literature. Prescribing **errors** are the prime cause of MEs that further leads to subsequent dispensing and administration **errors**. Medication **errors** are common cause of adverse drug events or subtherapeutic outcomes of pharmaceutical care.

students than to low-performing MT systems. Comparing the error distributions of the eight MT sys- tems, we observe that all eight MT systems have fairly similar distributions regardless of their source languages. Moreover, the four high-performing MT systems have er- ror distribution that are more similar to those of the low- performing MT systems than to those of ESL learners with the same L1. Thus, the results suggest that our two hy- potheses do not hold. However, it is also not the case that the source language has no impact on the performance of the systems. For example, consider the German-English case. Comparing to other ESL students, German students make a significant amount of punctuation mistakes (51%). In a more subdued fashion, the low-performing German- English MT system makes more punctuation **errors** than the high-performing system. In contrast, for the other lan- guages the low and high-performing machine translation systems make similar proportions of punctuation mistakes. There are two possible explanations for why the error dis- tribution patterns of MT systems behaved differently than what we hypothesized. One is that the MT systems have largely the same underlying model – they are statistical phrase-based systems. They use the same English language model; therefore, they have similar preferences in terms of the fluency of the output sentences. Another possibility is that because MT systems are still struggling with word choice decisions, which is an adequacy problem, their dis- tribution of **errors** is skewed by the high word choice **errors**, which are mostly due to unaligned words in the reference and MT output sentences. In contrast, the focus of the ESL error categories is on fluency problems only. To factor out the impact of word choice error, we examine article **errors** in greater detail.

The Maximum Likelihood PCA (MLPCA) method has been devised in chemometrics as a generalization of the well-known PCA method in order to derive consistent estimators in the presence of **errors** with known error distribution. For similar reasons, the Total Least Squares (TLS) method has been generalized in the field of computational mathematics and engineering to maintain consistency of the parameter estimates in linear models with measurement **errors** of known distribution. In a previous paper [M. Schuermans, I. Markovsky, P.D. Wentzell, S. Van Huffel, On the equivalance between total least squares and maximum likelihood PCA, Anal. Chim. Acta, 544 (2005), 254 – 267], the tight equivalences between MLPCA and Element-wise Weighted TLS (EW-TLS) have been explored. The purpose of this paper is to adapt the EW-TLS method in order to make it useful for problems in chemometrics. We will present a computationally efficient algorithm and compare this algorithm with the standard EW-TLS algorithm and the MLPCA algorithm in computation time and convergence behaviour on chemical data.

Nowadays localization has become an important necessity in life. One of the best methods for estimation of position is Global Positioning System (GPS). GPS receivers can estimate position, velocity and time. GPS position **errors** are determined by pseudo-range **errors** and satellite geometry. The main pseudo-range measurements **errors** can be divided into three groups: ephemeris **errors** and satellite clock **errors**, atmospheric **errors**, and user receiver **errors** (frequency drift, pseudo- noise sequence phase drift, and signal detection time). Ephemeris **errors** and satellite clock **errors** occur when the GPS message does not transmit the correct satellite location. With the use of measurements of pseudo- ranges on two frequencies, the ionospheric amendment (correction) of measurements of pseudo-range on a C/A code for ground receivers is determined. After obtaining the pseudo-range and Doppler frequency measurements **errors** connected to stability of a frequency generator, the stability of pseudo-noise sequence phase drift and stability signal detection time, are called by various synchronization of user's receiver time and GPS-system. The dynamics of an oscillator of receiver frequency generator and pseudo-noise sequence phase drift and accuracy of signal detection time is investigated [1].

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During the conduct of clinical trials, two types of **errors** can occur and they are 'Random **Errors**' and 'Systematic **Errors**' , Random **errors** include measurement **errors** (such as assay precision,frequency of visits ect) **errors** due to slopiness (such as transcription **errors**). Systematic **errors** include design flaws(such as exclusion of patients with incomplete treatment or unequal schedule of visits); apart from but cannot be classified either to the two **errors** are **Errors** resulting from “falsified data” (Fraud) are always serious and must be dealt with accordingly; other **errors** may be serious or trivial. However, every clinical study must include procedures to avoid or minimize data **errors**. Most frauds have little impact on the trial results because: they introduce random but not systematic **errors** (i.e. noise but no bias) in the analyzes they affect secondary variables (e.g. eligibility criteria) their magnitude is too small to have an influence (one site and/or few patients) [2,3]

**Errors** of commission are a serious threat to the patients health as compared to the **errors** of omission which though looks to be harmless but can create a problem for the patient and which occurs 3 to 4 folds more than the **errors** of commission [17,18,32,33]. Failure to mention the patient’s important information like name, age, M.R number and weight can create problem. If the patient age or weight is not mentioned than it can be problematic while dispensing medicines like cardiac or those related to CNS. The name of physician must be mentioned on the prescription along with his/her signature as in case of any query the pharmacist can easily contact him/her. And above all the prescription should be written clearly which can be read easily as bad handwriting can lead to dispensing of wrong medication. Absences of information related to the drug like dose, route, dosage form, strength and the refill time too should not be taken lightly as they can hinder in dispensing the correct and required dose of medication to the patient. **Errors** of commission are more severe than the **errors** of omission as the information is supplied but is incorrect. The wrong dose, strength or frequency may be dangerous for the patient, as the dose more than required can be toxic and below the therapeutic level will have provide effect.

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In this work DSBSenv minimal basis sets and matching auxiliary basis sets have been de- veloped for H–Ar for use as the environmental basis in the framework of the domain-speciﬁc basis set approach of the incremental scheme. These basis sets increase the computational speed performance of the incremental scheme and achieve a comparable accuracy to the pre- vious ad hoc choice of environmental basis. Using the DSBSenv/MP2Fit ABS, the density ﬁtting for the evaluation of the two-electron integrals are three to four orders of magnitude smaller than the BSIE of the DSBSenv OBS. Also the CABS approach to the RI with the DSBSenv/OptRI ABS introduces **errors** about two to three orders of magnitude smaller than the BSIE.

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Application of the proposed solution to the state-space models employed by the BLS introduces a serious computational problem. The dimension of the state vector in the separate models is of length 30 (see next section), implying that the dimension of the state vector of the joint model fitted to a group of say 12 States would be 360. A possible solution to this problem investigated in the present article is to include the sampling **errors** as part of the observation (measurement) equation instead of the current practice of modeling their stochastic evolvement over time and including them in the state vector. Implementation of this idea reduces the dimension of each of the separate state vectors by half, because the sampling **errors** make up 15 ele ments of the state vector.

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A quantum computer needs the help of a powerful classical computer to overcome the inherent fragility of entangled qubits. By encoding the quantum in- formation in a nonlocal way, local **errors** can be de- tected and corrected without destroying the entangle- ment [1, 2]. Since the efficiency of the quantum error correction protocol can make the difference between failure and success of a quantum computation, there is a major push towards more and more efficient de- coders [3]. Topological codes such as the surface code, which store a logical qubit in the topology of an array of physical qubits, are particularly attractive because they combine a favorable performance on small cir- cuits with scalability to larger circuits [4–9].

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However, these guidelines have emerged from investigations at the conventional MP2 level and there is no reason to assume that they will be appropriate in the speciﬁc context of explicitly **correlated** methods. As well as the additional two-electron integrals required in the aforementioned computation of the V and B matrices, BSIE is drastically reduced in explicitly **correlated** methods; meaning that the ﬁtting accuracy must be increased in order that any density ﬁtting **errors** remain negligible. Recently published MP2Fit sets matched to the cc-pVnZ-PP-F12 basis sets for the post-d main group elements Ga–Rn required functions with an angular momentum of ℓ occ + ℓ OBS + 1 in order to reach suﬃcient accuracy. This

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