6. Block-wise random weighting approach. Although the bootstrapped crit- ical values based on the RW method are valid for weak ARMA models, the condition in Assumption 2.4 seems to be slightly restrictive in practice. In this section, we propose a block-wise RW method to obtain the bootstrapped critical values for all **portmanteau** **tests**. Our bootstrapped critical values from the block-wise RW method are valid without posing Assumption 2.4, but it requires a selection of block size as many block-wise bootstrap methods in the literature; see, e.g., Romano and Thombs (1996), Horowitz, Lobato, Nankervis, and Savin (2006), and Shao (2011b).

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In Sections 3 and 4 we shall focus on **tests** with r, s ∈ { 1, 2 } . The use of higher values for (r, s) is, of course, possible but the asymptotic justification of the associated **portmanteau** **tests** requires finiteness of a fairly large number of moments (cf. Theo- rem 1). This requirement may be at odds with the characteristics of many economic and financial time series (e.g., equity returns, exchange rate returns, interest rates), for which it is often argued that they only possess unconditional moments of relatively low order (see, e.g., Koedijk, Schafgans, and de Vries (1990); Jansen and de Vries (1991); de Lima (1997)).

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Time series model diagnostic checking is the most important stage of time series model building. In examining the adequacy of a statistical model, an analysis of the residuals is often performed. The study of the distribution of residual autocorrelations in linear time- series models started with the seminal work of Box and Pierce [2]. If the appropriate model has been chosen, there will be zero autocorrelation in the errors and we use one of the **portmanteau** **tests** in time series analysis for testing the adequacy of a fitted linear time series model.

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In this section **portmanteau** **tests** for linearity are applied to a set of weekly stock re- turns, spanning the period 1993–2007 (781 observations), for 100 companies from the Standard & Poor’s 500 Composite index. The selected series are part of the data set analyzed by Kapetanios (2009) and are such that the hypothesis of strict stationarity cannot be rejected for any of them (at 5% significance level). The presence of nonlinear- ity in asset returns has important implications for, inter alia, pricing, risk management, and forecasting.

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Table 1 gives the results for empirical power of the goodness-of-fit **tests**. It can be very clearly noticed that CvM has less power while **portmanteau** **tests** have better power against this linear class of alternatives. Our results confirm the results reported in the literature, see e.g Hong and Lee (2003); Escanciano (2006). Though we have provided the power results for both of dynamic and fixed design bootstrap methods, we discuss the results for dynamic bootstrap method only, as dynamic bootstrapping provides the best approximation to the asymptotic distribution especially for the **portmanteau** **tests**, see e.g. Chand (2013).

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Since the seminal works of Box and Pierce (1970), Ljung and Box (1978) and McLeod (1978), **portmanteau** **tests** have been important tools in time series analysis, in particular for testing the adequacy of an estimated ARMA(p, q) model (see Section 9.4 in Brockwell and Davis (1991), and Li (2004) for an entire book devoted to the **portmanteau** **tests**). Under the null assumption that a model with iid innovations η t is appropriate for the

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the joint limiting distribution of the residual autocorrelation functions and the ab- solute residual autocorrelation functions, where the residual is obtained from model (1.1)-(1.2) fitted by the QMELE approach. Based on this, we propose a mixed port- manteau test statistic for model (1.1)-(1.2). Via some simplifications, we can show that our mixed **portmanteau** test nests two **portmanteau** **tests** Q r and Q a in Li

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Recently, a large number of research papers attempted to weaken the assumption of strong white noise for the **portmanteau** test (Romano and Thombs, 1996; Francq and Zakoïan, 1998; Francq et al., 2005). In order to solve this problem of non-i.i.d. noise, some researchers (Chen and Deo, 2004; Deo, 2000) derived the spectral density test for the martingale di ﬀ erence hy- pothesis in the presence of conditional heteroscedasticity. Later, Lobato et al. (2001, 2002) addressed the problems to test the null hypothesis with time series to uncorrelated up to a fixed order m and proposed a modified Box-Pierce test for this null hypothesis. However, these **tests** do not solve the problem of weak white noise including the important special case of GARCH innovations. Francq et al. (2005) successfully derived the distribution of the residuals under the null hypothesis of uncorrelated, but not independent errors and then proposed another mod- ification for Box-Pierce Test similar to McLeod (1978). They show the advantages and better performance of their **tests** compared to the original **portmanteau** **tests**.

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ual partial autocorrelation function. Wong and Li [10] made the **portmanteau** test for mul- tivariate conditional heteroscedasticity model. Francq et al. [11] proposed a diagnosis test method for weak ARMA model. Kwan et al. [12] studied the **portmanteau** test under the condition of ﬁnite sample. Francq [13] aiming at autoregressive models with uncorrelated but non-independent errors made the multivariate **portmanteau** test. And then Mainas- sara [14] also made a multivariate **portmanteau** test for structural VARMA models with uncorrelated but non-independent error terms. Kwan et al. [15] deﬁned two **portmanteau** **tests** based on residual autocorrelation function and square residual autocorrelation func- tion, respectively. Fisher and Gallagher [16] proposed a new weighted **portmanteau** statis- tic for the goodness of ﬁt for time series. Zhu and Ling [17] presented a Ljung–Box port- manteau test based on symbolic function in order to test the properties of ARMA model with fat-tailed noise. Zhu [18] used the random weighting method to make a bootstrap **portmanteau** test on the basis of residual autocorrelation function and residual partial au- tocorrelation function of weak ARMA model. Recently, Xuan [19] made a **portmanteau** test aiming at ARFIMA–GARCH model. Stefanos [20] studied time-varying parameter regression models with stochastic volatility and made a semiparametric Bayesian infer- ence.

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Both multivariate **portmanteau** **tests** (with the lag value p = 12) of Li & Mcleod (1981) and Reinsel (1997, p.149) for the residuals from the above fitted vector AR(1) model are insignificant at the 5% level. The univariate **portmanteau** test is insignificant at the level 5% for three (out of the four) component residual series, and is insignificant at the level 1% for the other component residual series. On the other hand, a vector AR(2) model was selected by the AIC for the 4 factor series with vector AR(1) as its closest competitor. In fact the AIC values are, respectively, 240.03, 0.11, 0.00, 6.38 and 18.76 for the AR-order 0, 1, 2, 3 and 4.

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After identification and estimation of the parameters in a fitted model, the good- ness of fit test is the next most important step for testing the selected model. In time series analysis, we assume that the series is stationary with white noise innovations. This implies that a good fitted model must produce residuals that are approximately uncorrelated in time. Box and Pierce (1970) show that the asymptotic distribution of the residual autocorrelations can be utilized to check the validity of this assumption under the ARMA models. They introduced to the literature the overall goodness- of-fit test on the residuals autocorrelations up to lag m. This test statistic is called **portmanteau** test. Since then there evolves many literature on **portmanteau** **tests** for ARMA and GARCH models (Ljung and Box, 1978; McLeod and Li, 1983; Peˇ na and Rodriguez, 2002; Rodr´ıguez and Ruiz, 2005; Peˇ na and Rodriguez, 2006). The **portmanteau** test is extended to the multivariate VARMA models by Chitturi (1974, 1976); Hosking (1980); Li and McLeod (1981); Francq and Ra¨ısi (2007) and to the MGARCH models by (Li and Mak, 1994; Ling and Li, 1997). Lin and McLeod (2006) introduce the Monte-Carlo **portmanteau** test and show that this test provides a test with the correct size. They show that the Monte-Carlo version of Peˇ na and Rodriguez (2002) is often more powerful than its competitors. Lin and McLeod (2008) extends the Monte-Carlo test of Peˇ na and Rodriguez (2002) to the ARMA models with stable Paretian errors.

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Theorem 1.7 is proved using a special test that we call a universal test, that works by selecting every index i for querying with probability ˜ O(n −1/3 −1 ) · log(k), independently of other indexes. We prove in Theorem 6.8 below that such a kind of test will work for any property admitting a proximity oblivious 2-test, regardless of how that 2-test works. This universal test is very close to what is defined as a sampling based test in a new work [14] of Goldreich and Ron. In particular, our proof yields the following corollary, which partially addresses a question from [14] about whether proximity oblivious **tests** are translatable to sample-based ones:

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This paper considers **tests** for the rank of a matrix for which a root-T consistent estimator is available + However , in contrast to **tests** associated with the minimum chi-square and asymptotic least squares principles , the estimator’s asymptotic vari- ance matrix is not required to be either full or of known rank + Test statistics based on certain estimated characteristic roots are proposed whose limiting distributions are a weighted sum of independent chi-squared variables + These weights may be simply estimated, yielding convenient estimators for the limiting distributions of the pro- posed statistics + A sequential testing procedure is presented that yields a consistent estimator for the rank of a matrix + A simulation experiment is conducted comparing the characteristic root statistics advocated in this paper with statistics based on the Wald and asymptotic least squares principles +

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15 These disagreements indicate that the **tests** have one characteristic of boundary objects: they allow for 'interpretive flexibility' (Star 2010: 602) since primary and secondary teachers understand the test to produce results to which they attach quite different meanings. For some, mainly primary teachers, the **tests** reveal high pupil attainment, which they value, and present externally to parents, other schools and school inspectors. For others - secondary teachers and some of the primary leaders that either decided not to enter pupils for the **tests** - the **tests** represent shallow learning and a stripped back curriculum. The Level 6 **tests** also share another characteristic of boundary objects: they act to reify concerns - they 'congeal' the complexities around pupil progress, attainment, ability into 'thingness' (Wenger, 1998: 58). Akkerman and Bakker (2011) refer to this process as crystallization: the crystallization of a set of concerns around the primary secondary border, usually not directly expressed, but brought out into the open by the **tests**.

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The likelihood ratio test (LRT) method is probably the most commonly used method of hypothesis test construction. Another method, which is appropriate when the null hypothesis is expressed as a union of sets, is the intersection- union test (IUT) method. We will explore some relationships between **tests** that result from these two methods. We will give conditions under which both methods yield the same test. But, we will also give conditions under which the size- IUT is uniformly more powerful than the size- LRT.

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Soft soils were clay soils found in many parts of the world. The clay soils possess excessive heave, low shear strength, internal erosion, swell shrink behaviour and poor drainage properties etc. When compared to other type of soils, the strength development of soft soil is time dependent. General construction problems in this soil deposit were insufficient bearing capacity, excessive post construction settlement and instability on excavation and embankment forming. The engineering characteristics on soft soil were well documented through researches and field trials. One of the possible solutions to overcome the undesirable properties of clayey soil is chemical stabilization to modify its characteristics by addition of admixtures like lime, cement, polymers, fly ash, polystyrene etc. The easily available additives among them were lime and fly ash. Stabilization of soils is essential for utilizing existing ground for various construction purposes. This paper represents the results of geotechnical investigations on lime treated and fly ash treated clay soil from a part of Kerala. Dosage of lime as well as fly ash applied in the order was 2%, 4%, 6%, 8% and 10% by weight. Laboratory experiments were done after a curing period of 7 days. Various **tests** including consistency limits, unconfined compressive strength **tests**, proctor compaction **tests**, permeability **tests** and California bearing ratio **tests** were conducted on the untreated, lime-treated and fly ash-treated soils. The optimum dosage of lime and fly ash required for the satisfactory stabilization of clay soils is acquired by the end of test results. The test results also indicated that the addition of lime to clayey soil was more effective in improving the properties than the addition of fly ash.

Among the different types of aptitude **tests**, the most common type is the intelligent quotient (IQ) test, which purports to measure high-level cognitive ability. However, IQ **tests** have been overused in personnel selection process and are found to be only suitable for jobs requiring high-level cognitive activity or learning ability. It is obvious that such abilities are less important to successful job performance of a vehicle driving task. Moreover, **tests** for jobs such as, secretary, engineer, accountant, fire-fighter, and military personnel, have been developed, but there is no special aptitude test available for occupational driver selection. Different careers and occupations need different abilities and skills for successful job performance. The **tests** for fire-fighters, secretaries or engineers apparently cannot identify the critical performance requirements of the drivers’ job. Also, although the forenamed special aptitude **tests** have good reliability and validity, and have been widely used, a problem is that with rapidly changing times and the advent of high technology, some items in these **tests** may be out of date. Kaplan [5] noted that ‘the individual will not take the test as seriously if most of the items represent items no longer found in a modern workplace’.

Indeed, the astrophysical probes presented here are far from exhausted and are mainly limited by the small number of dwarfs in the screening map. Future SDSS data releases, in particular MaNGA, could drastically increase the sample size and with it, the constraints. On a similar note, other proposed **tests** using the morphology and kinematics of dwarf galaxies [30] have yet to be performed but may yield new constraints. [84] considered several **tests** along these lines using SDSS optical and ALFALFA radio data but were unable to distinguish between modified gravity and GR due to the large scatter. Future radio observations such as VLA may improve the constraining power of such **tests**.

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The nonparametric test Statistics is one which requires few assumptions to be met,” The nonparametric **tests** do not assume the data is normal; rather they can be used on a much wider experiments. We sometimes want to make inferences that have nothing to do with parameters; or we may have data in a form that makes; say, normal theory **tests** inappropriate; we may not have precise measurement data, but only the rank order of observations. In general, these methods are applicable to estimation or hypothesis-testing problems when the populations distributions need only be specified in broad terms, e.g. as being continuous, symmetric, identical, differing to specific families the normal, uniform, exponential, etc. logically, the term distribution-free may then be more appropriate than nonparametric, but the latter term is well established in popular usages” Sprent (1989. P: 2-3).

¨Ozbal and Strapparava (2012) generate new words to describe a product given its category and prop- erties. However, their method is limited to hand- crafted rules as compared to our data driven ap- proach. Also, their focus is on brand names. Hiranandani et al. (2017) have proposed an ap- proach to recommend brand names based on brand/product description. However, they con- sider only a limited number of features like mem- orability and readability. Smith et al. (2014) de- vise an approach to generate portmanteaus, which requires user-defined weights for attributes like sounding good. Generating a **portmanteau** from two root words can be viewed as a S2S problem. Recently, neural approaches have been used for S2S problems (Sutskever et al., 2014) such as MT. Ling et al. (2015) and Chung et al. (2016) have shown that character-level neural sequence mod- els work as well as word-level ones for language modelling and MT. Zoph and Knight (2016) pro- pose S2S models for multi-source MT, which have multi-sequence inputs, similar to our case. 7 Conclusion