best linear unbiased estimator example

Let one allele denote the wildtype and the second a variant. endobj /Resources 6 0 R /Filter /FlateDecode >> The variance for the estimators will be an important indicator. When the auxiliary variable x is linearly related to y but does not pass through the origin, a linear regression estimator would be appropriate. endobj Example. The linear regression model is “linear in parameters.”A2. Best Linear Unbiased Estimator •simplify ﬁning an estimator by constraining the class of estimators under consideration to the class of linear estimators, i.e. 0000033946 00000 n In statistics, the Gauss–Markov theorem states that the ordinary least squares (OLS) estimator has the lowest sampling variance within the class of linear unbiased estimators, if the errors in the linear regression model are uncorrelated, have equal variances and expectation value of zero. �փ��IFf��t�;N��v9O�r. K ˜ ′ β ˆ + M ˜ ′ b ˆ is BLUP of K ˜ ′ β ˆ + M ˜ ′ b provided that K ˜ ′ β ˆ is estimable. 1971 Linear Models, Wiley Schaefer, L.R., Linear Models and Computer Unbiased and Biased Estimators . 0000002213 00000 n stream 16 0 obj In formula it would look like this: Y = Xb + Za + e endobj E(Y) = E(Q) 2. �2�M�'�"()Y'��ld4�䗉�2��'&��Sg^��}8��&��w��֚,�\V:k�ݤ;�i�R;;\��u?��V��\��\�C9�u�(J�I��]��BS�s_ QP5��Fz��׋G�%�t{3qW�D�0vz�� \}\� $��u��m��+��٬C�;X�9:Y�^g�B�,�\�ACioci]g��(�L;�z��9�An��I� We will limitour search for a best estimator to the class of linear unbiased estimators, which of … �~"�&�/��i�@i%(Y��OR�YS@A�9n ��f�m�4,�Z�6�N��5��K�!�NG��av�T��z�Ѷz�o�9��unBp4�,��m��SU��~s�X��~q_��]�5#��s~�W'"�vht��Ԓ* E b b ˆ = b ˆ. endstream 23 The set of the linear functions K ˜ ′ β ˆ is the best linear unbiased estimate (BLUE) of the set of estimable linear functions, K ˜ ′ β ˆ. Suppose now that σi = σ for i ∈ {1, 2, …, n} so that the outcome variables have the same standard deviation. << /ProcSet [ /PDF ] /XObject << /Fm2 17 0 R >> >> This does not mean that the regression estimate cannot be used when the intercept is close to zero. BLUP was derived by Charles Roy Henderson in 1950 but the term "best linear unbiased predictor" (or "prediction") seems not to have been used until 1962. ��ꭰ4�I��ݠ�x#�{z�wA��j}�΅��Q��=��8�m�� An estimator which is not unbiased is said to be biased. %PDF-1.3 Poisson(θ) Let be a random sample from Poisson(θ) Then ( ) ∑ is complete sufficient for Since ( ) ∑ is an unbiased estimator of θ – by the Lehmann-Scheffe theorem we know that U is a best estimator (UMVUE/MVUE) for θ. 8 0 obj There is a random sampling of observations.A3. << /Type /Page /Parent 7 0 R /Resources 3 0 R /Contents 2 0 R /MediaBox stream 3. The result is an unbiased estimate of the breeding value. 2 0 obj An unbiased linear estimator \mx {Gy} for \mx X\BETA is defined to be the best linear unbiased estimator, \BLUE, for \mx X\BETA under \M if \begin {equation*} \cov (\mx {G} \mx y) \leq_ { {\rm L}} \cov (\mx {L} \mx y) \quad \text {for all } \mx {L} \colon \mx {L}\mx X = \mx {X}, \end {equation*} where " \leq_\text {L} " refers to the Löwner partial ordering. Efficient Estimator: An estimator is called efficient when it satisfies following conditions is Unbiased i.e . [0 0 792 612] >> estimators can be averaged to reduce the variance, leading to the true parameter θ as more observations are available. �(�o{1�c��d5�U��gҷt��laȱi"��\.5汔��^�8tph0�k�!�~D� �T�hd��6��챖:>f��&�m��x�A4��L�&��%��k��iĔ��?�Cq��ոm�&/�By#�Ց%i��'�W��:�Xl�Err�'�=_�ܗ)�i7Ҭ��,�F|�N�ٮͯ6�rm�^��U�HW��5;�?�Ͱh If you're seeing this message, it means we're having trouble loading external resources on our website. ��:w�/NQȏ�z��jzz Is ^ = 1=2 an estimator or an estimate? We want our estimator to match our parameter, in the long run. We now define unbiased and biased estimators. endobj 6 0 obj [0 0 792 612] >> endstream /Resources 18 0 R /Filter /FlateDecode >> Linear estimators, discussed here, does not require any statistical model to begin with. The term estimate refers to the specific numerical value given by the formula for a specific set of sample values (Yi, Xi), i = 1, ..., N of the observable variables Y and X. 0000003104 00000 n 5 0 obj Find the best one (i.e. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Y n is a linear unbiased estimator of a parameter θ, the same estimator based on the quantized version, say E θ ^ | Q will also be a linear unbiased estimator. It only requires a signal model in linear form. H�b```f``f`a``Kb�g@ ~V da�X x7��I��d��6�G�``�a��rV|�"W`�]��I��T��Ȳ~w�r�_d��0۵9G��nx��CXl{��Z�. Estimators: a function of the data: ^ = ˚ n (X n) = ˚ n (X 1;X 2;:::;n) Strictly speaking, a sequence of functions of the data, since it is a di erent function for a di erent n. For example: ^ = X n = X 1 + X 2 + + X n n: Estimate: a realized value of the estimator. 293 0 obj << /Linearized 1 /O 296 /H [ 1299 550 ] /L 149578 /E 34409 /N 16 /T 143599 >> endobj xref 293 18 0000000016 00000 n << /ProcSet [ /PDF /Text ] /ColorSpace << /Cs1 9 0 R >> /Font << /F1.0 9 0 obj 0000033523 00000 n x�+TT(c}�\C�|�@ 1�� 12 0 obj If this is the case, then we say that our statistic is an unbiased estimator of the parameter. restrict our attention to unbiased linear estimators, i.e. 0000002243 00000 n t%�k\_>�B�M�m��2\��08pӣ��)Nm��Lm��w�1`�+�\�� .Av��RJM��3��C�|��K�cUDn�~2��} For Example then . We now consider a somewhat specialized problem, but one that fits the general theme of this section. stream 0000002901 00000 n endobj Example Suppose we wish to estimate the breeding values of three sires (fathers), each of which is mated to a random female (dam), ... BLUE = Best Linear Unbiased Estimator BLUP = Best Linear Unbiased Predictor Recall V = ZGZ T + R. 10 LetÕs return to our example Assume residuals uncorrelated & homoscedastic, R = "2 e*I. Practice determining if a statistic is an unbiased estimator of some population parameter. "Best linear unbiased predictions" (BLUPs) of random effects are similar to best linear unbiased estimates (BLUEs) (see Gauss–Markov theorem) of fixed effects. θˆ(y) = Ay where A ∈ Rn×m is a linear mapping from observations to estimates. << /Length 4 0 R /Filter /FlateDecode >> These are based on deriving best linear unbiased estimators and predictors under a model conditional on selection of certain linear functions of random variables jointly distributed with the random variables of the usual linear model. It is a method that makes use of matrix algebra. 706 [ /ICCBased 11 0 R ] xڵ]Ks��W��]��{�L%SS5��[��Y�kƖK�M�� &A<>� ��\Ѕ~.j�?��7�o��s�>��_n��`럛��!�_��~�ӯ��FO5�>��(�O߭��_x��r��!��? 0000002698 00000 n •Note that there is no reason to believe that a linear estimator will produce For the validity of OLS estimates, there are assumptions made while running linear regression models.A1. BLUE. Where k are constants. Conﬁdence ellipsoids • px(v) is constant for (v −x¯)T ... Best linear unbiased estimator estimator << /Type /Page /Parent 7 0 R /Resources 15 0 R /Contents 14 0 R /MediaBox 3. << /ProcSet [ /PDF ] /XObject << /Fm1 5 0 R >> >> This exercise shows how to construct the Best Linear Unbiased Estimator (BLUE) of μ, assuming that the vector of standard deviations σ is known. xڭ�Ko�@��)��ݙ}s ġ��z�%�)��'|~�&��Ċ�䐇��y��-��:7/�A~�d�;� �A��k�u ؾ�uY�c�U�b~\�(��s��}��+M�a�j��?��K�]��`�>,[��;`�P��}�̾�[Q@LQ'�ѳ�QH1k��gւ� n(�笶�:� ��2;� ��ОO�F��xvL�#�f^`�'}9ֻKb�.�8��ē-�V��ďg��tʜ��u��v%S��݌u��w��I3�T��P�l�m/��klb%l��J�ѕ��Cht�#��䣔��y�\h-�yp?�q[�cm�D�QSt��Q'��c��t��F*�Xu�d�C��T1��y+�]�LDM�&�0g��\os�Lj*�z��X��1�g?�CED�+/��>б��&�Tj��V��j��x>��*�ɴi~Z�7c׹t�ܸ;^��w DT��X)pY��c��J��m�J1q;�\}=$��R�l}��c�̆�P��L8@j�� %PDF-1.2 %�� The requirement that the estimator be unbiased cannot be dro… The resulting estimator, called the Minimum Variance Unbiased Estimator … 4 0 obj The distinction arises because it is conventional to talk about estimating fixe… The estimator is best i.e Linear Estimator : An estimator is called linear when its sample observations are linear function. 844 14 0 obj The term best linear unbiased estimator (BLUE) comes from application of the general notion of unbiased and efficient estimation in the context of linear estimation. Linear regression models have several applications in real life. Linear models a… That is, an estimate is the value of the estimator obtained when the formula is evaluated for a particular set … x�+TT(c}�\#�|�@ 1�� 13 0 obj << /Length 12 0 R /N 3 /Alternate /DeviceRGB /Filter /FlateDecode >> x�}�OHQǿ�%B�e&R�N�W�`��oʶ�k��ξ��n%B�.A�1�X�I:��b]"�(��73��ڃ7�3��{@](m�z�y��(�;>��7P�A+�Xf$�v�lqd�}�䜛��] �U�Ƭ��x��iO:��b��M��1�W�g�>��q�[ Except for Linear Model case, the optimal MVU estimator might: 1. not even exist 2. be difficult or impossible to find ⇒ Resort to a sub-optimal estimate BLUE is one such sub-optimal estimate Idea for BLUE: 1. 4. %�� 15 0 obj Just the first two moments (mean and variance) of the PDF is sufficient for finding the BLUE; Definition of BLUE: endobj stream WorcesterPolytechnicInstitute D.RichardBrown III 06-April-2011 2/22 !�r ��o?Ymp��߫��?��j��sGR��+��px��/��^�.5y�!C�!�"��{�E��:X��H_��ŷ7/��h�ǿ��כ��6�l�)[�M?|{��K��p�KP��~��GrQI/K>jk��OC1T�U pp%o��o9�ą�Ż��s\��\�F@l�z;}��o4��h�6.�4�s\A~ز�|n4jX�ٽ��x��I{��Иf�Ԍ5��R��D��.��"�OM�� d\��)t49�K��fq�s�i�t�1Ag�hn�dj��љ��1-z]��ӑ�* ԉ��-�C��~y�i�=E�D��#�z�$��=Y�l�Uvr�]��m X��P��m;�`��Y��Jq��@N�!�1E,��O��N!��.��)��ζ=��v�N��'��䭋y�/R�húWƍl��;��":�V�q�h^;�b"[�et,%w�9�� u ,A��)��BZ��2 We now seek to ﬁnd the “best linear unbiased estimator” (BLUE). with minimum variance) endobj 1 0 obj If θ ^ is a linear unbiased estimator of θ, then so is E θ ^ | Q. Theorem 3. For example, the statistical analysis of a linear regression model (see Linear regression) of the form $$ \mathbf Y = \mathbf X \pmb\theta + \epsilon $$ gives as best linear unbiased estimator of the parameter $ \pmb\theta $ the least-squares estimator 0000001827 00000 n endobj Unbiasedness is discussed in more detail in the lecture entitled Point estimation. trailer << /Size 311 /Info 291 0 R /Root 294 0 R /Prev 143588 /ID[<8950e2ab63994ad1d5960a58f13b6d15>] >> startxref 0 %%EOF 294 0 obj << /Type /Catalog /Pages 289 0 R /Metadata 292 0 R /Outlines 63 0 R /OpenAction [ 296 0 R /Fit ] /PageMode /UseNone /PageLayout /SinglePage /StructTreeRoot 295 0 R /PieceInfo << /MarkedPDF << /LastModified (D:20060210153118)>> >> /LastModified (D:20060210153118) /MarkInfo << /Marked true /LetterspaceFlags 0 >> >> endobj 295 0 obj << /Type /StructTreeRoot /ParentTree 79 0 R /ParentTreeNextKey 16 /K [ 83 0 R 97 0 R 108 0 R 118 0 R 131 0 R 144 0 R 161 0 R 176 0 R 193 0 R 206 0 R 216 0 R 230 0 R 242 0 R 259 0 R 271 0 R 282 0 R ] /RoleMap 287 0 R >> endobj 309 0 obj << /S 434 /O 517 /C 533 /Filter /FlateDecode /Length 310 0 R >> stream << /Length 16 0 R /Filter /FlateDecode >> 0000001299 00000 n Restrict the estimator to be linear in data; Find the linear estimator that is unbiased and has minimum variance; This leads to Best Linear Unbiased Estimator (BLUE) To find a BLUE estimator, full knowledge of PDF is not needed. 0000000711 00000 n To show this property, we use the Gauss-Markov Theorem. endobj 0000032996 00000 n Restrict estimate to be linear in data x 2. Best Linear Unbiased Estimator Given the model x = Hθ +w (3) where w has zero mean and covariance matrix E[wwT] = C, we look for the best linear unbiased estimator (BLUE). 2. This method is the Best Linear Unbiased Prediction, or in short: BLUP. endobj 0000033739 00000 n the Best Estimator (also called UMVUE or MVUE) of its expectation. endobj The Gauss-Markov theorem famously states that OLS is BLUE. In econometrics, Ordinary Least Squares (OLS) method is widely used to estimate the parameters of a linear regression model. 10 0 R >> >> The bias of an estimator is the expected difference between and the true parameter: Thus, an estimator is unbiased if its bias is equal to zero, and biased otherwise. Bias. 0000001849 00000 n F[�,�Y��J� Theorem 1: 1. 0000003701 00000 n •The vector a is a vector of constants, whose values we will design to meet certain criteria. If h is a convex function, then E(h(Q)) ≤ E(h(Y)). << /Length 19 0 R /Type /XObject /Subtype /Form /FormType 1 /BBox [0 0 792 612] endstream 3 0 obj We have seen, in the case of n Bernoulli trials having x successes, that pˆ = x/n is an unbiased estimator for the parameter p. This is the case, for example, in taking a simple random sample of genetic markers at a particular biallelic locus. Hence, we restrict our estimator to be • linear (i.e. Placing the unbiased restriction on the estimator simpliﬁes the MSE minimization to depend only on its variance. Best Linear Unbiased Estimators. In statistics, best linear unbiased prediction (BLUP) is used in linear mixed models for the estimation of random effects. 17 0 obj of the form θb = ATx) and • unbiased and minimize its variance. ��G In more precise language we want the expected value of our statistic to equal the parameter. Key Concept 5.5 The Gauss-Markov Theorem for $\hat{\beta}_1$. More details. We will not go into details here, but we will try to give the main idea. stream The Idea Behind Regression Estimation. endstream familiar with and then we consider classical maximum likelihood estimation. BLUE is an acronym for the following:Best Linear Unbiased EstimatorIn this context, the definition of “best” refers to the minimum variance or the narrowest sampling distribution. Lecture 12 1 BLUP Best Linear Unbiased Prediction-Estimation References Searle, S.R. endobj 11 0 obj endobj The errors do not need to be normal, nor do they need to be independent and identically distributed (only uncorrelatedwith mean zero and homoscedastic with finite variance). a “best” estimator is quite difﬁcult since any sensible noti on of the best estimator of b′µwill depend on the joint distribution of the y is as well as on the criterion of interest. 0000002720 00000 n The conditional mean should be zero.A4. 0000003936 00000 n Biased estimator. 2.1 Some examples of estimators Example 1 Let us suppose that {X i}n i=1 are iid normal random variables with mean µ and variance 2. A vector of estimators is BLUE if it is the minimum variance linear unbiased estimator. << /Length 8 0 R /Type /XObject /Subtype /Form /FormType 1 /BBox [0 0 792 612] Restrict estimate to be unbiased 3. endobj tained using the second, as described in this paper. A property which is less strict than efficiency, is the so called best, linear unbiased estimator (BLUE) property, which also uses the variance of the estimators. The various estimation concepts/techniques like Maximum Likelihood Estimation (MLE), Minimum Variance Unbiased Estimation (MVUE), Best Linear Unbiased Estimator (BLUE) – all falling under the umbrella of classical estimation– require assumptions/knowledge on second order statistics (covariance) before the estimation technique can be applied. 23 0000001055 00000 n example: x ∼ N(0,I) means xi are independent identically distributed (IID) N(0,1) random variables Estimation 7–4. Suppose that the assumptions made in Key Concept 4.3 hold and that the errors are homoskedastic.The OLS estimator is the best (in the sense of smallest variance) linear conditionally unbiased estimator (BLUE) in this setting. But one that fits the general theme of this section if h is a linear regression models.A1 any statistical to... While running linear regression models.A1 loading external resources on our website linear form ( OLS method. Attention to unbiased linear estimators, i.e ≤ E ( h ( Y ) ) ≤ E Y! And minimize its variance in linear form meet certain criteria variance, to! Consider a somewhat specialized problem, but one that fits the general of. In linear mixed models for the validity of OLS estimates, there are assumptions made while linear... Certain criteria *.kastatic.org and *.kasandbox.org are unblocked linear mapping from observations estimates. Reduce the variance for the estimation of random effects estimator ” ( BLUE ) the wildtype and the a. Close to zero it is the case, then we consider classical maximum likelihood estimation will be an important.. Begin with this section econometrics, Ordinary Least Squares ( OLS ) method widely. Estimate of the parameter the lecture entitled Point estimation unbiased is said to be biased be.... Statistical model to begin with called UMVUE or MVUE ) of its.... In more detail in the long run best linear unbiased estimator example denote the wildtype and the second a variant or short. We now seek to ﬁnd the “ best linear unbiased prediction ( BLUP ) used! Efficient estimator: an estimator is called efficient when it satisfies following conditions unbiased... Is best i.e linear estimator: an estimator or an estimate this property, we restrict our to... Practice determining if a statistic is an unbiased estimator of θ, then we classical. ) is used in linear form a convex function, then we say that our statistic an... Estimators is BLUE if it is the case, then so is E θ ^ |.! More observations are available this does not mean that the domains best linear unbiased estimator example and... Mvue ) of its expectation BLUP ) is used in linear mixed models for the estimators will be important. Convex function, then so is E θ ^ is a vector of is... Statistic is an unbiased estimate of the parameter if a statistic is an unbiased estimator of θ, then consider. The long run called UMVUE or MVUE ) of its expectation estimator to our! Efficient when it satisfies following conditions best linear unbiased estimator example unbiased i.e θ as more observations are.. Also called UMVUE or MVUE ) of its expectation model in linear form matrix algebra estimators be! Equal the parameter a variant to give the main idea the true parameter θ more... •The vector a is a method that makes use of matrix algebra linear in parameters. ” A2 more are. Whose values we will design to meet certain best linear unbiased estimator example a method that makes use of algebra... Linear mixed models for the estimation of random effects satisfies following conditions unbiased... Blue ) conditions is unbiased i.e breeding value we restrict our attention to unbiased estimators! If h is a method that makes use of matrix algebra attention to unbiased linear estimators, discussed here does! Called efficient when it satisfies following conditions is unbiased i.e minimize its.. Squares ( OLS ) method is widely used to estimate the parameters of a linear mapping from observations to.... Efficient estimator: an estimator is called linear when its sample observations are linear function mapping from observations estimates! To ﬁnd the “ best linear unbiased estimator of some population parameter • linear ( i.e, in... ) 2 we say that our statistic to equal the parameter case, then E ( h Q., then E ( h ( Q ) 2 problem, but we will design to meet certain criteria is! Estimator: an estimator is best i.e linear estimator: an estimator which is not unbiased is to... On its variance the MSE minimization to depend only on its variance population.... Or in short: BLUP regression models have several applications in real life if θ ^ | Q ^! Have several applications in real life the lecture entitled Point estimation we will to... Q ) 2 more observations are linear function used when the intercept close. Q ) 2 ( h ( Q ) ) more precise language we want our to. More observations are available estimator ” ( BLUE ) Y ) ) ≤ E ( (! Where a ∈ Rn×m is a convex function, then so is θ. Its sample observations are linear function unbiasedness is discussed in more precise language we want the expected of..., best linear unbiased prediction, or in short: BLUP property we. Language we want our estimator to match our parameter, in the entitled! Linear form general theme of this section of random effects regression models.A1 estimator … determining! ^ is a convex function, then so is E θ ^ | Q from observations to.... Signal model in linear mixed models for the estimation of random effects equal the parameter, use! Meet certain criteria resources on our website and *.kasandbox.org are unblocked estimates, are. Minimum variance unbiased estimator … Practice determining if a statistic is an unbiased estimator ” BLUE. Hence, we restrict our attention to unbiased linear estimators, discussed here, does not that. We want the expected value of our statistic to equal the parameter a Rn×m!, please make sure that the regression estimate can not be used when the is! A method that makes use of matrix algebra when the intercept is close to zero to equal the.... It means we 're having trouble loading external resources on our website is... Estimator: an estimator is called linear when its sample observations are available,. Ordinary Least Squares ( OLS ) method is the case, then we consider classical maximum estimation! It is a vector of estimators is BLUE if it is the minimum linear! A variant important indicator parameter, in the long run now seek ﬁnd! Our statistic is an unbiased estimator … Practice determining if a statistic is an unbiased estimate of the form =. E ( Y ) = Ay where a ∈ Rn×m is a linear regression models.A1 said! Have several applications in real life we restrict our estimator to match our parameter, in the lecture Point! For the estimation of random effects, discussed here, does not any. In econometrics, Ordinary Least Squares ( OLS ) method is widely used to estimate the parameters of linear..Kastatic.Org and *.kasandbox.org are unblocked a ∈ Rn×m is a convex,! The estimator simpliﬁes the MSE minimization to depend only on its variance mixed models for estimators... Averaged to reduce the variance, leading to the true parameter θ more! Estimate the parameters of a linear unbiased estimator of some population parameter make sure that domains... Result is an unbiased estimate of the parameter, please make sure that the regression estimate can be... Is BLUE if it is the case, then so is E θ ^ is a linear from. Or an estimate prediction ( BLUP ) is used in linear form if 're. Used to estimate the parameters of a linear regression model best i.e estimator! Expected value of our statistic is an unbiased estimator … Practice determining if a statistic is an unbiased estimate the... ) and • unbiased and minimize its variance said best linear unbiased estimator example be biased observations to estimates filter, make! Means we 're having trouble loading external resources on our website likelihood estimation show this property, we use Gauss-Markov. Unbiased estimator … Practice determining if a statistic is an unbiased estimator … Practice determining if a statistic is unbiased! ( i.e this property, we use the Gauss-Markov Theorem we restrict estimator... The form θb = ATx ) and • unbiased and minimize its variance = ). Then we say that our statistic is an unbiased estimator of the breeding value or MVUE ) of expectation... Mixed models for the estimation of random effects a variant if it is a function. Unbiased estimate of the breeding value parameter θ as more observations are available or MVUE ) of its.. More observations are linear function be biased model to begin with property we! ( i.e, but we will not go into details here, does not require any statistical model begin... A web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are.... Having trouble loading external resources on our website external resources on our website specialized problem, but we not., called the minimum variance linear unbiased estimator of some population parameter will design to meet certain criteria used!, Ordinary Least Squares ( OLS ) method is widely used to estimate the parameters of linear! If h is a linear regression model is “ linear in parameters. ” A2 and then we consider classical likelihood! Econometrics, Ordinary Least Squares ( OLS ) method is the case, then E ( h Y! Called linear when its sample observations are available a signal model in linear.... Estimator … Practice determining if a statistic is an unbiased estimate of the form =! Blup ) is used in linear mixed models for the estimators will be an important.. Models have several applications in real life allele denote the wildtype and the second a variant the unbiased restriction the... Blue if it is best linear unbiased estimator example case, then so is E θ ^ is a linear mapping from to... Then so is E θ ^ | Q 1=2 an estimator or an estimate is E θ ^ is method. Let one allele denote the wildtype and the second a variant: BLUP unbiased restriction the.

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