Ch. 3 Estimation 1 The Nature of statistical Inference It is argued that it is important to develop a mathematical model purporting to provide a generalized description of the data generating process. A prob bility model in the form of the parametric family of the density functions p=f(:0),0E e and its various ramifications formulated in last chapter provides such a mathematical model. By postulating p as a probability model for the distribution of the observation of interested, we could go on to consider questions about the unknown parameters 0(via estimation and hypothesis tests)as well as further observations from the probability model(prediction) In the next section the important concept of a sampleing model is introduced as a way to link the probability model postulated, say p= f(r: 0),0E 0] to the observed data a =(a1,. In)'available. The sampling model provided the second important ingredient needed to define a statistical model; the starting point of any parametric"statistical inference In short, a statistical model is defined as comprising (a). a probability model p=f(; 0),0E0f;and (b). a sampling model x≡(X1,…,Xxn)y The concept of a statistical model provide the starting point of all forms of sta- tistical inference to be considered in the sequel. To be more precise the concept of a statistical model forms the basis of what is known as parametric in ference There is also a branch of statistical inference known as non-parametric in ference where no gp is assumed a prior 1.1 The sampling model A sampleing model is introduced as a way to link the probability model postu ated,sayp={f(x;),θ∈θ} and the observed data a≡(x1,…xn) available It is designed to model the relationship between them and refers to the way theCh. 3 Estimation 1 The Nature of Statistical Inference It is argued that it is important to develop a mathematical model purporting to provide a generalized description of the data generating process. A prob￾ability model in the form of the parametric family of the density functions Φ = {f(x; θ), θ ∈ Θ} and its various ramifications formulated in last chapter provides such a mathematical model. By postulating Φ as a probability model for the distribution of the observation of interested, we could go on to consider questions about the unknown parameters θ (via estimation and hypothesis tests) as well as further observations from the probability model (prediction). In the next section the important concept of a sampleing model is introduced as a way to link the probability model postulated, say Φ = {f(x; θ), θ ∈ Θ}, to the observed data x ≡ (x1, ..., xn) ′ available. The sampling model provided the second important ingredient needed to define a statistical model; the starting point of any ”parametric” statistical inference. In short, a statistical model is defined as comprising (a). a probability model Φ = {f(x; θ), θ ∈ Θ}; and (b). a sampling model x ≡ (X1, ..., Xn) ′ . The concept of a statistical model provide the starting point of all forms of sta￾tistical inference to be considered in the sequel. To be more precise, the concept of a statistical model forms the basis of what is known as parametric inference. There is also a branch of statistical inference known as non−parametric inference where no Φ is assumed a priori. 1.1 The sampling model A sampleing model is introduced as a way to link the probability model postu￾lated, say Φ = {f(x; θ), θ ∈ Θ} and the observed data x ≡ (x1, ..., xn) ′ available. It is designed to model the relationship between them and refers to the way the 1